Physics-Informed Neural Networks for Optimal Vaccination Plan in SIR Epidemic Models

TL;DR

This paper employs Physics-Informed Neural Networks to efficiently compute the minimum eradication time and optimal vaccination strategies in time-homogeneous SIR epidemic models, offering a novel computational approach.

Contribution

It introduces a PINN-based method for solving PDEs related to eradication time and optimal control in epidemic models, with a focus on stable training and practical validation.

Findings

PINNs effectively approximate eradication time in SIR models

The variable scaling method improves PINN training stability

Numerical experiments validate the approach's accuracy and efficiency

Abstract

This work focuses on understanding the minimum eradication time for the controlled Susceptible-Infectious-Recovered (SIR) model in the time-homogeneous setting, where the infection and recovery rates are constant. The eradication time is defined as the earliest time the infectious population drops below a given threshold and remains below it. For time-homogeneous models, the eradication time is well-defined due to the predictable dynamics of the infectious population, and optimal control strategies can be systematically studied. We utilize Physics-Informed Neural Networks (PINNs) to solve the partial differential equation (PDE) governing the eradication time and derive the corresponding optimal vaccination control. The PINN framework enables a mesh-free solution to the PDE by embedding the dynamics directly into the loss function of a deep neural network. We use a variable scaling method to ensure stable training of PINN and mathematically analyze that this method is effective in our setting. This approach provides an efficient computational alternative to traditional numerical methods, allowing for an approximation of the eradication time and the optimal control strategy. Through numerical experiments, we validate the effectiveness of the proposed method in computing the minimum eradication time and achieving optimal control. This work offers a novel application of PINNs to epidemic modeling, bridging mathematical theory and computational practice for time-homogeneous SIR models.