Partial health status observability and time horizon uncertainty in mean-field game epidemiological models

TL;DR

This paper develops computational methods for mean-field game epidemiological models with partial immunity observability and uncertain time horizons, enabling more realistic disease spread analysis.

Contribution

It introduces an efficient approach to solve MFG systems with immunity uncertainty and partial observability, extending existing epidemiological modeling techniques.

Findings

Efficient solution method via two-point boundary value problem for ODEs.

Model accommodates immunity waning and instant loss with partial observability.

Extension to handle initial uncertainty in planning horizon.

Abstract

We introduce Mean-Field Game (MFG) epidemiological models, in which immunity either wanes with time in a fully observable way or disappears instantaneously with no direct observation (making a previously recovered individual fully susceptible again without realizing it). Both interpretations create computational challenges for rational noninfected individuals deciding on their contact rates based on their personal current immunity state and the changing epidemiological situation. Both require solving a forward-backward MFG system that includes PDEs (an advection-reaction equation for the immunity-structured population and a Hamilton-Jacobi-Bellman equation for the corresponding value function). We show how this can be done efficiently by solving a two-point boundary value problem for a system of approximating ODEs. We also show how the same approach can be extended to handle an initial uncertainty in the planning horizon.