Dynamics of a PDE viral infection model incorporating cell-to-cell transmission

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:444

Article

Wang, Jinliang¹  Yang, Jie¹  Kuniya, Toshikazu² 

[1] Heilongjiang Univ, Sch Math Sci, Harbin 150080, Peoples R China

[2] Kobe Univ, Grad Sch Syst Informat, Nada Ku, 1-1 Rokkodai Cho, Kobe, Hyogo 6578501, Japan

关键词: HIV-1 model;    Cell-to-cell transmission;    Spatial heterogeneity;    Global asymptotic stability;    Lyapunov functions;    Basic reproduction number;   

DOI  :  10.1016/j.jmaa.2016.07.027

来源: Elsevier

【 摘 要 】

This paper is concerned with the global dynamics of a PDE viral infection model with cell-to-cell transmission and spatial heterogeneity. The basic reproduction number R-0, which is a threshold value that predicts whether the infection will go to extinction or not, is defined in a variational characterization. In quite a general setting in which every parameter can be spatially heterogeneous, it is shown that if R-0 <= 1, then the infection-free steady state is globally asymptotically stable, while if R-0 > 1, then the system is uniformly persistent and the infection steady state is globally asymptotically stable. The proof is based on the construction of the Lyapunov functions and usage of the Green's first identity. Finally, numerical simulation is performed in order to verify the validity of our theoretical results. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free