Behavioral patterns and mean-field games in epidemiological models

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.