# American Institute of Mathematical Sciences

May  2014, 19(3): 735-745. doi: 10.3934/dcdsb.2014.19.735

## Analysis of a CD4$^+$ T cell viral infection model with a class of saturated infection rate

 1 Department of Applied Mathematics, University of Science and Technology Beijing, Beijing, 100083, China, China, China 2 Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083

Received  October 2012 Revised  October 2013 Published  February 2014

This paper formulates and analyzes an HIV-1 infection model with saturated infection rate. We first discuss the boundedness of the solution and the existence of the equilibrium. The local stability of the virus-free equilibrium and infected equilibrium is established by analyzing the roots of the characteristic equations. Furthermore, we study the global stability of the virus-free equilibrium and infected equilibrium by using suitable Lyapunov function and LaSalle's invariance principle, and obtain sufficient conditions for the global stability of the infected equilibrium. Finally, numerical simulations are presented to illustrate the main results.
Citation: Zhixing Hu, Weijuan Pang, Fucheng Liao, Wanbiao Ma. Analysis of a CD4$^+$ T cell viral infection model with a class of saturated infection rate. Discrete & Continuous Dynamical Systems - B, 2014, 19 (3) : 735-745. doi: 10.3934/dcdsb.2014.19.735
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