Mathematical Modelling of Human Behaviour (Part 1)

Iain Moyles

York University

"Fear dynamics in a mathematical model of disease transmission"

We explore a mathematical model of disease transmission with a fearful compartment. Susceptible individuals become afraid by either interacting with individuals who are already afraid or those who are infected. Individuals who are afraid take protective measures via contact reductions to reduce risk of transmission. Individuals can lose fear naturally over time or because they see people recovering from the disease. We consider two scenarios of the model, one where fear is obtained at a slower rate than disease spread and one where it is comparable. In the former we show that behavioural change cannot impact disease outcome, but in the latter, we observe that sufficient behavioural intervention can reduce disease impact. However, response to recovery can induce a bifurcation where contact reduction cannot mitigate disease spread. We identify this bifurcation and demonstrate its implication on disease dynamics and final size.

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Md. Mijanur Rahman

University of British Columbia Okanagan

"The role of opinion dynamics in generating multiple epidemic waves"

We develop and rigorously analyze a coupled opinion-disease framework in which the population is partitioned into two susceptible classes that differ in their infection rates and are linked by opinion switching. We show that the model preserves classic SIR-type dynamics for the total susceptible population but embeds a feedback loop through a time-varying effective transmission rate that depends on the opinion proportions. We define an effective reproduction rate based on the transmission rate and establish explicit criteria for epidemic peaks in terms of its sign changes. Two asymptotic regimes are examined using the scaled base opinion-switching rate. In the slow switching limit, opinion exchange freezes and guarantees at most one infection wave. In the fast switching limit, the opinion distribution equilibrates instantaneously to a quasi-steady state, which again leads to a single wave. Extending the model to Hill-type, infection-dependent switching rates yields the same one-wave result in both asymptotic limits. These findings imply that neither vanishingly slow nor extremely rapid opinion change, as modelled here, can sustain recurrent outbreaks. Repeated waves in this framework must arise from intermediate switching speeds or necessitate the inclusion of additional mechanisms not considered in these asymptotic limits. The work highlights the speed of opinion change as a potential public health leverage point.

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Azadeh Aghaeeyan

Brock University

"Understanding the Decision-Making of Late COVID-19 Vaccine Adopters"

Individuals responded differently to the COVID-19 vaccination campaign: some were early adopters, others delayed vaccination, and some refused it altogether. Despite the important role of late adopters in pandemic control, their behaviour remains understudied. We propose a mechanistic model that divides late adopters based on their decision-making strategies into two types: success-based learners, who are influenced by others’ vaccination experiences, and myopic rationalists, who receive their shots when the perceived benefit of vaccination outweighs the cost. The model also accounts for possible shifts in vaccination perception triggered by impactful events. Using a Bayesian framework, we fit the model to weekly COVID-19 vaccine uptake data from U.S. states, stratified by age and sex. Our results suggest that late adopters mainly behaved as success-based learners and that perception shifts varied across events—some increased and others reduced the perceived value of vaccination. These findings are a step toward tailoring vaccine promotion communication strategies to late adopters.

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Bouchra Nasri

University of Montreal

"Mathematical Modelling of Pregnant Women Co-infected with HIV and ZIKV: A Case Study in Endemic Latin American and Caribbean Countries"

Co-infection with HIV and Zika virus (ZIKV) in pregnant women remains under-documented, and its dynamics and impact on neonatal health are understudied. This gap raises public health concerns, particularly in Latin America and the Caribbean, where ZIKV vectors remain active. We conducted a cross-sectional ecological study using aggregated data (2015-2023). A compartmental model was developed: an SIR compartment for pregnant women (HIV and ZIKV), SI compartments for newborns and mosquito vectors. The basic reproduction number R0 for co-infection was estimated. Sensitivity analysis was used to identify influential parameters. The effect of different control measures (personal and sexual protection, ZIKV treatment, antiretrovirals) was simulated to assess their efficacy on neonatal health. As results, we found R0 ranging from 0.09 to 1.29 depending on the country and was most sensitive to mosquito-biting rates and mortality in pregnant women. ZIKV infection had a greater impact on neonatal complications than HIV infection. The introduction of ZIKV into this population resulted in a significant increase in adverse neonatal outcomes. Control strategies were most effective when combined and maintained over time, with ZIKV treatment having the least impact. It is important to improve prenatal care for women living with HIV, who are vulnerable to other infections such as ZIKV. Prevention of sexual transmission of HIV and better surveillance are also essential to protect maternal and child health. This is a joint work with: Sika-Rose Coffi, Jhoana P. Romero-Leiton, Idriss Sekak and Rado Ramasy

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