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Mathematical Biosciences and Engineering (MBE)
 

Global dynamics of a delay virus model with recruitment and saturation effects of immune responses

Pages: 1233 - 1246, Volume 14, Issue 5/6, October/December 2017      doi:10.3934/mbe.2017063

 
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Cuicui Jiang - Department of Mathematics, School of Biomedical Engineering, Third Military Medical University, Chongqing 400038, China (email)
Kaifa Wang - Department of Mathematics, School of Biomedical Engineering, Third Military Medical University, Chongqing 400038, China (email)
Lijuan Song - Department of Mathematics, School of Biomedical Engineering, Third Military Medical University, Chongqing 400038, China (email)

Abstract: In this paper, we formulate a virus dynamics model with the recruitment of immune responses, saturation effects and an intracellular time delay. With the help of uniform persistence theory and Lyapunov method, we show that the global stability of the model is totally determined by the basic reproductive number $R_0$. Furthermore, we analyze the effects of the recruitment of immune responses on virus infection by numerical simulation. The results show ignoring the recruitment of immune responses will result in overestimation of the basic reproductive number and the severity of viral infection.

Keywords:  Global stability, Lyapunov functional, viral dynamics, immune response, time delay.
Mathematics Subject Classification:  Primary: 92D30; Secondary: 34K20, 34K25.

Received: July 2016;      Accepted: October 2016;      Available Online: May 2017.

 References