Dynamics in a reaction-diffusion epidemic model via environmental driven infection in heterogenous space

Abstract

In this paper, a reaction-diffusion SIR epidemic model via environmental driven infection in heterogeneous space is proposed. To reflect the prevention and control measures of disease in allusion to the susceptible in the model, the nonlinear incidence function Ef (S) is applied to describe the protective measures of susceptible. In the general spatially heterogeneous case of the model, the wellposedness of solutions is obtained. The basic reproduction number R 0 is calculated. When R 0 ≤ 1 the global asymptotical stability of the disease-free equilibrium is obtained, while when R 0 > 1 the model is uniformly persistent. Furthermore, in the spatially homogeneous case of the model, when R 0 > 1 the global asymptotic stability of the endemic equilibrium is obtained. Lastly, the numerical examples are enrolled to verify the open problems.

A rigorous theoretical and numerical analysis of a nonlinear reaction-diffusion epidemic model pertaining dynamics of COVID-19

“…Majid et al 10 presented a compartmental PDE model to investigate the spatial dynamics of the COVID-19 epidemic, whereas Zafar et al 11 present nonlinear fractional mathematical model to analyze tuberculosis using different fractional operators. A new reaction-diffusion problem is developed in 12 to study the impact of infection transmission due to environmental load in a heterogeneous space. Fitzgibbon et al 13 presented a system of partial differential equations to investigate the dynamical study of the pandemic in a spatial inhomogeneous environment.…”