Chang, Ting-Ying

Du, Yihong

2022-01-04

<p>In this paper, we consider a reaction-diffusion epidemic model with nonlocal diffusion and free boundaries, which generalises the free-boundary epidemic model by Zhao et al. [1] by including spatial mobility of the infective host population. We obtain a rather complete description of the longtime dynamics of the model. For the reproduction number <i>R</i>₀ arising from the corresponding ODE model, we establish its relationship to the spreading-vanishing dichotomy via an associated eigenvalue problem. If <i>R</i>₀ ≤ 1, we prove that the epidemic vanishes eventually. On the other hand, if <i>R</i>₀ > 1, we show that either spreading or vanishing may occur depending on its initial size. In the case of spreading, we make use of recent general results by Du and Ni [2] to show that finite speed or accelerated spreading occurs depending on whether a threshold condition is satisfied by the kernel functions in the nonlocal diffusion operators. In particular, the rate of accelerated spreading is determined for a general class of kernel functions. Our results indicate that, with all other factors fixed, the chance of successful spreading of the disease is increased when the mobility of the infective host is decreased, reaching a maximum when such mobility is 0 (which is the situation considered by Zhao et al. [1]).</p>

Electronic Research Archive, 30(1), p. 289-313

2688-1594

https://hdl.handle.net/1959.11/56208

AIMS Press

Attribution 4.0 International

Long-time dynamics of an epidemic model with nonlocal diffusion and free boundaries

Journal Article

Publication