Wave propagation in an infectious disease model

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:449

Article

Xu, Zhiting¹ 

[1] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

关键词: Infectious disease model;    Lyapunov functional;    Schauder fixed point theorem;    Traveling wave;    Upper and lower solutions;   

DOI  :  10.1016/j.jmaa.2016.11.051

来源: Elsevier

【 摘 要 】

This paper is devoted to the study of the wave propagation in a reaction-convection infectious disease model with a spatio-temporal delay. Previous numerical studies have demonstrated the existence of traveling wave fronts for the system and obtained a critical value c*, which is the minimal wave speed of the traveling waves. In the present paper, we provide a complete and rigorous proof. To overcome the difficulty due to the lack of monotonicity for the system, we construct a pair of upper and lower solutions, and then apply the Schauder fixed point theorem to establish the existence of a nonnegative solution for the wave equation on a bounded interval. Moreover, we use a limiting argument and in turn generate the solution on the unbounded interval R. In particular, by constructing a suitable Lyapunov functional, we further show that the traveling wave solution converges to the epidemic equilibrium point as t = +infinity. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free