Existence and non-existence of traveling wave solutions for a nonlocal dispersal SIR epidemic model with nonlinear incidence rate. (June 2018)

• Record Type: Journal Article
• Authors: Zhou, Jiangbo; Xu, Jing; Wei, Jingdong; Xu, Haimei
• Is Part Of: Nonlinear analysis. Volume 41(2018)
• Page Start: 204
• Page End: 231
• Publication Date: 2018-06
• Subjects: 35Q92 -- 35R09 -- 35C07 -- 92D30; SIR epidemic model -- Nonlocal dispersal -- Traveling wave solution -- Schauder's fixed point theorem; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.10.016
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: A nonlocal dispersal SIR epidemic model with nonlinear incidence rate is introduced. It is shown that the existence and non-existence of nontrivial and nonnegative traveling wave solutions of this model are fully determined by the threshold values, that is, the basic reproduction number R 0 and the minimal wave speed c ∗ . For R 0 > 1 and c ≥ c ∗, the existence theorem is obtained by the method of auxiliary system, Schauder's fixed point theorem and three limiting arguments. For R 0 > 1 and 0 < c < c ∗, the non-existence theorem is derived by applying the two-sided Laplace transform and making full use of the structure of the model. For R 0 = 1 with c > 0 and R 0 < 1 with c > 0, the non-existence theorems are also established.