Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

The effect of immune responses in viral infections: A mathematical model view

Pages: 3379 - 3396, Volume 19, Issue 10, December 2014      doi:10.3934/dcdsb.2014.19.3379

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Kaifa Wang - School of Biomedical Engineering, Third Military Medical University, Chongqing, 400038, China (email)
Yu Jin - Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588, United States (email)
Aijun Fan - Chongqing Academy of Science & Technology, Chongqing, 401123, China (email)

Abstract: To study the effect of immune response in viral infections, a new mathematical model is proposed and analyzed. It describes the interactions between susceptible host cells, infected host cells, free virus, lytic and nonlytic immune response. Using the LaSalle's invariance principle, we establish conditions for the global stability of equilibria. Uniform persistence is obtained when there is a unique endemic equilibrium. Mathematical analysis and numerical simulations indicate that the basic reproduction number of the virus and immune response reproductive number are sharp threshold parameters to determine outcomes of infection. Lytic and nonlytic antiviral activities play a significant role in the amount of susceptible host cells and immune cells in the endemic steady state. We also present potential applications of the model in clinical practice by introducing antiviral effects of antiviral drugs.

Keywords:  Viral infection, immune responses, reproductive number, stability, uniform persistence.
Mathematics Subject Classification:  Primary: 92C60, 92D30; Secondary: 34D23.

Received: February 2013;      Revised: July 2013;      Available Online: October 2014.