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


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


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


(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


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

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