publications

2024

Redefining pandemic preparedness: Multidisciplinary insights from the CERP modelling workshop in infectious diseases, workshop report

Marta C. Nunes, Edward Thommes, Holger Fröhlich, and 33 more authors

Infectious Disease Modelling, 2024

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In July 2023, the Center of Excellence in Respiratory Pathogens organized a two-day workshop on infectious diseases modelling and the lessons learnt from the Covid-19 pandemic. This report summarizes the rich discussions that occurred during the workshop. The workshop participants discussed multisource data integration and highlighted the benefits of combining traditional surveillance with more novel data sources like mobility data, social media, and wastewater monitoring. Significant advancements were noted in the development of predictive models, with examples from various countries showcasing the use of machine learning and artificial intelligence in detecting and monitoring disease trends. The role of open collaboration between various stakeholders in modelling was stressed, advocating for the continuation of such partnerships beyond the pandemic. A major gap identified was the absence of a common international framework for data sharing, which is crucial for global pandemic preparedness. Overall, the workshop underscored the need for robust, adaptable modelling frameworks and the integration of different data sources and collaboration across sectors, as key elements in enhancing future pandemic response and preparedness.
Modelling disease mitigation at mass gatherings: A case study of COVID-19 at the 2022 FIFA World Cup

Martin Grunnill, Julien Arino, Zachary McCarthy, and 10 more authors

PLOS Computational Biology, 2024

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The 2022 FIFA World Cup was the first major multi-continental sporting Mass Gathering Event (MGE) of the post COVID-19 era to allow foreign spectators. Such large-scale MGEs can potentially lead to outbreaks of infectious disease and contribute to the global dissemination of such pathogens. Here we adapt previous work and create a generalisable model framework for assessing the use of disease control strategies at such events, in terms of reducing infections and hospitalisations. This framework utilises a combination of meta-populations based on clusters of people and their vaccination status, Ordinary Differential Equation integration between fixed time events, and Latin Hypercube sampling. We use the FIFA 2022 World Cup as a case study for this framework (modelling each match as independent 7 day MGEs). Pre-travel screenings of visitors were found to have little effect in reducing COVID-19 infections and hospitalisations. With pre-match screenings of spectators and match staff being more effective. Rapid Antigen (RA) screenings 0.5 days before match day performed similarly to RT-PCR screenings 1.5 days before match day. Combinations of pre-travel and pre-match testing led to improvements. However, a policy of ensuring that all visitors had a COVID-19 vaccination (second or booster dose) within a few months before departure proved to be much more efficacious. The State of Qatar abandoned all COVID-19 related travel testing and vaccination requirements over the period of the World Cup. Our work suggests that the State of Qatar may have been correct in abandoning the pre-travel testing of visitors. However, there was a spike in COVID-19 cases and hospitalisations within Qatar over the World Cup. Given our findings and the spike in cases, we suggest a policy requiring visitors to have had a recent COVID-19 vaccination should have been in place to reduce cases and hospitalisations.

2023

Investigating air travel network changes in Canada, USA and Europe during COVID-19 using open source data

Adriana-Stefania Ciupeanu, Ashani Wickramasinghe, Saman Muthukumarana, and 1 more author

Research Square, 2023

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We consider the evolution of the global air transportation network during the COVID-19 pandemic, using publicly available data from the OpenSky Network.
SARS-CoV-2 in Nursing Homes: Analysis of Routine Surveillance Data in Four European Countries

T. Delory, J. Arino, P.-E. Haÿ, and 2 more authors

Aging and Disease, 2023

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Transmission of SARS-CoV-2 in nursing homes is poorly documented. Using surveillance data of 228 European private nursing homes, we estimated weekly SARS-CoV-2 incidences among 21,467 residents and 14,371 staff members, compared to that in the general population, between August 3, 2020, and February 20, 2021. We studied the outcomes of “episodes of introduction” where one case was first detected and computed attack rates, reproduction ratio (R), and dispersion parameter (k). Out of 502 episodes of SARS-CoV-2 introduction, 77.1% (95%CI, 73.2%-80.6%) led to additional cases. Attack rates were highly variable, ranging from 0.4% to 86.5%. The R was 1.16 (95%CI, 1.11-1.22) with k at 2.5 (95%CI, 0.5-4.5). The timing of viral circulation in nursing homes did not mirror that in the general population (p-values<0.001). We estimated the impact of vaccination in preventing SARS-CoV-2 transmission. Before vaccination’s roll-out, a cumulated 5,579 SARS-CoV-2 infections were documented among residents and 2,321 among staff. Higher staffing ratio and previous natural immunization reduced the probability of an outbreak following introduction. Despite strong preventive measures, transmission likely occurred, regardless of building characteristics. Vaccination started on January 15, 2021, and coverage reached 65.0% among residents, and 42.0% among staff by February 20, 2021. Vaccination yielded a 92% reduction (95%CI, 71%-98%) of outbreak probability, and lowered R to 0.87 (95%CI, 0.69-1.10). In the post-pandemic era, much attention will have to be paid to multi-lateral collaboration, policy making, and prevention plans.
Pandemic modelling for regions implementing an elimination strategy

Amy Hurford, Maria M. Martignoni, J.C. Loredo-Osti, and 5 more authors

Journal of Theoretical Biology, 2023

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During the COVID-19 pandemic, some countries, such as Australia, China, Iceland, New Zealand, Thailand and Vietnam, successfully implemented an elimination strategy. Until June 2021, Atlantic Canada and Canada’s territories had also experienced prolonged periods with few SARS-CoV-2 community cases. Such regions had a need for epidemiological models that could assess the risk of SARS-CoV-2 outbreaks, but most existing frameworks are applicable to regions where SARS-CoV-2 is spreading in the community, and so it was necessary to adapt existing frameworks to meet this need. We distinguish between infections that are travel-related and those that occur in the community, and find that in Newfoundland and Labrador (NL), Nova Scotia, and Prince Edward Island the mean percentage of daily cases that were travel-related was 80% or greater (July 1, 2020 – May 31, 2021). We show that by December 24, 2021, the daily probability of an Omicron variant community outbreak establishing in NL was near one, and nearly twice as high as the previous high, which occurred in September 2021 when the Delta variant was dominant. We evaluate how vaccination and new variants might affect hypothetical future outbreaks in Mt. Pearl, NL. Our modelling framework can be used to evaluate alternative plans to relax public health restrictions when high levels of vaccination are achieved in regions that have implemented an elimination strategy.Competing Interest StatementAH, MM, and JL-O were members of the Newfoundland and Labrador Predictive Analytics Modelling team and AH received funding from the Newfoundland and Labrador Department of Health and Community Services. Some data was provided by the Newfoundland and Labrador Center for Health Information. This work was not influenced by representatives of the Government of Newfoundland and Labrador.Funding StatementThis study was funded by the Emerging Infectious Disease Modelling Initiative Consortium (Canadian Network for Modelling Infectious Disease, Mathematics for Public Health, and the One Health Modelling Network for Emerging Infections). AH and MM received a grant from the Department of Health and Community Services, Newfoundland and Labrador.Author DeclarationsI confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained.YesThe details of the IRB/oversight body that provided approval or exemption for the research described are given below:Health Research Ethics Board of Newfoundland and Labrador gave ethical approval for this workI confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals.YesI understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance).YesI have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable.YesAll publicly available data used in this study are available at https://github.com/ahurford/pandemic-COVID-zero, but until the work completes peer-review please request these data and code by emailing ahurford@mun.ca
Importation models for travel-related SARS-CoV-2 cases reported in Newfoundland and Labrador during the COVID-19 pandemic

Zahra Mohammadi, Monica Gabriela Cojocaru, Julien Arino, and 1 more author

medRxiv, 2023
Beyond Translation: An Overview of Best Practices for Evidence-Informed Decision Making for Public Health Practice

D. L. Schanzer, J. Arino, A. Asgary, and 6 more authors

2023

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The literature on best practices for evidence-informed decision-making has seen considerable growth from both knowledge users tasked with assessing the quality of the evidence and knowledge creators wishing to make a stronger contribution to evidence-based decisions. The knowledge translation process is highly dependent on the quality of the original research study, the completeness of the reporting, and the cross-discipline accessibility. The aim of this chapter is to introduce scientists interested in using their statistical, analytical, mathematical, or modelling skills to contribute evidence for evidence-informed decisions in public health to the various guideline systems used in the knowledge translation process. As these guideline systems are extensive, we have provided only an overview, highlighting recommendations of potential interest to researchers reporting statistical estimates, analytical results, or modelled output. We have also included a few references to published reporting recommendations by these analytical groups. Knowledge translation does not end with a policy decision. Public health messaging is needed to inform and often persuade the general public to take the appropriate action. We have included a discussion on public communication, as media coverage of research studies can often be traced to the abstracts of the original study.
Assessing transmission risks and control strategy for monkeypox as an emerging zoonosis in a metropolitan area

