Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 73, Issue 8, Pages 1707-1723Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2017.02.014
Keywords
Nonlocal dispersal; Relapse; Traveling wave solutions; Basic reproduction number; Schauder's fixed-point theorem
Categories
Funding
- NSF of China [11671180, 11601205]
- Fundamental Research Funds for the Central Universities [lzujbky-2016-ct12, lzujbky-2016-103]
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This paper is concerned with traveling wave solutions of a nonlocal dispersal Susceptible -Infective-Removal-Healing (for short SIRH) model with relapse. It is found that the existence and nonexistence of traveling waves of the system are not only determined by the critical wave speed c*, but also by the basic reproduction number Ro of the corresponding system of ordinary differential equations. More precisely, we use Schauder's fixed-point theorem to obtain the existence of traveling waves for R-0 > 1 and c > c*, and the nonexistence of traveling waves for R-0 > 1 and 0 < c < c*. Some numerical simulations and discussions are also provided to illustrate our analytical results. (C) 2017 Elsevier Ltd. All rights reserved.
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