Global dynamics and threshold behavior of an SEIR epidemic model with nonlocal diffusion

Subir Dey, Tapan Kumar Kar and Toshikazu Kuniya

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 226, issue C, 91-117

Abstract: This paper studies the global dynamics of an SEIR (Susceptible–Exposed–Infectious–Recovered) model with nonlocal diffusion. We show the model’s well-posedness, proving the solutions’ existence, uniqueness, and positivity, along with a disease-free equilibrium. Next, we prove that the model admits the global threshold dynamics in terms of the basic reproduction number R0, defined as the spectral radius of the next-generation operator. We show that the solution map has a global compact attractor, offering insights into long-term dynamics. In particular, the analysis shows that for R0<1, the disease-free equilibrium is globally stable. Using the persistence theory, we show that there is an endemic equilibrium point for R0>1. Moreover, by constructing an appropriate Lyapunov function, we establish the global stability of the unique endemic equilibrium in two distinct scenarios.

Keywords: Nonlocal diffusion; SEIR model; Basic reproduction number; Global compact attractor; Global stability; Lyapunov function (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:226:y:2024:i:c:p:91-117

DOI: 10.1016/j.matcom.2024.07.002

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