Modeling Presymptomatic Spread in Epidemics via Mean-Field Games

TL;DR

This paper develops mean-field game models to analyze how individuals decide to be socially active during an epidemic, considering both fully and partially observed information scenarios, and provides analytical insights into these models.

Contribution

It derives and analyzes mean-field game equations for epidemic spread under different information conditions, offering new theoretical frameworks for understanding presymptomatic transmission.

Findings

Derived equations for fully and partially observed mean-field games.

Provided a complete analysis of the fully observed case.

Presented analytical results for the partially observed case.

Abstract

This paper is concerned with developing mean-field game models for the evolution of epidemics. Specifically, an agent's decision -- to be socially active in the midst of an epidemic -- is modeled as a mean-field game with health-related costs and activity-related rewards. By considering the fully and partially observed versions of this problem, the role of information in guiding an agent's rational decision is highlighted. The main contributions of the paper are to derive the equations for the mean-field game in both fully and partially observed settings of the problem, to present a complete analysis of the fully observed case, and to present some analytical results for the partially observed case.