Analyzing Mask-Wearing Decisions Using Game Theory and the SIR Model with a Replicator Equation in Post-Pandemic Situations

Yuki Novia Nasution; Muhammad Abyan Rizqo; Nuning Nuraini; Mochamad Apri; Hadi Susanto

doi:10.5614/cbms.2026.9.1.1

Authors

Yuki Novia Nasution Department of Mathematics, Institut Teknologi Bandung, Bandung 40132, Indonesia & Department of Mathematics, Universitas Mulawarman, Samarinda 75119, Indonesia
Muhammad Abyan Rizqo Department of Mathematics, Institut Teknologi Bandung, Bandung 40132, Indonesia
Nuning Nuraini Department of Mathematics, Institut Teknologi Bandung, Bandung 40132, Indonesia & Center for Mathematical Modeling and Simulation, Institut Teknologi Bandung, Bandung, 40132, Indonesia & Predictive Risk Simulation and Modelling, Institut Teknologi Bandung, Bandung 40132, Indonesia
Mochamad Apri Department of Mathematics, Institut Teknologi Bandung, Bandung 40132, Indonesia
Hadi Susanto Department of Mathematics, Khalifa University, Abu Dhabi 127788, United Arab Emirates

DOI:

https://doi.org/10.5614/cbms.2026.9.1.1

Keywords:

mask, ARI, replicator equation, game theory, SIR, Nash equilibrium

Abstract

During the COVID-19 pandemic, many countries implemented policies on using masks to control the outbreak. This policy has been relaxed in almost all countries, after which. Respiratory disease outbreaks re-emerged in several countries, including Indonesia. This article presents a game-theoretic model of mask use by the community during the spread of the disease. Both the effectiveness of masks in preventing the spread of the disease and the proportion of the infected population are included in the payoff calculation. The model is combined a with the Susceptible-Infectious-Recovered (SIR) epidemic model with the replicator equation. The model is also evaluated under Nash equilibrium conditions. Simulations are carried out to effect of mask-wearing behavior on the incidence of acute respiratory infection in Jakarta. The results show that an individual's decision to use a mask is directly proportional to mask users. To reduce the number of infections, more than 10% of the population need to wear masks when the disease first appears. In the Nash equilibrium, we obtain a threshold value of the infected population at which the players decide not to use the mask. The results suggest that when respiratory infectious diseases emerge, governments must implement a stringent mask policy to control their spread and reduce infections.

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