Wave propagation in an infectious disease model

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• 作者：Zhiting Xu ^{xuzhit@126.com}
• 关键词：Infectious disease model ; Lyapunov functional ; Schauder fixed point theorem ; Traveling wave ; Upper and lower solutions
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 May 2017
• 年：2017
• 卷：449
• 期：1
• 页码：853-871
• 全文大小：398 K
• 卷排序：449

文摘

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⁎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 RR. In particular, by constructing a suitable Lyapunov functional, we further show that the traveling wave solution converges to the epidemic equilibrium point as t=+∞t=+∞.