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Wave propagation in a diffusive SAIV epidemic model with time delays

Part of: Parabolic equations and systems Representations of solutions

Published online by Cambridge University Press:  16 June 2021

JIANGBO ZHOU Open the ORCID record for JIANGBO ZHOU [Opens in a new window] ,
JINGHUAN LI ,
JINGDONG WEI  and
LIXIN TIAN
JIANGBO ZHOU*
Affiliation:
School of Mathematical Sciences, Jiangsu University, Zhenjiang, Jiangsu212013, P. R. China emails: ujszjb@126.com; l511309259@126.com; wjd19871022@126.com; tianlx@ujs.edu.cn
JINGHUAN LI
Affiliation:
School of Mathematical Sciences, Jiangsu University, Zhenjiang, Jiangsu212013, P. R. China emails: ujszjb@126.com; l511309259@126.com; wjd19871022@126.com; tianlx@ujs.edu.cn
JINGDONG WEI*
Affiliation:
School of Mathematical Sciences, Jiangsu University, Zhenjiang, Jiangsu212013, P. R. China emails: ujszjb@126.com; l511309259@126.com; wjd19871022@126.com; tianlx@ujs.edu.cn
LIXIN TIAN
Affiliation:
School of Mathematical Sciences, Jiangsu University, Zhenjiang, Jiangsu212013, P. R. China emails: ujszjb@126.com; l511309259@126.com; wjd19871022@126.com; tianlx@ujs.edu.cn School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu210046, P. R. China email: tianlixin@njnu.edu.cn
*
*Joint corresponding authors
*Joint corresponding authors
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Abstract

Based on the fact that the incubation periods of epidemic disease in asymptomatically infected and infected individuals are inevitable and different, we propose a diffusive susceptible, asymptomatically infected, symptomatically infected and vaccinated (SAIV) epidemic model with delays in this paper. To see whether epidemic disease can propagate spatially with a constant speed, we focus on the travelling wave solution for this model. When the basic reproduction number of the corresponding spatial-homogenous delayed differential system is greater than one and the wave speed is greater than or equal to the critical speed, we prove that this model admits nontrivial positive travelling wave solutions. Our theoretical results are of benefit to the prevention and control of epidemic.

Keywords

Reaction–diffusion equationepidemictravelling wavetime delay

MSC classification

Primary: 35K57: Reaction-diffusion equations
Secondary: 35C07: Traveling wave solutions
Type
Papers
Information
European Journal of Applied Mathematics , Volume 33 , Issue 4 , August 2022 , pp. 674 - 700
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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