Traveling wave solutions of the Kermack-McKendrick epidemic model with spatio-temporal delays and nonlinear saturated incidence
Abstract
This study explores the existence of traveling wave solutions connecting the disease-free equilibrium and the endemic equilibrium in the Kermack-McKendrick epidemic model. By constructing a pair of upper and lower solutions and applying Schauder's fixed point theorem, we establish the existence of non-negative traveling wave solutions. It is demonstrated that such traveling wave solutions persist even when considering nonlocal spatio-temporal delays and nonlinear saturated incidence. The approach primarily utilizes dynamical systems theory, including geometric singular perturbation theory, the center manifold theorem, and Fredholm theory.
Fields of Study & Subjects
Mathematical and Theoretical Epidemiology and Ecology Models
Nonlinear Differential Equations Analysis
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Communications on Pure & Applied Analysis
- Volume
- 30
- Issue
- 0
- Pages
- 1–20
- Publication date
- 1 January 2026
- Language
- EN