Agent-based models

6 April 2022

Julien Arino

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)

* The University of Manitoba campuses are located on original lands of Anishinaabeg, Cree, Oji-Cree, Dakota and Dene peoples, and on the homeland of the Métis Nation.

Outline

  • What are agent-based models (ABM)
  • When to use ABM
  • When not to use ABM
  • Some examples

What are agent-based models (ABM)

ABM IBM

  • Early in the life of these models, they were called IBM (individual-based models)
  • Over the years, a "philosophical" distinction has emerged:
    • IBM are mathematical models that consider individuals as the units; e.g., DTMC, CTMC, branching processes, etc.
    • ABM are computational models whose study is, for the most part, only possible numerically

ABM vs Network models

  • Network models endow vertices with simple systems and couple them through graphs
  • Can be ABM, but some networks can also be studied analytically
  • Not enough time to go into this, a very interesting subject!

When to use ABM

ABM are very useful to decipher contact processes

  • Classic mathematical models capture contact by using approximations of what contact could be like
  • Classic models allow some flexibility (see section about incidence functions in Lecture 02) but they remain limited
  • ABM can model actual trajectories of individuals, so given a definition of what a contact is (how close do you need to be for a contact to take place), can count them efficaciously

ABM are very useful to understand behavioural responses

When not to use ABM

As with all tools, beware!

  • There is a law of large numbers effects happening often: if you have many units, unless some emergent behaviour arises, you get the same results using ODEs...

With this specific tool, beware!

  • There is a certain tendency in CS people to create yet another system and seek adoption by users

Some examples

Some examples

  • Antibiotic resistance in hospitals
  • Effectiveness of contact tracing
  • Contacts during Hajj

Antibiotic resistance in hospitals

D’Agata, Magal, Olivier, Ruand & Webb. Modeling antibiotic resistance in hospitals: The impact of minimizing treatment duration, Journal of Theoretical Biology (2007)

An IBM that's almost an ABM

  • This work is a good illustration of the "cultural proximity" between IBM and ABM
  • Model is stochastic and individual-based, in good enough form that approximating ODE can be derived
  • Allows for very specific tracking of the status of individuals through the process (almost an ABM in this sense)

The setup

  • Three processes:
    1. admission and exit of patients
    2. infection of patients by HCW (health care workers)
    3. contamination of HCW by patients
  • Contamination of HCW is "transient": they are carriers, if they wash their hands properly, they become OK
  • Each day has 3 shifts of 8h for HCW
  • Patients are put in contact by visits of HCW
  • Rules for contaminations per unit time

Effectiveness of contact tracing

Tian, Osgood, Al-Azem & Hoeppner. Evaluating the Effectiveness of Contact Tracing on Tuberculosis Outcomes in Saskatchewan Using Individual-Based Modeling, Health Education & Behavior (2013)

Evaluation of contact tracing in TB

They can then formulate scenarios

They then run these scenarios and compare results

Contacts during Hajj

Tofighi, Asgary, Tofighi, Najafabadi, Arino, Amiche, Rahman, McCarthy, Bragazzi, Thommes, Coudeville, Grunnill, Bourouiba and Wu. Estimating Social Contacts in Mass Gatherings for Disease Outbreak Prevention and Management (Case of Hajj Pilgrimage), Tropical Diseases, Travel Medicine and Vaccines

Contacts during Hajj

  • In a mass gathering event like Hajj, lots of people come together originating from many countries
  • So if propagation occurs during the event, this has the capacity to spread infection far and wide when individuals (pilgrims here) return home
  • Contacts during part of the event are really specific in their configuration

Tofighi, Asgary, Tofighi, Najafabadi, Arino, Amiche, Rahman, McCarthy, Bragazzi, Thommes, Coudeville, Grunnill, Bourouiba and Wu. Estimating Social Contacts in Mass Gatherings for Disease Outbreak Prevention and Management (Case of Hajj Pilgrimage), Tropical Diseases, Travel Medicine and Vaccines

The setup

  • Word of warning: I am quite fuzzy on the specifics :)
  • Pilgrims enter Masjid al-Haram mosque through several gates
  • Proceed to Mataaf (area around Kaaba), circle the Kaaba 7 times counterclockwise (process is the Tawaf)
  • Then do seven trips between Safa and Marwah (process is the Sa'ee)

Tawaf in pre-COVID-19 times

Tawaf - Socially distanced version

Sa'ee in pre-COVID-19 times

Sa'ee - Socially distanced version

  • As you can gather from this:
    • Typically high density crowds
    • Very specific mixing patterns
  • Opportunities for transmission are very high
  • However, control mechanisms are also available

understanding contact patterns and frequency would help

Patient–HCW contact diagram for four patients and one HCW during one shift. Patient status: uninfected (green), infected with the non-resistant strain (yellow), infected with the resistant strain (red). HCW status: uncontaminated (______ ), contaminated with the non-resistant strain (………), contaminated with the resistant strain (- - - - - )

The left (respectively the right) figure corresponds to 1 trajectory (respectively the average over 80 trajectories) of the IBM during one shift, with no exit and admission of patients, and no changes in the infection status of patients