Pei Yuan, Yi Tan, Liu Yang, and 8 more authors

Journal of Medical Virology, 2023

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To model the spread of monkeypox (MPX) in a metropolitan area for assessing the risk of possible outbreaks, and identifying essential public health measures to contain the virus spread. The animal reservoir is the key element in the modeling of zoonotic disease. Using a One Health approach, we model the spread of the MPX virus in humans considering potential animal hosts such as rodents (e.g., rats, mice, squirrels, chipmunks, etc.) and emphasize their role and transmission of the virus in a high-risk group, including gay and bisexual men-who-have-sex-with-men (gbMSM). From model and sensitivity analysis, we identify key public health factors and present scenarios under different transmission assumptions. We find that the MPX virus may spill over from gbMSM high-risk groups to broader populations if the efficiency of transmission increases in the higher-risk group. However, the risk of outbreak can be greatly reduced if at least 65% of symptomatic cases can be isolated and their contacts traced and quarantined. In addition, infections in an animal reservoir will exacerbate MPX transmission risk in the human population. Regions or communities with a higher proportion of gbMSM individuals need greater public health attention. Tracing and quarantine (or “effective quarantine” by postexposure vaccination) of contacts with MPX cases in high-risk groups would have a significant effect on controlling the spreading. Also, monitoring for animal infections would be prudent.

2022

Describing, modelling and forecasting the spatial and temporal spread of COVID-19 – A short review

Julien Arino

Fields Institute Communications, 2022

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SARS-CoV-2 started propagating worldwide in January 2020 and has now reached virtually all communities on the planet. This short review provides evidence of this spread and documents modelling efforts undertaken to understand and forecast it, including a short section about the new variants that emerged in late 2020.
A model for the early COVID-19 outbreak in China with case detection and behavioural change

Julien Arino, Khalid El Hail, Mohamed Khaladi, and 1 more author

Biomath, 2022

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We investigate a model of the early stage of the COVID-19 epidemic comprising undetected infected individuals as well as behavioural change towards the use of self-protection measures. The model is fitted to China data reported between 22 January and 29 June 2020. Using fitting results, we then consider model responses to varying screening intensities.
Bistability in deterministic and stochastic SLIAR-type models with imperfect and waning vaccine protection

Julien Arino, and Evan M. Milliken

Journal of Mathematical Biology, 2022

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Various vaccines have been approved for use to combat COVID-19 that offer imperfect immunity and could furthermore wane over time. We analyze the effect of vaccination in an SLIARS model with demography by adding a compartment for vaccinated individuals and considering disease-induced death, imperfect and waning vaccination protection as well as waning infections-acquired immunity. When analyzed as systems of ordinary differential equations, the model is proven to admit a backward bifurcation. A continuous time Markov chain (CTMC) version of the model is simulated numerically and compared to the results of branching process approximations. While the CTMC model detects the presence of the backward bifurcation, the branching process approximation does not. The special case of an SVIRS model is shown to have the same properties.
Effect of mobility on the stochastic phase of an epidemic

Julien Arino, and Evan M. Milliken

Bulletin of Mathematical Biology, 2022

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The early phase of an epidemic is characterized by a small number of infected individuals, implying that stochastic effects drive the dynamics of the disease. Mathematically, we define the stochastic phase as the time during which the number of infected individuals remains small and positive. A continuous-time Markov chain model of a simple two-patch epidemic is presented. An algorithm for formalizing what is meant by small is presented, and the effect of movement on the duration of the early stochastic phase of an epidemic is studied.
Mathematical modelling of vaccination rollout and NPIs lifting on COVID-19 transmission with VOC: a case study in Toronto, Canada

Elena Aruffo, Pei Yuan, Yi Tan, and 7 more authors

BMC Public Health, 2022

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Background Since December 2020, public health agencies have implemented a variety of vaccination strategies to curb the spread of SARS-CoV-2, along with pre-existing Nonpharmaceutical Interventions (NPIs). Initial strategies focused on vaccinating the elderly to prevent hospitalizations and deaths, but with vaccines becoming available to the broader population, it became important to determine the optimal strategy to enable the safe lifting of NPIs while avoiding virus resurgence. Methods We extended the classic deterministic SIR compartmental disease-transmission model to simulate the lifting of NPIs under different vaccine rollout scenarios. Using case and vaccination data from Toronto, Canada between December 28, 2020, and May 19, 2021, we estimated transmission throughout past stages of NPI escalation/relaxation to compare the impact of lifting NPIs on different dates on cases, hospitalizations, and deaths, given varying degrees of vaccine coverages by 20-year age groups, accounting for waning immunity. Results We found that, once coverage among the elderly is high enough (80% with at least one dose), the main age groups to target are 20–39 and 40–59 years, wherein first-dose coverage of at least 70% by mid-June 2021 is needed to minimize the possibility of resurgence if NPIs are to be lifted in the summer. While a resurgence was observed for every scenario of NPI lifting, we also found that under an optimistic vaccination coverage (70% coverage by mid-June, along with postponing reopening from August 2021 to September 2021) can reduce case counts and severe outcomes by roughly 57% by December 31, 2021. Conclusions Our results suggest that focusing the vaccination strategy on the working-age population can curb the spread of SARS-CoV-2. However, even with high vaccination coverage in adults, increasing contacts and easing protective personal behaviours is not advisable since a resurgence is expected to occur, especially with an earlier reopening.
Disease transmission and mass gatherings: a case study on meningococcal infection during Hajj

Laurent Coudeville, Amine Amiche, Ashrafur Rahman, and 6 more authors

BMC Infectious Diseases, 2022

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Background Mass gatherings can not only trigger major outbreaks on-site but also facilitate global spread of infectious pathogens. Hajj is one of the largest mass gathering events worldwide where over two million pilgrims from all over the world gather annually creating intense congestion. Methods We developed a meta-population model to represent the transmission dynamics of Neisseria meningitidis and the impact of Hajj pilgrimage on the risk of invasive meningococcal disease (IMD) for pilgrims population, local population at the Hajj site and country of origin of Hajj pilgrims. This model was calibrated using data on IMD over 17 years (1995-2011) and further used to simulate potential changes in vaccine policy and endemic conditions. Results The effect of increased density of contacts during Hajj was estimated to generate a 78-fold increase in disease transmission that impacts not only pilgrims but also the local population. Quadrivalent ACWY vaccination was found to be very effective in reducing the risk of outbreak during Hajj. Hajj has more limited impact on IMD transmission and exportation in the pilgrim countries of origin, although not negligible given the size of the population considered. Conclusion The analysis performed highlighted the amplifying effect of mass gathering on N. meningitidis transmission and confirm vaccination as a very effective preventive measure to mitigate outbreak risks.
Estimating Social Contacts in Mass Gatherings Through Agent-Based Simulation Modeling: Case of Hajj Pilgrimage

Mohammadali Tofighi, Ali Asgary, Ghassem Tofighi, and 11 more authors

Tropical Diseases, Travel Medicine and Vaccines, 2022

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Most mass gathering events have been suspended due to the SARS-CoV-2 pandemic. However, with vaccination rollout, whether and how to organize some of these mass gathering events arises as part of the pandemic recovery discussions, and this calls for decision support tools. Hajj, one of the world’s largest religious gatherings, was substantively scaled down in 2020 and it is still unclear if it will take place in 2021 and sub-sequent years. Considering the disease trends and vaccination conditions in the pilgrims’ country of origin, and the operational and logistical aspects of implementing public health measures, Hajj reopening conditions could be very complex. Simulating disease transmission dynamics during the Hajj season under differ-ent conditions can provide some insights for better decision-making. Since most disease risk assessment models require data on the number and nature of possible close contacts between individuals, we seek to use integrated agent-based modeling and discrete events simulation techniques to capture risky contacts among the pilgrims in one of the Hajj major sites, namely Masjid-Al-Haram. In particular, we assessed different scenarios concerning the total number of pilgrims and enforced physical distancing measures. Our simulation results show that a plethora of risky contacts may occur during the rituals. Also, as the total number of pilgrims increases at each site, the number of risky contacts increases, and physical distancing measures may be challenging to maintain beyond a certain number of pilgrims in the site.
Evaluating the Risk of Reopening the Border: A Case Study of Ontario (Canada) to New York (USA) Using Mathematical Modeling

