UNIDIRECTIONAL WAVE PROPAGATION IN A NONLOCAL DISPERSAL ENDEMIC MODEL WITH NONLINEAR INCIDENCE

Jingdong Wei; Jiahe Li; Zaili Zhen; Jiangbo Zhou; Minjie Dong

doi:10.11948/20240115

2025 Volume 15 Issue 1

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Jingdong Wei, Jiahe Li, Zaili Zhen, Jiangbo Zhou, Minjie Dong. UNIDIRECTIONAL WAVE PROPAGATION IN A NONLOCAL DISPERSAL ENDEMIC MODEL WITH NONLINEAR INCIDENCE[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 391-421. doi: 10.11948/20240115

Citation:

Jingdong Wei, Jiahe Li, Zaili Zhen, Jiangbo Zhou, Minjie Dong. UNIDIRECTIONAL WAVE PROPAGATION IN A NONLOCAL DISPERSAL ENDEMIC MODEL WITH NONLINEAR INCIDENCE[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 391-421. doi: 10.11948/20240115

UNIDIRECTIONAL WAVE PROPAGATION IN A NONLOCAL DISPERSAL ENDEMIC MODEL WITH NONLINEAR INCIDENCE

1.
School of Mathematical Sciences, Jiangsu University, Zhenjiang, Jiangsu 212013, China
2.
School of Physical and Mathematical Sciences, Nanjing Tech University, Nanjing, Jiangsu 211816, China

Author Bio: Email: weijingdong@ujs.edu.cn(J. Wei); Email: ljh10000@126.com(J. Li); Email: ujszjb@126.com(J. Zhou); Email: dongminjiepoppy@126.com(M. Dong)
Corresponding author: Email: zhenzaili@ujs.edu.cn(Z. Zhen)

Abstract

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.
- Traveling waves /
- nonlocal dispersal /
- endemic model /
- nonlinear incidence
MSC: 35K57, 37C65, 92D30

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References

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