Analysis of a Spatial SIRS Epidemic Model with General Incidence
Abstract
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.
Key Points
Objective
The aim is to explore the dynamics of a spatial SIRS epidemic model and determine conditions for epidemic behavior.
Methods
- Examined the well-posedness and existence of classical solutions in the SIRS model
- Characterized threshold dynamics using the basic reproduction number R0
- Investigated endemic equilibria under the condition R0 > 1
- Analyzed local and global stability with Lyapunov functionals
- Complemented theoretical findings with numerical simulations
Results
- Demonstrated the existence of endemic equilibria when R0 is greater than 1
- Established conditions for stability in both local and global dimensions
- Numerical simulations showed convergence to equilibria in spatially structured environments
- Highlighted the influence of spatial heterogeneity on epidemic dynamics