A reaction–diffusion Susceptible–Vaccinated–Infected–Recovered model in a spatially heterogeneous environment with Dirichlet boundary condition

Jinliang Wang, Ran Zhang and Toshikazu Kuniya

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 190, issue C, 848-865

Abstract: In this paper, we study a Susceptible–Vaccinated–Infected–Recovered (SVIR) epidemic model in a spatially heterogeneous environment under the Dirichlet boundary condition. We define the basic reproduction number ℜ0 by the spectral radius of the next generation operator, and show that it is a threshold parameter. The disease extinction and persistence in the case of a bounded domain are considered. More precisely, we show that the disease-free equilibrium is globally asymptotically stable if ℜ0<1; the system is uniformly persistent and an endemic equilibrium exists if ℜ0>1. To verify our theoretical results, we perform some numerical simulations, using the Fredholm discretization method to identify ℜ0.

Keywords: SVIR epidemic model; Diffusion; Basic reproduction number; Dirichlet boundary condition; Vaccination (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:190:y:2021:i:c:p:848-865

DOI: 10.1016/j.matcom.2021.06.020

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