Dynamics and profiles of a diffusive host-pathogen system with distinct dispersal rates

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:264

Article

Wu, Yixiang¹  Zou, Xingfu^2,3 

[1] Vanderbilt Univ, Dept Math, Nashville, TN 37212 USA

[2] Western Univ, Dept Appl Math, London, ON N6A 3K7, Canada

[3] Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

关键词: Host-pathogen;    Reaction-diffusion;    Global attractor;    Uniform persistence;    Basic reproduction number;    Concentration phenomenon;   

DOI  :  10.1016/j.jde.2017.12.027

来源: Elsevier

【 摘 要 】

In this paper, we investigate a diffusive host-pathogen model with heterogeneous parameters and distinct dispersal rates for the susceptible and infected hosts. We first prove that the solution of the model exists globally and the model system possesses a global attractor. We then identify the basic reproduction number R-0 for the model and prove its threshold role: if R-0 <= 1, the disease free equilibrium is globally asymptotically stable; if R-0 > 1, the solution of the model is uniformly persistent and there exists a positive (pathogen persistent) steady state. Finally, we study the asymptotic profiles of the positive steady state as the dispersal rate of the susceptible or infected hosts approaches zero. Our result suggests that the infected hosts concentrate at certain points which can be characterized as the pathogen's most favoured sites when the mobility of the infected host is limited. (c) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free