Mathematical Modelling of Human Behaviour (Part 2)

Sarah Machado-Marques

York University

"Considering the effects of pair formation dynamics on mpox and HIV co-infection in the gbMSM community"

There is a growing need to explicitly consider how behaviour plays a role in the spread of diseases transmitted through close, prolonged contact. In particular, the duration individuals spend single or in relationships has yet to be incorporated into co-infection models, potentially underestimating the protective effects of stable partnerships. We propose an mpox and HIV co-infection model that explicitly incorporates the formation of pairs between individuals. We demonstrate that considering pair formation and dissolution rates are critical in determining outbreak potential and severity. These considerations remain important beyond the initial stages of the outbreak and can lead to more accurate predictions. Our work highlights that the particular pairing context and serological status of the population should always be carefully considered prior to intervention on behavioural patterns.

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Bridgette Amoako

University of Guelph

"Sexual Behaviour and Mpox Transmission in an Agent Based Model"

We present an agent-based framework that uses a dynamic signaling game to model mpox transmission in a population of gay and bisexual men who have sex with men (gbMSM). The model focuses on how agents' beliefs about a partner’s infection status influence their decisions to pursue or abstain from casual sexual encounters. Agents are subject to mpox’s typical incubation and infectious periods and become immune upon recovery. Immunity could also be obtained through vaccination. Within this framework, each agent updates their risk perception based on both individual encounters and broader disease prevalence, then selects a strategic response to potential partners. By examining how risk perception interacts with behavior, as well as how the timing and efficacy of vaccination factor into disease spread, we aim to provide insights into which conditions are most conducive to large outbreaks or successful containment. This approach highlights the role of dynamic, feedback-driven behaviors in shaping the course of mpox epidemics and can help inform strategies for more effective vaccination and public health interventions.

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Pouria Ramazi

Brock University

"Enough but Not Too Many: Modeling and Dynamics of Bi-Threshold Social Behavior"

This work introduces and analyzes bi-threshold models of social behavior, where individuals adopt actions only when their prevalence lies between a personal lower and upper threshold. This captures real-world dynamics like fashion trends or information spread, where behaviors are appealing when moderately common but lose appeal if too rare or too widespread. Theoretical results show that while small populations may exhibit persistent fluctuations, these fade as population size increases, with dynamics converging to equilibrium. Empirical validation on social media data confirms the model’s superior predictive power over traditional threshold models, particularly in capturing phases of behavioral decline.

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Clark KendrickGo

Ateneo de Manila University

"Exploring Mathematical Techniques in Collective Behaviour and Decision Making in Animal Groups"

Collective behaviour in animal groups are coordinated movements and interactions among members that aim to achieve a common goal. Whether these goals are for allocation of resources or defence from predators, the collective behaviour appears to be largely a group activity initiated by a member, known as the leader. In the absence of high-resolution spatio-temporal data, various qualitative studies offer a glimpse of how leader-follower interactions take place. For example, Nagy, et al., studied the average delay in response when pigeons change the direction inflight. Next, Bourjade, et al., studied the first mover and the succeeding order of movements of Przewalski's Horses. Furthermore, various studies on the collective motion in the animal kingdom offer mathematical models and infer how the interactions and decision making take place. Important questions arise during an event of coordinated motion in animals. During such an event, do individuals move according to a certain set of natural rules? Or certain patterns form due to the influence of a leader? How is this influence measured? Finally, how is influence transferred to other members of the group? In this study, we discuss the role of information theory to quantitatively uncover leader-follower relationship in a horse group. Specifically, we introduce concepts from information theory, specifically global and local transfer entropy being applied to a harem of horses. We will discuss their definitions, and how these key concepts are used to support causation in events. We will then discuss some important implications on how this technique can be used to analyse collective motion where data is scarce.

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