Article ID Journal Published Year Pages File Type
4614575 Journal of Mathematical Analysis and Applications 2016 18 Pages PDF
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⁎>0c⁎>0 such that this system admits a traveling wave solution with speed c   iff c≥c⁎c≥c⁎.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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