Partial health status observability and time horizon uncertainty in mean-field game epidemiological models
Carlos Doebeli, Alexander Vladimirsky
TLDR
MFG epidemiological models are introduced to handle partial immunity observability and time horizon uncertainty using efficient ODE approximations.
Key contributions
- Introduces Mean-Field Game (MFG) models for epidemiology with partial immunity observability.
- Addresses challenges of immunity waning or instantaneous disappearance without direct observation.
- Proposes an efficient solution using approximating ODEs for complex MFG systems with PDEs.
- Extends the approach to incorporate initial uncertainty in the planning horizon.
Why it matters
This paper offers a novel framework for modeling complex epidemiological dynamics, accounting for realistic uncertainties in immunity and planning. By providing an efficient computational method, it enables better decision-making for public health interventions. This advances the practical application of MFG theory in epidemiology.
Original 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.
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