Optimal Bayesian Persuasion for Containing SIS Epidemics

TL;DR

This paper develops an optimal Bayesian signaling framework to influence individual decisions in SIS epidemic models, aiming to minimize overall infection levels through static and dynamic information strategies.

Contribution

It introduces a novel approach to designing optimal static and dynamic signals for epidemic containment in a Bayesian persuasion setting.

Findings

Static signals can reduce infection at equilibrium.

Dynamic signals outperform static ones in controlling epidemic spread.

Numerical simulations demonstrate the effectiveness of the dynamic signaling scheme.

Abstract

We consider a susceptible-infected-susceptible (SIS) epidemic model in which a large group of individuals decide whether to adopt partially effective protection without being aware of their individual infection status. Each individual receives a signal which conveys noisy information about its infection state, and then decides its action to maximize its expected utility computed using its posterior probability of being infected conditioned on the received signal. We first derive the static signal which minimizes the infection level at the stationary Nash equilibrium under suitable assumptions. We then formulate an optimal control problem to determine the optimal dynamic signal that minimizes the aggregate infection level along the solution trajectory. We compare the performance of the dynamic signaling scheme with the optimal static signaling scheme, and illustrate the advantage of the former through numerical simulations.