Impact of quarantine measures on the global stability of an epidemiological model

Abstract

This article presents an investigation of the SIQR epidemic model of a reaction-diffusion system involving the $ p $-Laplacian operator and by considering different diffusion coefficients. The main objective is to assess the impact of quarantine measures on the spread of the disease within a defined time and space, as well as to study the stability analysis of equilibria. The study established the existence and uniqueness of a positive solution to the proposed model. Furthermore, an investigation into the global stability properties of the disease-free equilibrium and the endemic equilibrium is conducted through an examination of their respective characteristic equations. To obtain numerical solutions for the state system, we developed a discrete iterative scheme based on the finite difference method. Extensive numerical simulations thoroughly demonstrate the effectiveness of the proposed control strategy (quarantine) and illustrate the obtained theoretical stability results.