Pei Yuan, Elena Aruffo, Qi Li, and 17 more authors

Fields Institute Communications, 2022

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Many countries have adopted border closures and other jurisdictions (provinces, states, cities, etc.) to control the spread of SARS-CoV-2. Such measures have significantly restricted population movement and have thus led to immense economic and social fallouts. We build a Susceptible-Exposed-Asymptomatic- Infectious (prodromal phase)- Infectious (with symptoms) -Recovered (SEAIR) model with a household structure to investigate the potential of a safe reopening of a border, which can control disease spread but also allow for economic growth. We focus on the Ontario-USA border, considering an opening date of September 21, 2020. In addition to the instantaneous reproduction number, we also define a novel risk indicator by calculating daily new infections’ percentile to inform risk levels promptly. Under ideal conditions, assuming extremely efficient border testing and strict traveler adherence to quarantine policy, the Ontario-USA can be reopened for a maximum daily number of 500 travelers entering Canada. A number exceeding 500 will stem an uncontrollable spread of the virus. Additionally, the current quarantine policy may not be sufficient under specific scenarios; hence testing measures at the border must be extremely efficient. Reopening of the Ontario-USA must consider the potential for disease spread (which can overburden healthcare resources) and economic growth. If a reopening plan is implemented, the local government must limit the number of daily entrances to 500 and enforce a mandatory quarantine, which may need to be stricter than current policy practice.
Efficacy of “stay-at-home” policy of SARS-CoV-2 transmission in Toronto, Canada: a mathematical modelling study

Pei Yuan, Juan Li, Elena Aruffo, and 15 more authors

CMAJ Open, 2022

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Background: Globally, nonpharmaceutical interventions for COVID-19, including stay-at-home policies, limitations on gatherings and closure of public spaces, are being lifted. We explored the effect of lifting a stay-at-home policy on virus resurgence under different conditions. Methods: Using confirmed case data from Toronto, Canada, between Feb. 24 and June 24, 2020, we ran a compartmental model with household structure to simulate the impact of the stay-at-home policy considering different levels of compliance. We estimated threshold values for the maximum number of contacts, probability of transmission and testing rates required for the safe reopening of the community. Results: After the implementation of the stay-at-home policy, the contact rate outside the household fell by 39% (from 11.58 daily contacts to 7.11). The effective reproductive number decreased from 3.56 (95% confidence interval [CI] 3.02-4.14) on Mar. 12 to 0.84 (95% CI 0.79-0.89) on May 6. Strong adherence to stay-at-home policies appeared to prevent SARS-CoV-2 resurgence, but extending the duration of stay-at-home policies beyond 2 months had little added effect on cumulative cases (25 958 for 65 days of a stay-at-home policy and 23 461 for 95 days, by July 2, 2020) and deaths (1404 for 65 days and 1353 for 95 days). To avoid a resurgence, the average number of contacts per person per day should be kept below 9, with strict nonpharmaceutical interventions in place. Interpretation: Our study demonstrates that the stay-at-home policy implemented in Toronto in March 2020 had a substantial impact on mitigating the spread of SARS-CoV-2. In the context of the early pandemic, before the emergence of variants of concern, reopening schools and workplaces was possible only with other nonpharmaceutical interventions in place.
Modelling vaccination and control strategies of outbreaks of monkeypox at gatherings

Pei Yuan, Yi Tan, Liu Yang, and 8 more authors

Frontier in Public Health, 2022

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Background: The monkeypox outbreak in non-endemic countries in recent months has led the World Health Organization (WHO) to declare a public health emergency of international concern (PHEIC). It is thought that festivals, parties, and other gatherings may have contributed to the outbreak. Methods: We considered a hypothetical metropolitan city and modeled the transmission of the monkeypox virus in humans in a high-risk group (HRG) and a low-risk group (LRG) using a Susceptible-Exposed-Infectious-Recovered (SEIR) model and incorporated gathering events. Model simulations assessed how the vaccination strategies combined with other public health measures can contribute to mitigating or halting outbreaks from mass gathering events. Results: The risk of a monkeypox outbreak was high when mass gathering events occurred in the absence of public health control measures. However, the outbreaks were controlled by isolating cases and vaccinating their close contacts. Furthermore, contact tracing, vaccinating, and isolating close contacts, if they can be implemented, were more effective for the containment of monkeypox transmission during summer gatherings than a broad vaccination campaign among HRG, when accounting for the low vaccination coverage in the overall population, and the time needed for the development of the immune responses. Reducing the number of attendees and effective contacts during the gathering could also prevent a burgeoning outbreak, as could restricting attendance through vaccination requirements. Conclusion: Monkeypox outbreaks following mass gatherings can be made less likely with some restrictions on either the number and density of attendees in the gathering or vaccination requirements. The ring vaccination strategy inoculating close contacts of confirmed cases may not be enough to prevent potential outbreaks; however, mass gatherings can be rendered less risky if that strategy is combined with public health measures, including identifying and isolating cases and contact tracing. Compliance with the community and promotion of awareness are also indispensable to containing the outbreak.

2021

Risk of COVID-19 variant importation - How useful are travel control measures?

Julien Arino, Pierre-Yves Boelle, Evan M Milliken, and 1 more author

Infectious Disease Modelling, 2021

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We consider models for the importation of a new variant COVID-19 strain in a location already seeing propagation of a resident variant. By distinguishing contaminations generated by imported cases from those originating in the community, we are able to evaluate the contribution of importations to the dynamics of the disease in a community. We find that after an initial seeding, the role of importations becomes marginal compared to that of community-based propagation. We also evaluate the role of two travel control measures, quarantine and travel interruptions. We conclude that quarantine is an efficacious way of lowering importation rates, while travel interruptions have the potential to delay the consequences of importations but need to be applied within a very tight time window following the initial emergence of the variant.
An evolving pandemic: the origins and potential future of COVID-19 variants of concern

S.P. Otto, T. Day, J. Arino, and 8 more authors

Current Biology, 2021

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One year into the global COVID-19 pandemic, the focus of attention has shifted to the emergence and spread of SARS-CoV-2 variants of concern (VOCs). After nearly a year of the pandemic with little evolutionary change affecting human health, several variants have now been shown to have substantial detrimental effects on transmission and severity of the virus. Public health officials, medical practitioners, scientists, and the broader community have since been scrambling to understand what these variants mean for diagnosis, treatment, and the control of the pandemic through nonpharmaceutical interventions and vaccines. Here we explore the evolutionary processes that are involved in the emergence of new variants, what we can expect in terms of the future emergence of VOCs, and what we can do to minimise their impact.

2020

Mathematical epidemiology in a data-rich world

J. Arino

Infectious Disease Modelling, 2020

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I discuss the acquisition and use of “background” data in mathematical epidemiology models, advocating a proactive approach to the incorporation of said data. I illustrate various mechanisms for acquiring data, mainly from open data sources. I also discuss incorporating this data into models.
Review of ’Dynamical System Models in the Life Sciences and Their Underlying Scientific Issues, by Y. M. Wan’

J. Arino

SIAM Review, 2020

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Quarantine and the risk of COVID-19 importation

Julien Arino, Nicolas Bajeux, Stephanie Portet, and 1 more author

Epidemiology & Infection, 2020

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Using a stochastic model, we assess the risk of importation-induced local transmission chains in locations seeing few or no local transmissions and evaluate the role of quarantine in the mitigation of this risk. We find that the rate of importations plays a critical role in determining the risk that case importations lead to local transmission chains, more so than local transmission characteristics, i.e. strength of social distancing measures (NPI). The latter influences the severity of the outbreaks when they do take place. Quarantine after arrival in a location is an efficacious way to reduce the rate of importations. Locations that see no or low-level local transmission should ensure that the rate of importations remains low. A high level of compliance with post-arrival quarantine followed by testing achieves this objective with less of an impact than travel restrictions or bans.
A simple model for COVID-19

J. Arino, and S. Portet

Infectious Disease Modelling, 2020

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An SL_1L_2I_1I_2A_1A_2R epidemic model is formulated that describes the spread of an epidemic in a population. The model incorporates an Erlang distribution of times of sojourn in incubating, symptomatically and asymptomatically infectious compartments. Basic properties of the model are explored, with focus on properties important in the context of current COVID-19 pandemic.
Investigation of global and local COVID-19 importation risks

Julien Arino, Stephanie Portet, Nicolas Bajeux, and 1 more author

2020
Spread of Dutch Elm Disease in an urban forest

Nicolas Bajeux, Julien Arino, Stephanie Portet, and 1 more author

Ecological Modelling, 2020

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A complex network model for the spread of Dutch Elm Disease in an urban forest is formulated. American elms are the focus of the model. Each elm can be in one of five states, a combination of their life and epidemiological status. Each tree is also potentially a host to a population of elm bark beetles, the vectors of Dutch Elm Disease. The epidemiological dynamics of trees is governed by a stochastic process that takes into account the dispersal of spore-carrying beetles between trees and potential contacts between tree root systems. The model describes seasonal variations of beetle activity and population dynamics. Numerical simulations and sensitivity analyses of the model are carried out. In this introductory paper, we use data from the City of Winnipeg, where Dutch Elm Disease is prevalent, and focus on two neighbourhoods representative of a residential area and an area with urban parks.
Quantifying the annual incidence and underestimation of seasonal influenza: A modelling approach.

