Considerations on the spatial and temporal spread of infectious pathogens in the COVID-19 era

5 November 2021

Julien Arino (Julien.Arino@umanitoba.ca)

Department of Mathematics & Data Science Nexus
University of Manitoba*

Canadian Centre for Disease Modelling
Canadian COVID-19 Mathematical Modelling Task Force
NSERC-PHAC EID Modelling Consortium (CANMOD, MfPH, OMNI/RÉUNIS)

It first began, it is said, in the parts of Ethiopia above Egypt, and thence descended into Egypt and Libya and into most of the King's country [Persia]. Suddenly falling upon Athens, it first attacked the population in Piraeus [..] and afterwards appeared in the upper city, when the deaths became much more frequent.

Outline

• Human habitat fragmentation, mobility and the spread of infectious diseases
• The first wave of COVID-19
• Case importations
• Spread of SARS-CoV-2 variants
• Role of transport restrictions
• Role of quarantine
• Lessons learned and key knowledge gaps

Human habitat fragmentation, mobility and the spread of infectious diseases

• Political divisions (jurisdictions): nation groups (e.g., EU), nations, provinces/states, regions, counties, cities..
• Travel between jurisdictions can be complicated or impossible
• Data is integrated at the jurisdicional level
• Policy is decided at the jurisdictional level
• Long range mobility is a bottom$\to$top$\to$top$\to$bottom process

• Multiple modalities: foot, bicycle, personal vehicle, bus, train, boat, airplane
• Various durations: trip to the corner shop $\neq$ commuting $\neq$ multi-day trip for work or leisure $\neq$ relocation, immigration or refuge seeking
• Volumes are hard to fathom

And yet mobility drives spatio-temporal spread:

• Black Death 1347-1353 arrived in Europe and spread following trade routes
• SARS-CoV-1 spread out of HKG following the GATN
• Khan, Arino, Hu et al, Spread of a novel influenza A (H1N1) virus via global airline transportation, New England Journal of Medicine (2009)

Amplification in Wuhan (Hubei province)

• Details of emergence and precise timeline before amplification started unknown
• Amplification in Wuhan
  • Cluster of pneumonia cases mostly related to the Huanan Seafood Market
  • 27 December 2019: first report to local government
  • 31 December 2019: publication
  • 8 January 2020: identification of SARS-CoV-2 as causative agent
• $\sim$ 23 January 2020: lockdown Wuhan and Hubei province + face mask mandates

By 29 January, virus was found in all provinces of mainland China

First detections outside China

Caveat : evidence of earlier spread

• Report to Wuhan authorities on 27 December 2019
• First export detections in Thailand and Japan on 13 and 16 January 2020 (with actual importations on 8 and 6 January)

$\implies$ amplification must have been occuring for a while longer

• France: sample taken from 42-year-old male (last foreign travel to Algeria in August 2019) who presented to ICU on 27 December 2019
• Retrospective studies in United Kingdom and Italy also showed undetected COVID-19 cases in prepandemic period

Untangling the first case issue

• Robert, Rossman & Jaric. Dating first cases of COVID-19. PLoS Pathogens (2021). Find likely timing of first case of COVID-19 in China as November 17 (95% CI October 4)
• Pekar, Worobey, Moshiri, Scheffler & Wertheim. Timing the SARS-CoV-2 index case in Hubei province. Science (2021). Period between mid-October and mid-November 2019 is plausible interval when the first case of SARS-CoV-2 emerged in Hubei province.

