Mathematical Epidemiology and Evolutionary Games

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E3: Mathematical Biology".

Deadline for manuscript submissions: 31 December 2025 | Viewed by 1206

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Informatics and Knowledge Management Graduate Program, Universidade Nove de Julho, São Paulo 01504-001, SP, Brazil
Interests: mathematical epidemiology; evolutionary game theory
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Special Issue Information

Dear Colleagues,

During an epidemic outbreak, people change their habits and take personal actions to minimize the impact of the disease on their health and daily routines. These actions are the strategies people use to cope with the epidemic. Researchers have studied not only the analysis of the disease within the population but also how the evolution of individual strategies in a population affects the disease dynamics using models from the fields of mathematical epidemiology and evolutionary games.

Therefore, this Special Issue, entitled "Mathematical Epidemiology and Evolutionary Games", will consider novel articles that explore the evolution of population strategies and the dynamics of disease spread. Potential contributions should present mathematical studies on the following topics (among other related topics):

  • Epidemic modeling;
  • Evolutionary biology;
  • Evolutionary epidemiological processes;
  • Opinion dynamics;
  • Population dynamics;
  • Voluntary quarantine, isolation, and the use of masks.
  • Vaccination games.

Dr. Pedro Henrique Triguis Schimit
Guest Editor

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Keywords

  • agent-based models
  • complex networks
  • disease invasion
  • epidemic models
  • epidemiology
  • evolutionary game theory
  • mathematical epidemiology
  • population dynamics
  • spatial games
  • vaccination game

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Published Papers (3 papers)

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Research

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18 pages, 573 KiB  
Article
A Game-Theoretic Model of Optimal Clean Equipment Usage to Prevent Hepatitis C Among Injecting Drug Users
by Kristen Scheckelhoff, Ayesha Ejaz and Igor V. Erovenko
Mathematics 2025, 13(14), 2270; https://doi.org/10.3390/math13142270 - 15 Jul 2025
Viewed by 257
Abstract
Hepatitis C is an infectious liver disease which contributes to an estimated 400,000 deaths each year. The disease is caused by the hepatitis C virus (HCV) and is spread by direct blood contact between infected and susceptible individuals. While the magnitude of its [...] Read more.
Hepatitis C is an infectious liver disease which contributes to an estimated 400,000 deaths each year. The disease is caused by the hepatitis C virus (HCV) and is spread by direct blood contact between infected and susceptible individuals. While the magnitude of its impact on human populations has prompted a growing body of scientific work, the current epidemiological models of HCV transmission among injecting drug users treat risk behaviors as fixed parameters rather than as outcomes of a dynamic, decision-making process. Our study addresses this gap by constructing a game-theoretic model to investigate the implications of voluntary participation in clean needle exchange programs on the spread of HCV among this high-risk population. Individual drug users weigh the (perceived) cost of clean equipment usage relative to the (perceived) cost of infection, as well as the strategies adopted by the rest of the population, and look for a selfishly optimal level of protection. We find that the spread of HCV in this population can theoretically be eliminated if individuals use sterile equipment approximately two-thirds of the time. Achieving this level of compliance, however, requires that the real and perceived costs of obtaining sterile equipment are essentially zero. Our study demonstrates a robust method for integrating game theory with epidemiological models to analyze voluntary health interventions. It provides a quantitative justification for public health policies that eliminate all barriers—both monetary and social—to comprehensive harm-reduction services. Full article
(This article belongs to the Special Issue Mathematical Epidemiology and Evolutionary Games)
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20 pages, 430 KiB  
Article
Resource Allocation in Multi-Objective Epidemic Management: An Axiomatic Analysis
by Jong-Chin Huang, Kelvin H.-C. Chen and Yu-Hsien Liao
Mathematics 2025, 13(13), 2182; https://doi.org/10.3390/math13132182 - 3 Jul 2025
Viewed by 184
Abstract
This study presents a novel game-theoretical framework designed to support epidemic management, with a specific focus on the allocation of limited resources across competing public health objectives and intervention strategies. Recognizing the varied roles and capacities of participatory agents, we model their involvement [...] Read more.
This study presents a novel game-theoretical framework designed to support epidemic management, with a specific focus on the allocation of limited resources across competing public health objectives and intervention strategies. Recognizing the varied roles and capacities of participatory agents, we model their involvement as occurring at multiple levels, reflecting the complex decision-making processes encountered in real-world situations. To account for the unequal influence or priority of different agents and strategies, we further propose a suite of weighted allocation measures grounded in well-established theoretical principles. In response to ongoing concerns over the arbitrariness of externally assigned weights, we also construct a refined metric based on endogenous marginal intervention effects, offering a more organically derived representation of participator impact. A series of illustrative examples demonstrates the practical relevance of these models, revealing how they can capture key dynamics such as behavioral diversity, the coexistence of overlapping policies, and logical independence under distinct weighting perspectives. Collectively, these contributions aim to provide epidemic response teams with a set of interpretable and adaptable tools tailored to the complexity of real-world public health crises. Full article
(This article belongs to the Special Issue Mathematical Epidemiology and Evolutionary Games)
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Review

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30 pages, 435 KiB  
Review
Vaccination as a Game: Behavioural Dynamics, Network Effects, and Policy Levers—A Comprehensive Review
by Pedro H. T. Schimit, Abimael R. Sergio and Marco A. R. Fontoura
Mathematics 2025, 13(14), 2242; https://doi.org/10.3390/math13142242 - 10 Jul 2025
Viewed by 346
Abstract
Classical epidemic models treat vaccine uptake as an exogenous parameter, yet real-world coverage emerges from strategic choices made by individuals facing uncertain risks. During the last two decades, vaccination games, which combine epidemic dynamics with game theory, behavioural economics, and network science, have [...] Read more.
Classical epidemic models treat vaccine uptake as an exogenous parameter, yet real-world coverage emerges from strategic choices made by individuals facing uncertain risks. During the last two decades, vaccination games, which combine epidemic dynamics with game theory, behavioural economics, and network science, have become a very important tool for analysing this problem. Here, we synthesise more than 80 theoretical, computational, and empirical studies to clarify how population structure, psychological perception, pathogen complexity, and policy incentives interact to determine vaccination equilibria and epidemic outcomes. Papers are organised along five methodological axes: (i) population topology (well-mixed, static and evolving networks, multilayer systems); (ii) decision heuristics (risk assessment, imitation, prospect theory, memory); (iii) additional processes (information diffusion, non-pharmacological interventions, treatment, quarantine); (iv) policy levers (subsidies, penalties, mandates, communication); and (v) pathogen complexity (multi-strain, zoonotic reservoirs). Common findings across these studies are that voluntary vaccination is almost always sub-optimal; feedback between incidence and behaviour can generate oscillatory outbreaks; local network correlations amplify free-riding but enable cost-effective targeted mandates; psychological distortions such as probability weighting and omission bias materially shift equilibria; and mixed interventions (e.g., quarantine + vaccination) create dual dilemmas that may offset one another. Moreover, empirical work surveys, laboratory games, and field data confirm peer influence and prosocial motives, yet comprehensive model validation remains rare. Bridging the gap between stylised theory and operational policy will require data-driven calibration, scalable multilayer solvers, and explicit modelling of economic and psychological heterogeneity. This review offers a structured roadmap for future research on adaptive vaccination strategies in an increasingly connected and information-rich world. Full article
(This article belongs to the Special Issue Mathematical Epidemiology and Evolutionary Games)
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