Zachary McCarthy, Safia Athar, Mahnaz Alavinejad, and 22 more authors

Theoretical Biology & Medical Modelling, Jul 2020

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Seasonal influenza poses a significant public health and economic burden, associated with the outcome of infection and resulting complications. The true burden of the disease is difficult to capture due to the wide range of presentation, from asymptomatic cases to non-respiratory complications such as cardiovascular events, and its seasonal variability. An understanding of the magnitude of the true annual incidence of influenza is important to support prevention and control policy development and to evaluate the impact of preventative measures such as vaccination. We use a dynamic disease transmission model, laboratory-confirmed influenza surveillance data, and randomized-controlled trial (RCT) data to quantify the underestimation factor, expansion factor, and symptomatic influenza illnesses in the US and Canada during the 2011-2012 and 2012-2013 influenza seasons. Based on 2 case definitions, we estimate between 0.42-3.2% and 0.33-1.2% of symptomatic influenza illnesses were laboratory-confirmed in Canada during the 2011-2012 and 2012-2013 seasons, respectively. In the US, we estimate between 0.08-0.61% and 0.07-0.33% of symptomatic influenza illnesses were laboratory-confirmed in the 2011-2012 and 2012-2013 seasons, respectively. We estimated the symptomatic influenza illnesses in Canada to be 0.32-2.4 million in 2011-2012 and 1.8-8.2 million in 2012-2013. In the US, we estimate the number of symptomatic influenza illnesses to be 4.4-34 million in 2011-2012 and 23-102 million in 2012-2013. We illustrate that monitoring a representative group within a population may aid in effectively modelling the transmission of infectious diseases such as influenza. In particular, the utilization of RCTs in models may enhance the accuracy of epidemiological parameter estimation.
Modelling scenarios of the epidemic of COVID-19 in Canada

N.H. Ogden, A. Fazil, J. Arino, and 9 more authors

Canada Communicable Disease Report (CCDR), Jul 2020

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Background: Severe acute respiratory syndrome virus 2 (SARS-CoV-2), likely a bat-origin coronavirus, spilled over from wildlife to humans in China in late 2019, manifesting as a respiratory disease. Coronavirus disease 2019 (COVID-19) spread initially within China and then globally, resulting in a pandemic. Objective: This article describes predictive modelling of COVID-19 in general, and efforts within the Public Health Agency of Canada to model the effects of non-pharmaceutical interventions (NPIs) on transmission of SARS-CoV-2 in the Canadian population to support public health decisions. Methods: The broad objectives of two modelling approaches, 1) an agent-based model and 2) a deterministic compartmental model, are described and a synopsis of studies is illustrated using a model developed in Analytica 5.3 software. Results: Without intervention, more than 70% of the Canadian population may become infected. Non-pharmaceutical interventions, applied with an intensity insufficient to cause the epidemic to die out, reduce the attack rate to 50% or less, and the epidemic is longer with a lower peak. If NPIs are lifted early, the epidemic may rebound, resulting in high percentages (more than 70%) of the population affected. If NPIs are applied with intensity high enough to cause the epidemic to die out, the attack rate can be reduced to between 1% and 25% of the population. Conclusion: Applying NPIs with intensity high enough to cause the epidemic to die out would seem to be the preferred choice. Lifting disruptive NPIs such as shut-downs must be accompanied by enhancements to other NPIs to prevent new introductions and to identify and control any new transmission chains.
Effect of media-induced modification of travel rates on disease transmission in a multiple patch setting

W. Yang, C. Sun, and J. Arino

Journal of Applied Analysis and Computation, Jul 2020

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A general SIS epidemic model is formulated that incorporates media-induced modification of travel rates. Basic local properties of solutions to the model are established. In particular, it is shown that the basic reproduction number does not involve parameters related to the effect of media on travel. The general model is subsequently specialised to two-patch models, with two different scenarios regarding patch population size. Qualitative analyses show that the basic reproduction number acts as a sharp threshold between disease persistence and extinction. The concept of uniform weak persistence is used to prove the existence of an endemic equilibrium and disease uniform strong persistence under a certain condition. Numerical investigations are carried out to gain insight into the analytically tractable and intractable cases, highlighting the importance of considering not only the basic reproduction number but also other measures of disease severity.

2019

Number of source patches required for population persistence in a source-sink metapopulation

J. Arino, N. Bajeux, and S. Kirkland

Bulletin of Mathematical Biology, Jul 2019

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We consider a simple metapopulation model with explicit movement of individuals between patches, in which each patch is either a source or a sink. We prove that similarly to the case of patch occupancy metapopulations with implicit movement, there exists a threshold number of source patches such that the population potentially becomes extinct below the threshold and established above the threshold. In the case where the matrix describing the movement of populations between spatial locations is irreducible, the result is global; further, assuming a complete mobility graph with equal movement rates, we use the principle of equitable partitions to obtain an explicit expression for the threshold. Brief numerical considerations follow.
Current Trends in Mathematical Epidemiology

J. Arino, and J. Watmough

Bulletin of Mathematical Biology, Nov 2019

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Special Issue: Mathematical Epidemiology

Nov 2019

2017

Spatio-temporal spread of infectious pathogens of humans

J. Arino

Infectious Disease Modelling, Nov 2017

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Spatio-temporal aspects in the propagation of infectious pathogens of humans are reviewed. Mathematical modelling of these issues using metapopulation models is presented.
Intermediate filament dynamics: disassembly regulation

C. Sun, J. Arino, and S. Portet

International Journal of Biomathematics, Nov 2017

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A mechanism of intermediate filament disassembly regulation is proposed in which disassembly is regulated by the amount of proteins assembled in networks. It is also hypothesized that a delay might exist between regulation and actual disassembly. Under realistic biological conditions of assembly and disassembly, it is shown that such a delay is harmless and does not destabilize the organization of intermediate filaments in networks. However, for high rates of disassembly, the model predicts that delay can destabilize the organization, with the intermediate filament material oscillating between organizations mainly in networks and in nonfilamentous particles.

2016

Revisiting a two-patch SIS model with infection during transport

J. Arino, C. Sun, and W. Yang

Mathematical Medicine and Biology, Nov 2016

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We incorporate parameter heterogeneity in a two-patch SIS epidemic model with infection during transport and prove that the disease free and endemic equilibria are globally asymptotically stable when the basic reproduction number \R_0<1 and \R_0>1, respectively. We find that infection during transport increases the possibility that the disease persists in both patches and amplifies prevalence when disease is present. We then study the effect of a perfect unilateral exit screening program. Finally, we compare numerically the effects of using different incidence functions for infection within and while travelling between patches, and find that using mass action incidence to model infection during transport has the effect of maintaining disease prevalence at a higher level compared to when standard incidence is used.
Toward standardizing a lexicon of infectious disease modeling terms

R. Milwid, A. Steriu, J. Arino, and 8 more authors

Frontiers in Public Health, Nov 2016

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Disease modelling is increasingly being used to evaluate the effect of health intervention strategies, particularly for infectious diseases. However, the utility and application of such models are hampered by the inconsistent use of infectious disease modelling terms between and within disciplines. We sought to standardize the lexicon of infectious disease modelling terms, and develop a glossary of terms commonly used in describing models’ assumptions, parameters, variables, and outcomes. We combined a comprehensive literature review of relevant terms with an online forum discussion in a virtual community of practice, mod4PH (Modelling for Public Health). Using a convergent discussion process and consensus amongst the members of mod4PH, a glossary of terms was developed as an online resource. We anticipate that the glossary will improve inter- and intra-disciplinary communication, and will result in a greater uptake and understanding of disease modelling outcomes in heath policy decision-making. We highlight the role of the mod4PH community of practice and the methodologies used in this endeavour to link theory, policy, and practice in the public health domain.

