Analysis of a Spatial SIRS Epidemic Model with General Incidence

This article presents a comprehensive study of a reaction–diffusion SIRS epidemic model with general incidence. We provide a detailed treatment that includes: (i) the well-posedness of the system and the existence of classical solutions, (ii) the threshold dynamics characterized by the basic reproduction number R0, (iii) the existence of endemic equilibria when R0 > 1, and (iv) the analysis of both local and global stability using Lyapunov functionals. The theoretical findings are complemented by numerical simulations illustrating convergence to equilibria and the influence of spatial heterogeneity. This work offers a coherent picture of the epidemic dynamics in spatially structured populations.