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Dynamics of an infection age-space structured cholera model with Neumann boundary condition

Part of: Applications - Dynamical systems and ergodic theory Partial differential equations Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  08 April 2021

WEIWEI LIU ,
JINLIANG WANG Open the ORCID record for JINLIANG WANG [Opens in a new window]  and
RAN ZHANG
WEIWEI LIU
Affiliation:
School of Mathematical Science, Heilongjiang University, Harbin 150080, P. R. China emails: 2180944@s.hlju.edu.cn; jinliangwang@hit.edu.cn
JINLIANG WANG
Affiliation:
School of Mathematical Science, Heilongjiang University, Harbin 150080, P. R. China emails: 2180944@s.hlju.edu.cn; jinliangwang@hit.edu.cn
RAN ZHANG
Affiliation:
Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing210016, P. R. China email: ranzhang90@nuaa.edu.cn
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Abstract

This paper investigates global dynamics of an infection age-space structured cholera model. The model describes the vibrio cholerae transmission in human population, where infection-age structure of vibrio cholerae and infectious individuals are incorporated to measure the infectivity during the different stage of disease transmission. The model is described by reaction–diffusion models involving the spatial dispersal of vibrios and the mobility of human populations in the same domain Ω ⊂ ℝn. We first give the well-posedness of the model by converting the model to a reaction–diffusion model and two Volterra integral equations and obtain two constant equilibria. Our result suggest that the basic reproduction number determines the dichotomy of disease persistence and extinction, which is achieved by studying the local stability of equilibria, disease persistence and global attractivity of equilibria.

Keywords

Cholerainfection age-space structured modeluniform persistencebasic reproduction numberglobal stability

MSC classification

Primary: 35B35: Stability 35B40: Asymptotic behavior of solutions 35Q92: PDEs in connection with biology and other natural sciences
Secondary: 37N25: Dynamical systems in biology 92D30: Epidemiology
Type
Papers
Information
European Journal of Applied Mathematics , Volume 33 , Issue 3 , June 2022 , pp. 393 - 422
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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