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Communications on Pure and Applied Analysis (CPAA)
 

A class of virus dynamic model with inhibitory effect on the growth of uninfected T cells caused by infected T cells and its stability analysis

Pages: 795 - 806, Volume 15, Issue 3, May 2016      doi:10.3934/cpaa.2016.15.795

 
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Wenbo Cheng - Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing100083, China (email)
Wanbiao Ma - Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China (email)
Songbai Guo - Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing100083, China (email)

Abstract: A class of virus dynamic model with inhibitory effect on the growth of uninfected T cells caused by infected T cells is proposed. It is shown that the infection-free equilibrium of the model is globally asymptotically stable, if the reproduction number $R_0$ is less than one, and that the infected equilibrium of the model is locally asymptotically stable, if the reproduction number $R_0$ is larger than one. Furthermore, it is also shown that the model is uniformly persistent, and some explicit formulae for the lower bounds of the solutions of the model are obtained.

Keywords:  Virus dynamic model, time delay, stability, persistence.
Mathematics Subject Classification:  Primary: 34K20, 34D23; Secondary: 92D30.

Received: January 2015;      Revised: October 2015;      Available Online: February 2016.

 References