2013/01/01 by Hongying Shu, Lin Wang, James Watmough · 2 citations
Biochemistry, Genetics and Molecular Biology · Immunology and Microbiology · Medicine · #Evolution and Genetic Dynamics #Immune Cell Function and Interaction #Mathematical and Theoretical Epidemiology and Ecology Models
paper · doi:10.1137/120896463
crossref issued 2013/01/01 · crossref published 2013/01/01 · crossref published-print 2013/01/01 · openalex publication_date 2013/01/01 · crossref created 2013/06/27 · crossref deposited 2017/01/29 · openalex created_date 2025/10/10 · crossref indexed 2026/07/30 · openalex updated_date 2026/07/30
Determining sharp conditions for the global stability of equilibria remains one of the most challenging problems in the analysis of models for the management and control of biological systems. Yet such results are necessary for derivation of parameter thresholds for eradication of pests or clearing infections. This applies particularly to models involving nonlinearity and delays. In this paper, we provide some general results applicable to immune system dynamics: we consider a viral model with general target-cell dynamics, nonlinear incidence functions, state dependent removal functions, infinitely distributed intracellular delays, and the cytotoxic T lymphocyte response (CTL). This general model admits three types of equilibria: infection-free equilibria, CTL-inactivated infection equilibria, and CTL-activated infection equilibria. The model admits two critical values: R0 (the basic reproduction number for viral infection) and R1 (the viral reproduction number at the CTL-inactivated infection equilibrium). Under certain assumptions, it is shown that if R0≤ 1, then the infection-free equilibrium E0 is globally stable and the viruses are cleared. If R1≤ 1<R0, then there exists a unique CTL-inactivated infection equilibrium E1 which is globally stable and the infection becomes chronic with no sustained immune response. If R1>1, then there is a unique CTL-activated infection equilibrium, which is globally stable implying persistent immune responses. Our results cover and improve many existing ones and include the case when the nonlinear functions are nonmonotone.