2015

Epidemiological implications of mobility between a large urban centre and smaller satellite cities

J. Arino, and S. Portet

Journal of Mathematical Biology, Nov 2015

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An SIR infectious disease propagation model is considered that incorporates mobility of individuals between a large urban centre and smaller satellite cities. Because of the difference in population sizes, the urban centre has standard incidence and satellite cities have mass action incidence. It is shown that the general basic reproduction number \R_0 acts as a threshold between global asymptotic stability of the disease free equilibrium and disease persistence. The case of Winnipeg (Manitoba, Canada) and some neighbouring satellite communities is then considered numerically to complement the mathematical analysis, highlighting the importance of taking into account not only \R_0 but also other measures of disease severity. It is found that the large urban centre governs most of the behaviour of the general system and control of the spread is better achieved by targeting it rather than reducing movement between the units. Also, the capacity of a satellite city to affect the general system depends on its population size and its connectivity to the main urban centre.
A model for the spread of tuberculosis with drug-sensitive and emerging multidrug-resistant and extensively drug resistant strains

J. Arino, and I.A. Soliman

In Mathematical and Computational Modelling, Nov 2015

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We consider a model for tuberculosis that incorporates three strains (drug-sensitive and emerging multi-drug resistant and extensively drug-resistant). We study the dynamics of the model and in particular, characterize parameter regions where so-called backward bifurcations occur and regions where they do not occur. We show the global stability of the disease free equilibrium in regions with no backward bifurcation.

2014

Using mathematical modelling to integrate disease surveillance and global air transportation data

J. Arino, and K. Khan

In Analyzing and Modeling Spatial and Temporal Dynamics of Infectious Diseases, Nov 2014

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Modern disease surveillance systems such as the Global Public Health Intelligence Network (GPHIN) generate alerts by continuously monitoring internet news sources for the occurrence of keywords related to infectious diseases. However, all of these alerts do not correspond to events that carry the same potential to generate infectious disease outbreaks in distant locations. In this chapter, we discuss how modeling can help bridge knowledge about health conditions in the locations where the alerts are being generated and the global air transportation network. This serves to assess the potential for an emerging or reemerging disease to quickly spread across large distances and quantify the risk represented to a given public health district by an alert generated elsewhere in the world.

2013

Quelques notions d’épidémiologie mathématique

J. Arino

Bulletin de l’Association mathématique du Québec, Nov 2013

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On présente ici quelques notions élémentaires d’épidémiologie mathématique en formulant et analysant un modèle très simple de la propagation d’une maladie infectieuse dans une population. Bien que simple, le modèle SIS étudié comporte néanmoins certaines des caractéristiques de modèles plus complexes et permet d’introduire quelques concepts fondamentaux du domaine. On en profite aussi pour présenter quelques outils d’analyse qualitative des systèmes différentiels non linéaires, comparant les résultats pouvant être obtenus de cette façon avec ceux obtenus en résolvant explicitement le système.
Impact of viral mutation on suppression of infection by cytotoxic T lymphocytes

J. Arino, N. Madras, S. Portet, and 1 more author

Canadian Applied Mathematics Quarterly, Nov 2013

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We develop a deterministic model describing the dynamics of infected cells wearing n epitopes recognizable by n CTL clones, in which mutation can lead to the epitopes becoming unrecognizable by their cognate CTL clone. Some mathematical and computational analyses of the resulting large scale system of 2^n+n equations are conducted. The model is used to examine the ability of CTL response to suppress infection in the presence of mutations. Several situations in which CTL escape happens are identified and conditions in which infection is controlled are also derived. The influence of the probability of mutation is numerically investigated.
Entry and exit screening of airline travellers during the A(H1N1) 2009 pandemic: a retrospective evaluation

K. Khan, R. Eckhardt, J.S. Brownstein, and 9 more authors

Bulletin of the World Health Organization, Nov 2013

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Objective To evaluate the screening measures that would have been required to assess all travellers at risk of transporting A(H1N1)pdm09 out of Mexico by air at the start of the 2009 pandemic. Methods Data from flight itineraries for travellers who flew from Mexico were used to estimate the number of international airports where health screening measures would have been needed, and the number of travellers who would have had to be screened, to assess all air travellers who could have transported the H1N1 influenza virus out of Mexico during the initial stages of the 2009 A(H1N1) pandemic. Findings Exit screening at 36 airports in Mexico, or entry screening of travellers arriving on direct flights from Mexico at 82 airports in 26 other countries, would have resulted in the assessment of all air travellers at risk of transporting A(H1N1)pdm09 out of Mexico at the start of the pandemic. Entry screening of 116 travellers arriving from Mexico by direct or connecting flights would have been necessary for every one traveller at risk of transporting A(H1N1)pdm09. Screening at just eight airports would have resulted in the assessment of 90% of all air travellers at risk of transporting A(H1N1)pdm09 out of Mexico in the early stages of the pandemic. Conclusion During the earliest stages of the A(H1N1) pandemic, most public health benefits potentially attainable through the screening of air travellers could have been achieved by screening travellers at only eight airports.

2012

A metapopulation model for malaria with transmission-blocking partial immunity in hosts

J. Arino, A. Ducrot, and P. Zongo

Journal of Mathematical Biology, Nov 2012

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A metapopulation malaria model is proposed using SI and SIRS models for the vectors and hosts, respectively. Recovered hosts are partially immune to the disease and while they cannot directly become infectious again, they can still transmit the parasite to vectors. The basic reproduction number R0 is shown to govern the local stability of the disease free equilibrium but not the global behavior of the system because of the potential occurrence of a backward bifurcation. Using type reproduction numbers, we identify the reservoirs of infection and evaluate the effect of control measures. Applications to the spread to non-endemic areas and the interaction between rural and urban areas are given.
Infectious disease surveillance and modelling across geographic frontiers and scientific specialties

K. Khan, S.J.N. McNabb, Z.A. Memish, and 11 more authors

The Lancet Infectious Diseases, Nov 2012

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Infectious disease surveillance for mass gatherings (MGs) can be directed locally and globally; however, epidemic intelligence from these two levels is not well integrated. Modelling activities related to MGs have historically focused on crowd behaviours around MG focal points and their relation to the safety of attendees. The integration of developments in internet-based global infectious disease surveillance, transportation modelling of populations travelling to and from MGs, mobile phone technology for surveillance during MGs, metapopulation epidemic modelling, and crowd behaviour modelling is important for progress in MG health. Integration of surveillance across geographic frontiers and modelling across scientific specialties could produce the first real-time risk monitoring and assessment platform that could strengthen awareness of global infectious disease threats before, during, and immediately after MGs. An integrated platform of this kind could help identify infectious disease threats of international concern at the earliest stages possible; provide insights into which diseases are most likely to spread into the MG; help with anticipatory surveillance at the MG; enable mathematical modelling to predict the spread of infectious diseases to and from MGs; simulate the effect of public health interventions aimed at different local and global levels; serve as a foundation for scientific research and innovation in MG health; and strengthen engagement between the scientific community and stakeholders at local, national, and global levels.
Mathematical Modelling of Natural Phenomena (Epidemiology)

Nov 2012

2011

Some methodological aspects involved in the study by the Bio.Diaspora Project of the spread of infectious diseases along the global air transportation network

J. Arino, W. Hu, K. Khan, and 2 more authors

Canadian Applied Mathematics Quarterly, Nov 2011

Published in 2012 with 2011 date [publisher delay]. So actual reference is Vol. 19, 2011.

