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

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.

Keywords: existence and uniqueness of solutions, optimal control in coefficients, partial differential equations, reaction-diffusion system, epidemic models, COVID- 19