Epidemic waves of a spatial SIR model in combination with random dispersal and non-local dispersal

Chufen Wu, Yong Yang, Qianyi Zhao, Yanling Tian and Zhiting Xu

Applied Mathematics and Computation, 2017, vol. 313, issue C, 122-143

Abstract: In this paper, a spatial SIR model in combination with random dispersal and non-local dispersal is proposed. We establish the existence and non-existence of the traveling wave solutions connecting the disease-free equilibrium and the endemic equilibrium for the model. The main difficulties lie in the fact that the semiflow generated here does not admit the order-preserving property and the solutions lack of regularity. We use a proper iteration scheme to construct a pair of upper and lower solutions and then apply the Schauder’s fixed-point theorem, polar coordinates transform to study the threshold dynamics of the model. That is, we show that if the basic reproduction number of the model R0>1, there is a positive constant critical number c* such that for each c ≥ c*, the model admits a non-trivial and positive traveling wave with wave speed c; and if R0>1 and 0 < c < c*, the model admits no non-trivial and non-negative traveling waves. In view of the numerical simulations, we see that the epidemic waves are not monotone and the non-local dispersal may cause them to oscillate more frequently.

Keywords: SIR model; Nonlocal dispersal; Traveling wave solutions; Minimal wave speed (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:313:y:2017:i:c:p:122-143

DOI: 10.1016/j.amc.2017.05.068

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