Stability of a general adaptive immunity virus dynamics model with multistages of infected cells and two routes of infection

• Published in: Mathematical methods in the applied sciences 2020-02, Vol.43 (3), p.1145-1175
• Main Authors: Elaiw, Ahmed, AlShamrani, Noura
• Format: Article
• Language: English
• Subjects: adaptive immune response; Computer simulation; Dynamic stability; Economic models; global stability; Liapunov functions; Lyapunov function; Lymphocytes; Mathematical models; multistaged infected cells; Nonlinear dynamics; viral and cellular infections; Viruses
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.5923

This paper studies an (n+4)‐dimensional nonlinear virus dynamics model that characterizes the interactions of the viruses, susceptible host cells, n‐stages of infected cells, B cells and cytotoxic T lymphocyte (CTL) cells. Both viral and cellular infections have been incorporated into the model. The infected‐susceptible and virus‐susceptible infection rates as well as the generation and removal rates of all compartments are described by general nonlinear functions. Five threshold parameters are computed, which insure the existence of the equilibria of the model under consideration. A set of conditions on the general functions has been established, which is sufficient to investigate the global dynamics of the model. The global asymptotic stability of all equilibria is proven by utilizing Lyapunov function and LaSalle's invariance principle. The theoretical results are illustrated by numerical simulations of the model with specific forms of the general functions.