Global solution and optimal control of an epidemic propagation with a heterogeneous diffusion

TL;DR

This paper investigates a reaction-diffusion epidemic model with heterogeneous infection risk, establishing global solvability and optimal control strategies to minimize infection spread in specific regions.

Contribution

It introduces a nonlinear reaction-diffusion model with dynamic heterogeneity and proves global existence and optimal control conditions for the epidemic.

Findings

Proves existence of a global solution for the model.

Derives conditions for optimal control to reduce infection.

Provides a framework for spatially targeted epidemic management.

Abstract

In this paper, we explore the solvability and the optimal control problem for a compartmental model based on reaction-diffusion partial differential equations describing a transmissible disease. The nonlinear model takes into account the disease spreading due to the human social diffusion, under a dynamic heterogeneity in infection risk. The analysis of the resulting system provides the existence proof for a global solution and determines the conditions of optimality to reduce the concentration of the infected population in certain spatial areas.