Global and local asymptotic stability of an epidemic reaction‐diffusion model with a nonlinear incidence

The aim of this paper is to study the dynamics a reaction-diffusion SI (susceptible-infectious) epidemic model with nonlinear incidence rate describing transmission communicable disease between individuals. We prove that proposed has two steady states under one condition. By analyzing eigenvalues and using linearization method an appropriately constructed Lyapunov functional, we establish local global asymptotic stability non-negative constant subject basic reproduction number being greater than unity disease-free equilibrium smaller or equal in ODE case. applying identify condition PDE Finally, present some numerical examples illustrating confirming analytical results obtained throughout paper.