Local and Global Stabilities of a Viral Dynamics Model with Infection-Age and Immune Response
- 296 Downloads
In this paper, we construct an infection-age model to study the interaction between viruses and the immune system within the host. In the model, the mortality rate of infected cells, the rate that cytotoxic T lymphocytes (CTL) kill infected cells, the rate that infected cells produce new virus, and the CTL proliferate rate may depend on the infection-age. The basic reproduction number and the threshold for the existence of steady states are obtained. Local stability of both the infection-free and infection steady states is studied by analyzing the linearized systems. Global stability of the infection-free steady state is obtained by investigating a renewal integral equation and global stability of the infection steady state is obtained by constructing a Liapunov functional. Numerical simulations are presented to verify the theoretical results.
KeywordsAge-structured model Viral dynamics Integrated solution Liapunov functional Local and global stabilities
We would like to thank the reviewers for their constructive comments, which greatly improve this paper. This research was partially supported by National Natural Science Foundation of China (11401117, 11401060, 11401217, 11771168), Improvement Project for Young Teachers of Guangxi Province (KY2016YB246), and National Science Foundation (DMS-1412454).
- 2.Anderson, R.M., May, R.M.: Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, Oxford (1991)Google Scholar
- 10.Hale, J.K.: Asymptotic Behavior of Dissipative Systems, Mathematical Surveys and Monographs, vol. 25. American Mathematical Society, Providence (1988)Google Scholar
- 13.Iannelli, M.: Mathematical Theory of Age-Structured Population Dynamics. Giardini Editori e Stampatori, Pisa (1995)Google Scholar
- 15.Magal, P.: Compact attrators for time-periodic age-structured population models. Electron. J. Differ. Equ. 65, 1–35 (2001)Google Scholar
- 23.Nelson, P.W., Gilchrist, M.A., Coombs, D., Hyman, J., Perelson, A.S.: An age-structured model of HIV infection that allows for variations in the production rate of viral particles and the death rate of productively infected cells. Math. Biosci. Eng. 1, 267–288 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
- 25.Nowak, M.A., May, R.M.: Viral Dynamics. Oxford University Press, Oxford (2000)Google Scholar