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The Bio.Diaspora Project studies infectious disease threats involving the rapid translocation of an infectious agent across vast distances induced by the travel of infected individuals using the global air transportation network. In this paper, the basic methodology used in the project is described.
Pandemic influenza: modelling and public health perspectives

J. Arino, C. Bauch, F. Brauer, and 10 more authors

Mathematical Biosciences and Engineering, Nov 2011

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We describe the application of mathematical models in the study of disease epidemics with particular focus on pandemic influenza. We outline the general mathematical approach and the complications arising from attempts to apply it for disease outbreak management in a real public health context.
Evaluation of vaccination strategies during pandemic outbreaks

C. Bowman, J. Arino, and S.M. Moghadas

Mathematical Biosciences and Engineering, Nov 2011

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During pandemic in influenza, several factors could significantly impact the outcome of vaccination campaigns, including the delay in pandemic vaccine availability, inadequate protective efficacy, and insufficient number of vaccines to cover the entire population. Here, we incorporate these factors into a vaccination model to investigate and compare the effectiveness of the single-dose and two-dose vaccine strategies. The results show that, if vaccination starts early enough after the onset of the outbreak, a two-dose strategy can lead to a greater reduction in the total number of infections. This, however, requires the second dose of vaccine to confer a substantially higher protection compared to that induced by the first dose. For a sufficiently long delay in start of vaccination, the single-dose strategy outperforms the two-dose vaccination program regardless of its protection efficacy. These findings suggest that the population-wide benefits of a single-dose strategy could in general be greater than the two-dose vaccination program, in particular when the second dose offers marginal increase in the protection induced by the first dose.
Effect of media-induced social distancing on disease transmission in a two patch setting

C. Sun, W. Yang, J. Arino, and 1 more author

Mathematical Biosciences, Nov 2011

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We formulate an SIS epidemic model on two patches. In each patch, media coverage about the cases present in the local population leads individuals to limit the number of contacts they have with others, inducing a reduction in the rate of transmission of the infection. A global qualitative analysis is carried out, showing that the typical threshold behavior holds, with solutions either tending to an equilibrium without disease, or the system being persistent and solutions converging to an endemic equilibrium. Numerical analysis is employed to gain insight in both the analytically tractable and intractable cases; these simulations indicate that media coverage can reduce the burden of the epidemic and shorten the duration of the disease outbreak.

2010

Effect of a sharp change of the incidence function on the dynamics of a simple disease

J. Arino, and C.C. McCluskey

Journal of Biological Dynamics, Nov 2010

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We investigate two cases of a sharp change of incidencec functions on the dynamics of a susceptible-infective-susceptible epidemic model. In the first case, low population levels have mass action incidence, while high population levels have proportional incidence, the switch occurring when the total population reaches a certain threshold. Using a modified Dulac theorem, we prove that this system has a single equilibrium which attracts all solutions for which the disease is present and the population remains bounded. In the second case, an increase of the number of infectives leads to a mass action term being added to a standard incidence term. We show that this allows a Hopf bifurcation to occur, with periodic orbits being generated when a locally asymptotically stable equilibrium loses stability.
Strategies for use of Oseltamivir and Zanamivir during pandemic outbreaks

E. Hansen, T. Day, J. Arino, and 2 more authors

Canadian Journal of Infectious Diseases & Medical Microbiology, Nov 2010

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BACKGROUND: The use of neuraminidase inhibitors (oseltamivir and zanamivir) for the treatment of ill individuals has been an important intervention during the 2009 H1N1 pandemic. However, the emergence and spread of drug resistance remains a major concern and, therefore, optimizing antiviral strategies is crucial to retain the longterm effectiveness of these pharmaceutical interventions. METHODS: A dynamic model of disease transmission was developed to investigate optimal scenarios for the use of a secondary drug (eg, zanamivir). Considering both small and large stockpiles, attack rates were projected by simulating the model to identify "tipping points" for switching to zanamivir as resistance to oseltamivir develops. RESULTS: The use of a limited stockpile of zanamivir can substantially reduce the overall attack rate during pandemic outbreaks. For a reasonably large stockpile of zanamivir, it is optimal to delay the use of this drug for a certain amount of time during which oseltamivir is used as the primary drug. For smaller stockpiles, however, earlier use of zanamivir will be most effective in reducing the overall attack rate. Given a limited stockpile of zanamivir (1.8% in the Canadian plan) without replenishment, and assuming that the fraction of ill individuals being treated is maintained below 60%, the results suggest that zanamivir should be dispensed as the primary drug for thresholds of the cumulative number of oseltamivir resistance below 20%. INTERPRETATION: Strategic use of a secondary drug becomes crucial for pandemic mitigation if vaccination and other interventions fail to sufficiently reduce disease transmission in the community. These findings highlight the importance of enhanced surveillance and clinical monitoring for rapid identification of resistance emergence and its population incidence, so that optimal timing for adaptation to the use of drugs can be achieved.
Global Air Traffic Patterns During the H1N1 Influenza Pandemic and their Public Health Implications

K. Khan, J. Arino, R. Eckhard, and 4 more authors

Nov 2010

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Global public health implications of a mass gathering in Mecca, Saudi Arabia during the midst of an influenza pandemic

K. Khan, Z.A. Memish, A. Chabbra, and 13 more authors

Journal of Travel Medicine, Nov 2010

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Background. Every year millions of pilgrims from around the world gather under extremely crowded conditions in Mecca, Saudi Arabia to perform the Hajj. In 2009, the Hajj coincided with influenza season during the midst of an influenza A (H1N1) pandemic. After the Hajj, resource-limited countries with large numbers of traveling pilgrims could be vulnerable, given their limited ability to purchase H1N1 vaccine and capacity to respond to a possible wave of H1N1 introduced via returning pilgrims. Methods. We studied the worldwide migration of pilgrims traveling to Mecca to perform the Hajj in 2008 using data from the Saudi Ministry of Health and international air traffic departing Saudi Arabia after the 2008 Hajj using worldwide airline ticket sales data. We used gross national income (GNI) per capita as a surrogate marker of a country’s ability to mobilize an effective response to H1N1. Results. In 2008, 2.5 million pilgrims from 140 countries performed the Hajj. Pilgrims (1.7 million) were of international (non-Saudi) origin, of which 91.0% traveled to Saudi Arabia via commercial flights. International pilgrims (11.3%) originated from low-income countries, with the greatest numbers traveling from Bangladesh (50,419), Afghanistan (32,621), and Yemen (28,018). Conclusions. Nearly 200,000 pilgrims that performed the Hajj in 2008 originated from the world’s most resource-limited countries, where access to H1N1 vaccine and capacity to detect and respond to H1N1 in returning pilgrims are extremely limited. International efforts may be needed to assist resource-limited countries that are vulnerable to the impact of H1N1 during the 2009 to 2010 influenza season.
Global analysis for a general epidemiological model with vaccination and varying population

W. Yang, C. Sun, and J. Arino

Journal of Mathematical Analysis and Applications, Nov 2010

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An SIR model with vaccination and varying population is formulated. The global dynamics of this model and its corresponding proportionate system are investigated. The correlations between the two systems in terms of disease eradication and persistence are presented. Three critical vaccination rates phi1c, phi2c and phi3c are obtained. It is found that when phi>phi1c the disease can be eradicated by increasing the vaccination rate until it exceeds phi3c. When phi<phi1c, the disease can be controlled to an endemic level by taking the appropriate vaccination rate phi2c.

2009

Competitive interference between influenza viral strains

S.M. Moghadas, C.S. Bowman, and J. Arino

Canadian Applied Mathematics Quarterly, Nov 2009

Published in 2011 with 2009 date [publisher delay]. So actual reference is Vol. 17, 2009.

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We propose a modelling framework for investigating the dynamics of competition between immunologically- related in uenza viral strains in the absence of pre-existing immunity. Assuming that the host immune system will mount partial protection (cross-immunity) against one strain by virtue of having interacted with the other through exposure, we discuss the conditions for the occurrence of two distinct waves of infection during a single epidemic episode. Numerical simulations are presented to illustrate the possibility of infection waves with respect to the protection level induced by the first strain, and the time-lag for evolving the second strain. We propose directions for future work that involves extension of the model to include vaccination.
Diseases in metapopulations

J. Arino

In Modeling and Dynamics of Infectious Diseases, Nov 2009

Also CDM Preprint Series report 2008-04

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Metapopulation models consist of graphs, with systems of differential equations at each vertex. This modeling paradigm is appropriate for the description of the spatio-temporal spread of infectious diseases. In this document, I present the setting of these models, and some of the mathematical techniques that can be used to study them. I conclude with a brief review of some models using this approach.
Antiviral resistance during pandemic influenza: implications for stockpiling and drug use

J. Arino, C.S. Bowman, and S.M. Moghadas

BMC Infectious Diseases, Nov 2009

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Background The anticipated extent of antiviral use during an influenza pandemic can have adverse consequences for the development of drug resistance and rationing of limited stockpiles. The strategic use of drugs is therefore a major public health concern in planning for effective pandemic responses. Methods We employed a mathematical model that includes both sensitive and resistant strains of a virus with pandemic potential, and applies antiviral drugs for treatment of clinical infections. Using estimated parameters in the published literature, the model was simulated for various sizes of stockpiles to evaluate the outcome of different antiviral strategies. Results We demonstrated that the emergence of highly transmissible resistant strains has no significant impact on the use of available stockpiles if treatment is maintained at low levels or the reproduction number of the sensitive strain is sufficiently high. However, moderate to high treatment levels can result in a more rapid depletion of stockpiles, leading to run-out, by promoting wide-spread drug resistance. We applied an antiviral strategy that delays the onset of aggressive treatment for a certain amount of time after the onset of the outbreak. Our results show that if high treatment levels are enforced too early during the outbreak, a second wave of infections can potentially occur with a substantially larger magnitude. However, a timely implementation of wide-scale treatment can prevent resistance spread in the population, and minimize the final size of the pandemic. Conclusion Our results reveal that conservative treatment levels during the early stages of the outbreak, followed by a timely increase in the scale of drug-use, will offer an effective strategy to manage drug resistance in the population and avoid run-out. For a 1918-like strain, the findings suggest that pandemic plans should consider stockpiling antiviral drugs to cover at least 20% of the population.
Editorial

