Traveling Waves for an Epidemic Model with Vaccination and Nonlocal Diffusion

WANG Zhi-ping, XU Rui, ZHANG Shi-hua

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

Traveling Waves for an Epidemic Model with Vaccination and Nonlocal Diffusion

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Department of Basic Courses, Shijiazhuang Mechanical Engineering College

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.

Received date: 2013-12-10

Online published: 2020-11-23

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)；

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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

Cite this article

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

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