Modeling Epidemic Spread with Strategic Vaccination and Socialization: a Mean Field Game Analysis
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| Format: | Preprint |
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2026
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| _version_ | 1866915956089946112 |
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| author | Liu, Huaning Dayanikli, Gokce |
| author_facet | Liu, Huaning Dayanikli, Gokce |
| contents | We study a game-theoretic model of epidemic control in a large population with finitely many groups and non-cooperative individuals. In the model, individuals jointly choose their socialization levels and vaccination rates, and vaccination is subject to a linear individual cost structure. We derive a forward-backward ordinary differential equations (FBODE) system that characterizes the mean field Nash equilibrium, show that the equilibrium vaccination rate exhibits an at-most one-jump bang-bang structure, and establish the existence of a Carathéodory solution to the FBODE. This establishes a realistic interpretation of the vaccination decisions, meaning individuals decide to vaccinate until a time point which is determined by model parameters and then stop after. We further consider a population-awareness extension in which individuals incorporate population infection information into their objective functions, and we prove a similar at-most one-jump bang-bang property under suitable conditions. Finally, we propose a numerical algorithm for solving the FBODE and conduct simulations to validate the theoretical findings. The experiments highlight two main insights: the trade-off between socialization and vaccination, and the greater importance of quarantining infected individuals instead of restricting susceptible individuals. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_22946 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Modeling Epidemic Spread with Strategic Vaccination and Socialization: a Mean Field Game Analysis Liu, Huaning Dayanikli, Gokce Optimization and Control We study a game-theoretic model of epidemic control in a large population with finitely many groups and non-cooperative individuals. In the model, individuals jointly choose their socialization levels and vaccination rates, and vaccination is subject to a linear individual cost structure. We derive a forward-backward ordinary differential equations (FBODE) system that characterizes the mean field Nash equilibrium, show that the equilibrium vaccination rate exhibits an at-most one-jump bang-bang structure, and establish the existence of a Carathéodory solution to the FBODE. This establishes a realistic interpretation of the vaccination decisions, meaning individuals decide to vaccinate until a time point which is determined by model parameters and then stop after. We further consider a population-awareness extension in which individuals incorporate population infection information into their objective functions, and we prove a similar at-most one-jump bang-bang property under suitable conditions. Finally, we propose a numerical algorithm for solving the FBODE and conduct simulations to validate the theoretical findings. The experiments highlight two main insights: the trade-off between socialization and vaccination, and the greater importance of quarantining infected individuals instead of restricting susceptible individuals. |
| title | Modeling Epidemic Spread with Strategic Vaccination and Socialization: a Mean Field Game Analysis |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2604.22946 |