J. Arino, and S. Portet

In Proceedings of the Second International Conference of the French-speaking Society for Theoretical Biology (Winnipeg, Manitoba, Canada, 4-6 June, 2007). Acta Biotheoretica, Nov 2009

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An analysis of Canada’s vulnerability to emerging infectious disease threats via the global airline transportation network

K. Khan, J. Arino, F. Calderon, and 9 more authors

Nov 2009

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Spread of a novel influenza A (H1N1) virus via global airline transportation

K. Khan, J. Arino, W. Hu, and 8 more authors

New England Journal of Medicine, Nov 2009

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An in vivo intermediate filament assembly model

S. Portet, and J. Arino

Mathematical Biosciences and Engineering, Nov 2009

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A model is developed to study the in vivo intermediate filament organization in terms of repartition between four different structural states: soluble proteins, particles, short, and long filaments. An analysis is conducted, showing that the system has a unique, globally asymptotically stable equilibrium. By means of sensitivity analysis, the influence of parameters on the system is studied. It is shown that, in agreement with biological observations, posttranslational modifications of intermediate filament proteins resulting in filament solubilization are the main regulators of the intermediate filament organization. A high signalling-dependent solubilization of filaments favours the intermediate filament aggregation in particles.
Proceedings of the Second International Conference of the French-speaking Society for Theoretical Biology (Winnipeg, Manitoba, Canada, 4-6 June, 2007)

Nov 2009

2008

Optimal Treatment Rate During an Influenza Pandemic in the Presence of Drug-Resistance Emergence

Julien Arino

Nov 2008

Proceedings of the 2nd Fields–MITACS Industrial Problem-Solving Workshop

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A model for influenza with vaccination and antiviral treatment

J. Arino, F. Brauer, P. Driessche, and 2 more authors

Journal of Theoretical Biology, Nov 2008

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Compartmental models for influenza that include control by vaccination and antiviral treatment are formulated. Analytic expressions for the basic reproduction number, control reproduction number and the final size of the epidemic are derived for this general class of disease transmission models. Sensitivity and uncertainty analyses of the dependence of the control reproduction number on the parameters of the model give a comparison of the various intervention strategies. Numerical computations of the deterministic models are compared with those of recent stochastic simulation influenza models. Predictions of the deterministic compartmental models are in general agreement with those of the stochastic simulation models.

2007

Effect of pathogen-resistant vectors on the transmission dynamics of a vector-borne disease

J. Arino, C.S. Bowman, A. Gumel, and 1 more author

Journal of Biological Dynamics, Nov 2007

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A model is introduced for the transmission dynamics of a vector-borne disease with two vector strains, one wild and one pathogen-resistant; resistance comes at the cost of reduced reproductive fitness. The model, which assumes that vector reproduction can lead to the transmission or loss of resistance (reversion), is analyzed in a particular case with specified forms for the birth and force of infection functions. The vector component can have, in the absence of disease, a coexistence equilibrium where both strains survive. In the case where reversion is possible, this coexistence equilibrium is globally asymptotically stable when it exists. This equilibrium is still present in the full vector-host system, leading to a reduction of the associated reproduction number, thereby making elimination of the disease more feasible. When reversion is not possible, there can exist an additional equilibrium with only resistant vectors.
A final size relation for epidemic models

J. Arino, F. Brauer, P. Driessche, and 2 more authors

Mathematical Biosciences and Engineering, Nov 2007

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A final size relation is derived for a general class of epidemic mod els, including models with multiple susceptible classes. The derivation depends on an explicit formula for the basic reproduction number of a general class of disease transmission models, which is extended to calculate the basic reproduction number in models with vertical transmission. Applications are given to specific models for influenza and SARS.
Quarantine in a multi-species epidemic model with spatial dynamics

J. Arino, R. Jordan, and P. Driessche

Mathematical Biosciences, Nov 2007

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Motivation is provided for the development of infectious disease models that incorporate the movement of individuals over a range of spatial scales. A general model is formulated for a disease that can be transmitted between different species and multiple patches, and the behavior of the system is investigated in the case in which the spatial component consists of a ring of patches. The influence of various parameters on the spatial and temporal spread of the disease is studied numerically, with particular focus on the role of quarantine in the form of travel restriction.

2006

Simple models for containment of a pandemic

J. Arino, F. Brauer, P. Driessche, and 2 more authors

Journal of the Royal Society Interface, Nov 2006

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Stochastic simulations of network models have become the standard approach to studying epidemics. We show that many of the predictions of these models can also be obtained from simple classical deterministic compartmental models. We suggest that simple models may be a better way to plan for a threatening pandemic with location and parameters as yet unknown, reserving more detailed network models for disease outbreaks already underway in localities where the social networks are well identified. We formulate compartmental models to describe outbreaks of influenza and attempt to manage a disease outbreak by vaccination or antiviral treatment. The models give an important prediction that may not have been noticed in other models, namely that the number of doses of antiviral treatment required is extremely sensitive to the number of initial infectives. This suggests that the actual number of doses needed cannot be estimated with any degree of reliability. The model is applicable to pre-epidemic vaccination, such as annual vaccination programs in anticipation of an "ordinary" influenza outbreak with limited drift, and as a combination of treatment both before and during an epidemic.
Disease spread in metapopulations

J. Arino, and P. Driessche

Fields Institute Communications, Nov 2006

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Some continuous time, discrete space, metapopulation models that have been formulated for disease spread are presented. Motivation for such a formulation with travel between discrete patches is presented. A system of 4p ordinary differential equations describes disease spread in an environment divided into p patches. The basic reproduction number R0 is calculated, with the disease dying out in each patch if R_0 < 1. If travel is assumed to be independent of disease status, then numerical results are cited that indicate that for R_0 > 1 solutions tend to an endemic equilibrium with the disease present in each patch. The system is extended to include cross infection between several species. A second extension involves keeping track of both the current patch and the patch in which an individual usually resides. Travel can change disease spread in a complicated way; it may help the disease to persist or may aid disease extinction. Complexity that can be built into metapopulation models is illustrated by three case-study examples from the literature.
Time delays in epidemic models: modeling and numerical considerations

J. Arino, and P. Driessche

In Delay Differential Equations and Applications, Nov 2006

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Continuous time deterministic epidemic models are traditionally formulated as systems of ordinary differential equations for the numbers of individuals in various disease states, with the sojourn time in a state being exponentially distributed. Time delays are introduced to model constant sojourn times in a state, for example, the infective or immune state. Models then become delay-differential and/or integral equations. For a review of some epidemic models with delay see van den Driessche [228]. More generally, an arbitrarily distributed sojourn time in a state, for example, the infective or immune state, is used by some authors (see [69] and the references therein).
An alternative formulation for a delayed logistic equation

J. Arino, L. Wang, and G.S.K. Wolkowicz

Journal of Theoretical Biology, Jul 2006

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We derive an alternative expression for a delayed logistic equation, assuming that the rate of change of the population depends on three components: growth, death, and intraspecific competition, with the delay in the growth component. In our formulation, we incorporate the delay in the growth term in a manner consistent with the rate of instantaneous decline in the population given by the model. We provide a complete global analysis, showing that, unlike the dynamics of the classical logistic delay differential equation (DDE) model, no sustained oscillations are possible. Just as for the classical logistic ordinary differential equation (ODE) growth model, all solutions approach a globally asymptotically stable equilibrium. However, unlike both the logistic ODE and DDE growth models, the value of this equilibrium depends on all of the parameters, including the delay, and there is a threshold that determines whether the population survives or dies out. In particular, if the delay is too long, the population dies out. When the population survives, i.e., the attracting equilibrium has a positive value, we explore how this value depends on the parameters. When this value is positive, solutions of our DDE model seem to be well approximated by solutions of the logistic ODE growth model with this carrying capacity and an appropriate choice for the intrinsic growth rate that is independent of the initial conditions.
Delay Differential Equations and Applications

In , Jul 2006

I (JA) became main (uncredited) editor of this book after the death of my father, Ovide Arino.

