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On a reaction–diffusion system modelling infectious diseases without lifetime immunity

Part of: Physiological, cellular and medical topics Parabolic equations and systems

Published online by Cambridge University Press:  09 August 2021

HONG-MING YIN Open the ORCID record for HONG-MING YIN [Opens in a new window]
HONG-MING YIN*
Affiliation:
Department of Mathematics and Statistics, Washington State University, Pullman, WA 99164, USA email: hyin@wsu.edu
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Abstract

In this paper, we study a mathematical model for an infectious disease caused by a virus such as Cholera without lifetime immunity. Due to the different mobility for susceptible, infected human and recovered human hosts, the diffusion coefficients are assumed to be different. The resulting system is governed by a strongly coupled reaction–diffusion system with different diffusion coefficients. Global existence and uniqueness are established under certain assumptions on known data. Moreover, global asymptotic behaviour of the solution is obtained when some parameters satisfy certain conditions. These results extend the existing results in the literature. The main tool used in this paper comes from the delicate theory of elliptic and parabolic equations. Moreover, the energy method and Sobolev embedding are used in deriving a priori estimates. The analysis developed in this paper can be employed to study other epidemic models in biological, ecological and health sciences.

Keywords

Infectious disease model for Cholerareaction–diffusion systemglobal existence and uniquenessasymptotic behaviour and global attractor

MSC classification

Primary: 35K57: Reaction-diffusion equations
Secondary: 92C60: Medical epidemiology
Type
Papers
Information
European Journal of Applied Mathematics , Volume 33 , Issue 5 , October 2022 , pp. 803 - 827
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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