Traveling waves for a discrete diffusive SIR epidemic model with treatment. (October 2021)

• Record Type: Journal Article
• Authors: Deng, Dong; Zhang, Dongpei
• Is Part Of: Nonlinear analysis. Volume 61(2021)
• Publication Date: 2021-10
• Subjects: Traveling waves -- Discrete diffusive -- SIR epidemic model with treatment -- Critical wave speed; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103325
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: The main purpose of this paper is to study the existence of traveling waves for a discrete diffusive SIR epidemic model with treatment. Compared to the work in Zhang and Wang (2014), more accurate results about the existence and nonexistence of nontrivial traveling wave solutions are obtained. We prove that when the basic reproduction number R 0 > 1, there exists a critical number c ∗ > 0 such that for each c > c ∗, the system admits a nontrivial traveling wave solution with speed c, and for 0 < c < c ∗, the system has no nontrivial traveling wave solution. When R 0 < 1, we show that there exists no nontrivial traveling wave solution by an integration argument. In addition, based on Deng and Zhang (2020), we obtain the existence of traveling waves with the critical speed c = c ∗ under some assumptions.