Stability Analysis and Turing Instability of A SIR Model with Reaction - Diffusion

The spatio-temporal dynamic of diffusion-driven epidemic model is an original, cutting-edge and practical research. In order to improve the accuracy of epidemic modelling, a new SIR epidemic model with diffusion is developed in this paper. We determine the position of all equilibria and discuss the existence of the positive equilibrium in the reaction-diffusion epidemic model. The theory of partial differential equations is adopted to establish the occurrence conditions of Turing instability. Numerical simulation examples show the accuracy of theoretical derivation.