Traveling Waves for an Epidemic Model with Vaccination and Nonlocal Diffusion

doi:10.13371/j.cnki.chin.q.j.m.2015.02.017

Chinese Quarterly Journal of Mathematics ›› 2015, Vol. 30 ›› Issue (2): 287-299.doi: 10.13371/j.cnki.chin.q.j.m.2015.02.017

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Traveling Waves for an Epidemic Model with Vaccination and Nonlocal Diffusion

Department of Basic Courses, Shijiazhuang Mechanical Engineering College

Received:2013-12-10 Online:2015-06-30 Published:2020-11-23
About author:WANG Zhi-ping(1981-), female, native of Hengshui, Hebei, a lecturer of Shijiazhuang Mechanical Engineering College, M.S.D., engages in dynamical system; XU Rui(1962-), male, native of Zhangjiakou, Hebei, a professor of Shijiazhuang Mechanical Engineering College, Ph.D., engages in dynamical system.
Supported by:
Supported by the National Natural Science Foundation of China(11371368)； Supported by the Natural Science Foundation of Hebei Province(A2013506012)； Supported by the Foundation of Shijiazhuang Mechanical Engineering College(JCB1201,YJJXM13008)；

Abstract

Abstract: An epidemic model with vaccination and nonlocal diffusion is proposed, and the existence of traveling wave solutions of this model is studied. By the cross-iteration scheme companied with a pair of upper and lower solutions and Schauder’s fixed point theorem,sufficient conditions are obtained for the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state.

Key words: vaccination, traveling wave solution, nonlocal diffusion, upper-lower solutions

CLC Number:

O175

WANG Zhi-ping, XU Rui, ZHANG Shi-hua. Traveling Waves for an Epidemic Model with Vaccination and Nonlocal Diffusion[J]. Chinese Quarterly Journal of Mathematics, 2015, 30(2): 287-299.

Traveling Waves for an Epidemic Model with Vaccination and Nonlocal Diffusion

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