Important when trying to understand global spread, so let me illustrate with the model I used (J. Arino & S. Portet. A simple model for COVID-19. Infectious Disease Modelling 2020) [taking into account model evolution since]

Cumulative confirmed case counts in China as reported to WHO was $c=547$ cases on $t_c=\textrm{2020-01-22}$

Let $u$ be a point in parameter space. Solve ODE numerically over $[0,t]$, with $S(0)$ the population of China, $L_1(0)=1$ and other state variables 0. This gives a solution $x(t,t_0=0,u)$. Extracting $L_2(t,t_0=0,u)$ from this solution, obtain cumulative number of new detections as

Let $t^*$ be s.t. $C(t^*)=547$; then $t_i=\textrm{2020-01-22}-t^*$

• For SARS-CoV-1 (2003), the point of introduction on the GATN is known with certainty (Metropole Hotel, HKG, 2003-02-21)
• For SARS-CoV-2, uncertainty remains and will probably never be lifted

Back to the spatio-temporal spread of the detected first wave..

Moving from ISO-3166-3 (nation or territory) level to smaller sub-national jurisdictions, the picture is more contrasted

Next slide: Example of activation of North American health regions/municipios/counties

Importations

• In Ecology, importations are called introductions and have been studied for a while, because they are one of the drivers of evolution and, more recently, because of invasive species

• An importation occurs when an individual who acquired the infection in a jurisdiction makes their way to another jurisdiction while still infected with the disease

• Geographies greatly influence reasoning

  • At the country level, importations quickly become less relevant
  • Consider an isolated location of 500 people.. disease may become extinct then be reimported

• Suppose a resident variant is propagating in a population, say, the original wild type or, now, B.1.1.7
• A novel variant comes along, say B.1.617.2 (SARS-CoV-2 Delta) that is more transmissible

Q:

• How long until novel replaces resident variant in terms of propagation?
• What role do importations play in this?
• How does one diminish role of importations and how useful are measures used to do so?

Measures to control spatial spread

• Almost exclusively attacked from the perspective of would-be importer

In practice:

• Travel interruptions
• Quarantine

Interruption of travel

Quarantine $\neq$ Isolation

• Quarantine is indiscriminate and applies to all incoming flux
• Isolation is imposed to known or suspected cases and known contacts
• First used in (the lazzarettos of) Dubrovnik in 1377
• Name comes from Venitian quarantena

Effect of quarantine on importation rates

$1/\lambda$ the mean time between case importations, $1/\lambda_q$ the mean quarantine-regulated time between case importations, $c$ the efficacy of quarantine (in %). Then

Suppose $1/\lambda=$ 5 days and efficacy of quarantine is 90% at 7 days and 98% at 14 days, respectively

Then $1/\lambda_q=$ 50 and 250 days, respectively

Lessons learned

• Airport screening sometimes worked to detect the first imports
• Travel interruptions work .. sometimes (e.g., ISL, NZL, CAN-NL)
• Travel interruptions often do not work (e.g., world $\setminus$ very few)
• Governments like travel interruptions regardless
• Quarantine seems to work quite well but needs to be applied homogeneously
• Open Data has finally landed in public health. Still some issues (e.g., Canadian data), but we're moving in the right direction. Also saw emergence of scientist/journalistic/citizen data collection and dissemination initiatives

Key questions/knowledge gaps

• How to get governments to understand that a pandemic is a global phenomenon with local "phenotypes", so that uncoordinated unilateral travel policies have virtually no chance of success (treat the symtoms, not the cause)
• How to apprehend/model the absolutely colossal amount of mobility taking place and the not less consequent variety of transport modalities and purposes
• What are the necessary conditions for travel interruptions to work?
• Because of scapegoating, the borders were closed in theory. However, because of .. real life, they were not in practice. How closed is closed?

Arrival into CAN from 2020-04-01 to 2021-03-31

(border was "closed")

80/100K/day on average (678/100K/day 2019-04 $\to$ 2020-03)

Key questions/knowledge gaps (cont.)

• Effect of heterogeity of vaccination methods/protocols (vaccine type/number of doses/ages)
• What is the effect of local vaccine uptake discrepancies?
• Variants emerge typically in high propagation areas. How will the vaccine divide play into this?

In conclusion

Space is a fundamental component of the epidemic spread process and cannot be ignored, both in modelling and in public health decision making