Mathematical analysis and computation of a spatiotemporal SIQR model

This article proposes a reaction-diffusion SIQR epidemiological model with the inclusion of the Laplacian operator and by considering two diffusion coefficients. Our primary focus is to investigate the influence of quarantine measures on disease transmission dynamics within a specific spatiotemporal context. We prove the existence, uniqueness, positivity, and boundedness of the solution to the proposed model by using $C_0$ semigroup theory. Furthermore, an investigation of the stability properties, both locally and globally, 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 develop a discrete iterative scheme based on the finite difference method. Through extensive numerical simulations, the effectiveness of the proposed control strategy is thoroughly demonstrated. The obtained results underscore the remarkable significance of the suggested quarantine control approach, emphasizing its pivotal role in attaining highly meaningful outcomes. Those outcomes also show that the evolution of the epidemics depend heavily on the place where the disease originates.