Learning Contact Policies for SEIR Epidemics on Networks: A Mean-Field Game Approach

TL;DR

This paper models how individuals in a network choose contact efforts during SEIR epidemics using a mean-field game approach, revealing how incubation periods and incentives influence epidemic dynamics.

Contribution

It introduces a mean-field game framework for SEIR epidemics on networks, incorporating the exposed compartment and analyzing equilibrium contact policies.

Findings

Longer incubation delays weaken behavioral responses.

Network degree and cost influence equilibrium contact efforts.

Explicit characterization of equilibrium contact strategies.

Abstract

In this paper, we develop a mean-field game model for SEIR epidemics on heterogeneous contact networks, where individuals choose state-dependent contact effort to balance infection losses against the social and economic costs of isolation. The Nash equilibrium is characterized by a coupled Hamilton--Jacobi--Bellman/Kolmogorov system across degree classes. An important feature of the SEIR setting is the exposed compartment: the incubation period separates infection from infectiousness and changes incentives after infection occurs. In the baseline formulation, exposed agents optimally maintain full contact, while susceptible agents reduce contact according to an explicit best-response rule driven by infection pressure and the value gap. We also discuss extensions that yield nontrivial exposed precaution by introducing responsibility or compliance incentives. We establish existence of equilibrium via a fixed-point argument and prove the uniqueness under a suitable monotonicity condition. The analysis identifies a delay in the onset of precaution under longer incubation, which can lead to weaker behavioral responses and larger outbreaks. Numerical experiments illustrate how network degree and the cost exponent shape equilibrium policies and epidemic outcomes.