Spreading speeds and traveling waves for a time periodic DS-I-A epidemic model. (August 2022)

• Record Type: Journal Article
• Authors: Yang, Xiying; Lin, Guo
• Is Part Of: Nonlinear analysis. Volume 66(2022)
• Publication Date: 2022-08
• Subjects: Nonmonotone system -- Generalized upper and lower solutions -- Asymptotic spreading -- Minimal wave speed; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103515
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper is devoted to studying the speed of asymptotic spreading and minimal wave speed of traveling wave solutions for a time periodic and diffusive DS-I-A epidemic model, which describes the propagation threshold of disease spreading. The main feature of this model is the possible deficiency of the classical comparison principle such that many known results do not directly work. The speed of asymptotic spreading is estimated by constructing auxiliary equations and applying the classical theory of asymptotic spreading for Fisher type equation. The minimal wave speed is established by proving the existence and nonexistence of the nonconstant traveling wave solutions. Moreover, some numerical examples are presented to model the propagation dynamics of this system.