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Title: Traveling waves for a diffusive SIR model with delay
Authors: Fu, Sheng-Chen
Contributors: 應數系
Keywords: SIR model;Traveling wave;Time delay;Upper/lower solution;Schauder fixed point theorem
Date: 2016-03
Issue Date: 2016-01-15 14:22:07 (UTC+8)
Abstract: In this paper, we study traveling waves connecting the infection-free equilibrium state and the endemic equilibrium state for a diffusive SIR model with delay and saturated incidence rate. Since this system does not enjoy the comparison principle, we will use an iteration process to construct a pair of upper and lower solutions. With the aid of the pair of upper and lower solutions, we can apply the Schauder fixed point theorem to construct a family of solutions of the truncated problems, which, via the limiting argument, can generate the traveling wave. Indeed, we show that there exists c ⁎ > 0 such that this system admits a traveling wave solution with speed c iff c ≥ c ⁎ .
Relation: Journal of Mathematical Analysis & Applications, 435(1), 20-37
Data Type: article
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