In this paper, we study a diffusive SIRS-type epidemic model with transfer from the infectious to the susceptible class. Our model includes a general nonlinear incidence rate and spatially heterogeneous diffusion coefficients. We compute the basic reproduction number R of our model and establish the global stability of the disease-free steady state when R< 1. Furthermore, we study the uniform persistence when R> 1 and perform a bifurcation analysis for a special case of our model. Some numerical simulations are presented to illustrate the dynamics of the solutions as the model parameters are varied.
Mendeley helps you to discover research relevant for your work.
CITATION STYLE
Avila-Vales, E., & Pérez, Á. G. C. (2022). Dynamics of a reaction–diffusion SIRS model with general incidence rate in a heterogeneous environment. Zeitschrift Fur Angewandte Mathematik Und Physik, 73(1). https://doi.org/10.1007/s00033-021-01645-0