Behavioral patterns and mean-field games in epidemiological models

TL;DR

This paper develops a novel mean-field game model for epidemiology that incorporates diverse behavioral patterns and switching behaviors, providing insights into how these factors influence disease spread and resource strain.

Contribution

It introduces a new mean-field game framework for epidemiological modeling that accounts for rational and non-rational behaviors and their switches, bridging epidemiology and game theory.

Findings

Behavioral diversity affects disease dynamics significantly.

Switching behaviors increase the impact of infectious diseases.

Model simulations highlight the importance of behavioral patterns in epidemic outcomes.

Abstract

We introduce a new type of Mean Field Game epidemiological models, in which subpopulations have different behavioral patterns: some are viewed as "highly rational" (choosing Nash-equilibrium long-term strategies) while others follow pre-specified "non-rational" patterns (e.g., either sticking to their usual habits or trying to mimic those around them). Our model also allows for occasional behavioral switches, which rational individuals also take into account when formulating their Nash-equilibrium strategies. While this modeling approach is general, here we develop it for individuals choosing their "contact rates" within a particular Susceptible-Infected-Recovered-Susceptible-Dead (SIRSD) epidemics model. The latter is based on a frequency-based force of infection and the mortality rate that rapidly increases once the proportion of infected individuals exceeds some prescribed threshold, resulting in a strain on medical resources. Numerical tests illustrate the properties of our model and highlight the ways in which additional/non-rational behavioral patterns and behavioral switching increase the impact of infectious diseases. The paper aims to build a bridge between two distinct communities of epidemiological modelers and to promote the consideration of behavioral patterns in broader Mean Field Games literature.