| Volume 15, Number 1, 2025, Pages - DOI：10.11948/JAAC-2024-0115 |
| Unidirectional Wave Propagation in a Nonlocal Dispersal Endemic Model with Nonlinear Incidence |
| Jingdong Wei,Jiahe Li,Zaili Zhen,Jiangbo Zhou,Minjie Dong |
| Keywords:Traveling Waves Nonlocal Dispersal Endemic Model Nonlinear Incidence. |
| Abstract: |
| This paper is concerned with existence and non-existence of traveling wave solutions in a nonlocal dispersal endemic model with nonlinear incidence. With the aid of upper-lower solutions method and Schauder"s fixed point theorem together with Lyapunov functional technique, we derive the existence of super-critical and critical traveling wave solutions connecting disease-free equilibrium to endemic equilibrium. In a combination with the theory of two-sided Laplace transform and local skilled analysis, we obtain the non-existence of sub-critical traveling wave solutions. Our results illustrate that: (i) the existence and non-existence of traveling waves are determined by the basic reproduction number and the wave speed; (ii) the critical wave speed is equal to the minimal wave speed; (iii) the traveling waves only propagate along one direction. |
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