Dynamical analysis of a multi-group SIR epidemic model with nonlocal diffusion and nonlinear incidence rate. (December 2022) - Wang, Jianpeng; Dai, Binxiang
Abstract: In this paper, a multi-group SIR epidemic model with nonlocal diffusion and nonlinear incidence rate in spatially heterogeneous environment is proposed. The well-posedness, including the existence, positivity and boundedness of solutions, is achieved. The basic reproduction number R 0 is defined, and the existence of principal eigenvalue is studied. Further, the threshold criteria on the global dynamics of the model are established in terms of R 0 . That is, when R 0 < 1, the disease-free steady state is globally asymptotically stable, when R 0 > 1, the disease is uniformly persistent. Particularly, a single-group degenerated SIR epidemic model is also studied. We give some properties on the principle eigenvalue and prove that there exists a compact global attractor for the solution semiflow. Furthermore, when the basic reproduction number R ̄ 0 > 1, we obtain that the endemic steady state is unique to exist and globally asymptotically stable.