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Archives of Current Research International, ISSN: 2454-7077,Vol.: 15, Issue.: 2

Original-research-article

Traveling Waves with Critical Speed in a Delayed Diffusive Epidemic Model

 

Haimei Xu1, Jiangbo Zhou1* and Liyuan Song1

1Faculty of Science, Jiangsu University, Zhenjiang 212013, Jiangsu, P.R. China.

Article Information

Editor(s):

(1) Dr. Basak Taseli, Professor, Department of Environmental Engineering, Faculty of Engineering, Giresun University, Turkey.

Reviewers:

(1) Kejun Zhuang, Anhui University of Finance and Economics, P.R. China.

(2) S. K. Asha, Gulbarga University, India.

Complete Peer review History: http://www.sciencedomain.org/review-history/27304

Abstracts

In a recent paper [K. Zhou, M. Han, Q. Wang, Math. Method. Appl. Sci. 40 (2016) 2772-2783], the authors investigated the traveling wave solutions of a delayed diffusive SIR epidemic model.  When the basic reproduction number R0 > 1 and the wave speed C = C* ( C* is the critical speed), they obtained the existence of a non-trivial and non-negative traveling wave solution. When R0 > 1 and 0 < C < C*, they established non-existence of the non-trivial and non-negative traveling wave solutions. When R0 > 1 and C = C*, the existence of traveling waves was left as an open problem. The aim of this paper is to solve this problem by applying upper-lower solution method and Schauder's fixed point theorem.

Keywords :

Diffusive epidemic model; traveling wave; reaction-diffusion equation; critical speed.

Full Article - PDF    Page 1-14

DOI : 10.9734/ACRI/2018/44885

Review History    Comments

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