Dynamics of reaction–diffusion equations for modeling CD4+ T cells decline with general infection mechanism and distinct dispersal rates. (February 2020)

• Record Type: Journal Article
• Authors: Wang, Wei; Ma, Wanbiao; Feng, Zhaosheng
• Is Part Of: Nonlinear analysis. Volume 51(2020)
• Publication Date: 2020-02
• Subjects: Reaction–diffusion equations -- Basic reproduction number -- Global attractor -- Asymptotical stability -- Threshold dynamics -- Asymptotic profiles; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.102976
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we are concerned with a diffusive viral infection dynamical model with general infection mechanism and distinct dispersal rates. In a general setting in which the model parameters are spatially heterogeneous, it is shown that if ℛ 0 ≤ 1, the infection-free steady state is globally asymptotically stable; while if ℛ 0 > 1, the model is uniformly persistent. The asymptotic profiles of the infection steady state are discussed as the dispersal rate of uninfected CD4 + T cells approaches zero by means of the persistence theory of semidynamical systems and the eigenvalue theory of elliptic equations.