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Three different outcomes to the same problem in population dynamics

Jul 2006

Manitoba Math Links

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2005

A multi-species epidemic model with spatial migration

J. Arino, J.R. Davis, D. Hartley, and 3 more authors

Mathematical Medicine and Biology, Jul 2005

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A model is formulated that describes the spatial propagation of a disease that can be transmitted between multiple species. The spatial component consists, for each species, of a certain number of patches that make up the vertices of a digraph, the arcs of which represent the movement of the various species between the patches. In each of the patches and for each species, a susceptible-exposed-infectious-recovered (SEIR) epidemic model describes the evolution of the disease status of individuals. Also in each patch, there is transmission of the disease from species to species. An analysis of the system is given, beginning with results on the mobility component. A formula is derived for the computation of the basic reproduction number R0 for sspecies and npatches, which then determines the global stability properties of the disease free equilibrium. Simulations for the spread of a disease in one species and two patches are presented.
Considerations on yield, nutrient uptake, cellular growth, and competition in chemostat models

J. Arino, S.Y. Pilyugin, and G.S.K. Wolkowicz

Canadian Applied Mathematics Quarterly, Jul 2005

Published in 2005 with 2003 date [publisher delay]. So exact reference is Vol. 11, 2003.

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We investigate some properties of a very general model of growth in the chemostat. In the classical models of the chemostat, the function describing cellular growth is assumed to be a constant multiple of the function modeling substrate uptake. The constant of proportionality is called the growth yield constant. Here, this assumption of a constant describing growth yield is relaxed. Instead, we assume that the relationship between uptake and growth might depend on the substrate concentration and hence that the yield is variable. We obtain criteria for the stability of equilibria and for the occurrence of a Hopf bifurcation. In particular, a Hopf bifurcation can occur if the uptake function is unimodal. Then, in this setting, we consider competition in the chemostat for a single substrate, in order to challenge the principle of competitive exclusion. We consider two examples. In the first, the function describing the growth process is monotone and in the second it is unimodal. In both examples, in order to obtain a Hopf bifurcation, one of the competitors is assumed to have a variable yield, and its "uptake" is described by a unimodal function. However, the interpretation is different in each case. We provide a necessary condition for strong coexistence and a sufficient condition that guarantees the extinction of one or more species. We show numerically by means of bifurcation diagrams and simulations, that the competitive exclusion principle can be breached resulting in oscillatory coexistence of more than one species, that competitor-mediated coexistence is possible, and that these simple systems can have very complicated dynamics.

2004

An epidemiology model that includes a leaky vaccine with a general waning function

J. Arino, K.L. Cooke, P. Driessche, and 1 more author

DCDS-B, Jul 2004

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Vaccination that gives partial protection for both newborns and susceptibles is included in a transmission model for a disease that confers no immunity. A general form of the vaccine waning function is assumed, and the interplay of this together with the vaccine efficacy and vaccination rates is discussed. The integro-differential system describing the model is studied for a constant vaccine waning rate, in which case it reduces to an ODE system, and for a constant waning period, in which case it reduces to a system of delay differential equations. For some parameter values, the model is shown to exhibit a backward bifurcation, leading to the existence of subthreshold endemic equilibria. Numerical examples are presented that demonstrate the consequence of this bifurcation in terms of epidemic control. The model can alternatively be interpreted as one consisting of two social groups, with education playing the role of vaccination.
Intermediate filament network organization: in vitro and in vivo kinetic models

S. Portet, J. Vassy, C. Hogue, and 2 more authors

Comptes Rendus: Biologies, Jul 2004

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We propose two systems of ordinary differential equations modeling the assembly of intermediate filament networks. The first one describes the in vitro intermediate filament assembly dynamics. The second one deals with the in vivo evolution of cytokeratin, which is the intermediate filament protein expressed by epithelial cells. The in vitro model is then briefly analyzed in a simplified case

2003

A multi-city epidemic model

J. Arino, and P. Driessche

Mathematical Population Studies, Jul 2003

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Some analytical results are given for a model that describes the propagation of a disease in a population of individuals who travel between n cities. The model is formulated as a system of 2n 2 ordinary differential equations, with terms accounting for disease transmission, recovery, birth, death, and travel between cities. The mobility component is represented as a directed graph with cities as vertices and arcs determined by outgoing (or return) travel. An explicit formula that can be used to compute the basic reproduction number, lcub\cal Rrcub_0 , is obtained, and explicit bounds on lcub\cal Rrcub_0 are determined in the case of homogeneous contacts between individuals within each city. Numerical simulations indicate that lcub\cal Rrcub_0 is a sharp threshold, with the disease dying out if lcub\cal Rrcub_0 1 .
The basic reproduction number in a multi-city compartmental epidemic model

J. Arino, and P. Driessche

Lecture Notes in Control and Information Science, Jul 2003

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A directed graph with cities as vertices and arcs determined by outgoing (or return) travel represents the mobility component in a population of individuals who travel between n cities. A model with 4 epidemiological compartments in each city that describes the propagation of a disease in this population is formulated as a system of 4n^2 ordinary differential equations. Terms in the system account for disease transmission, latency, recovery, temporary immunity, birth, death, and travel between cities. The basic reproduction number R0 is determined as the spectral radius of a nonnegative matrix product, and easily computable bounds on R0 are obtained.
Global results for an epidemic model with vaccination that exhibits backward bifurcation

J. Arino, C.C. McCluskey, and P. Driessche

SIAM J Appl Math, Jul 2003

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Vaccination of both newborns and susceptibles is included in a transmission model for a disease that confers immunity. The interplay of the vaccination strategy together with the vaccine efficacy and waning is studied. In particular, it is shown that a backward bifurcation leading to bistability can occur. Under mild parameter constraints, compound matrices are used to show that each orbit limits to an equilibrium. In the case of bistability, this global result requires a novel approach since there is no compact absorbing set.

2002

A size-structured, non conservative ODE model of the chemostat

J. Arino, and J.-L. Gouzé

Mathematical Biosciences, Jul 2002

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We study a class of size-structured, ODE models of growth in the chemostat, that take into account cell maintenance and substrate dependent cell mortality. Unlike most classical chemostat models, they are supposed to be non-conservative, in the sense that they do not verify the mass conservation principle. However, using a change of time scale, we are able to obtain qualitative results. Then, using a Lyapunov functional, we prove the global stability of the non-trivial equilibrium. Some examples of the possible structure of the models are given to finish with.
A discrete, size-structured model of phytoplankton growth in the chemostat. Introduction of inhomogeneous cell division size

J. Arino, J.-L. Gouzé, and A. Sciandra

Journal of Mathematical Biology, Jul 2002

Also INRIA Research Report 3963

Abstract DOI PDF

We introduce inhomogeneous, substrate dependent cell division in a time discrete, nonlinear matrix model of size-structured population growth in the chemostat, first introduced by Gage et al. [8] and later analysed by Smith [13]. We show that mass conservation is verified, and conclude that our system admits one non zero globally stable equilibrium, which we express explicitly. Then we run numerical simulations of the system, and compare the predictions of the model to data related to phytoplankton growth, whose obtention we discuss. We end with the identification of several parameters of the system.

2001

Modélisation structurée de la croissance du phytoplancton en chemostat

J. Arino

Université Grenoble 1, Jul 2001

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This thesis deals with the formulation and analysis of structured models of growth in a chemostat, an experimental device used for the culture of micro-organisms in idealized conditions. More specifically, we will be concerned with the description of the size of phytoplanktonic organisms. In a first part, we give some biological indications concerning phytoplankton, then describe the experimental apparatus and finally introduce the mathematical models used for an elementary description of the chemostat. The second and main part of this thesis begins by an introduction to structured population models, with emphasis on cellular division description. Then time discrete models describing in a detailed way cellular division are studied, followed by ordinary differential equations systems verifying the mass conservation principle, and finally by a class of models that do not verify this property. We end this thesis by considering possible applications to other contexts or populations of the type of models developped herein.

2000

A discrete, size-structured model of phytoplankton growth in the chemostat. Introduction of non constant cell division

J. Arino, J.-L. Gouzé, and A. Sciandra

Jul 2000

Abstract PDF

We introduce inhomogeneous, substrate dependent cell division in a nonlinear matrix model of size-structured population growth in the chemostat, first introduced by Gage et al. [7] and later analyzed by Smith [11]. We show that mass conservation is verified, and conclude that our system admits one non zero globally stable equilibrium, which we express explicitly. We then proceed to several numerical simulations, and briefly compare the prediction of the model to data, whose obtention we discuss.