The dynamics of a degenerate epidemic model with nonlocal diffusion and free boundaries

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Zhao, Meng¹  Zhang, Yang²  Li, Wan-Tong¹  Du, Yihong³ 

[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China

[2] Harbin Engn Univ, Dept Math, Harbin 150001, Peoples R China

[3] Univ New England, Sch Sci & Technol, Armidale, NSW 2351, Australia

关键词: Epidemic model;    Nonlocal diffusion;    Free boundary;    Spreading and vanishing;   

DOI  :  10.1016/j.jde.2020.02.029

来源: Elsevier

【 摘 要 】

We consider an epidemic model with nonlocal diffusion and free boundaries, which describes the evolution of an infectious agents with nonlocal diffusion and the infected humans without diffusion, where humans get infected by the agents, and infected humans in return contribute to the growth of the agents. The model can be viewed as a nonlocal version of the free boundary model studied by Ahn, Beak and Lin [2], with its origin tracing back to Capasso et al. [5,6]. We prove that the problem has a unique solution defined for all t > 0, and its long-time dynamical behaviour is governed by a spreading-vanishing dichotomy. Sharp criteria for spreading and vanishing are also obtained, which reveal significant differences from the local diffusion model in [2]. Depending on the choice of the kernel function in the nonlocal diffusion operator, it is expected that the nonlocal model here may have accelerated spreading, which would contrast sharply to the model of [2], where the spreading has finite speed whenever spreading happens [33]. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free