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

Global stability of a delayed viral infection model with nonlinear immune response and general incidence rate

Pages: 133 - 149, Volume 21, Issue 1, January 2016      doi:10.3934/dcdsb.2016.21.133

 
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Yu Ji - Department of Mathematics, Beijing Technology and Business University, Beijing, 100048, China (email)
Lan Liu - Department of Mathematics, Beijing Technology and Business University, Beijing 100048, China (email)

Abstract: In this paper, a delayed viral infection model with nonlinear immune response and general incidence rate is discussed. We prove the existence and uniqueness of the equilibria. We study the effect of three kinds of time delays on the dynamics of the model. By using the Lyapunov functional and LaSalle invariance principle, we obtain the conditions of global stabilities of the infection-free equilibrium, the immune-exhausted equilibrium and the endemic equilibrium. It is shown that an increase of the viral-infection delay and the virus-production delay may stabilize the infection-free equilibrium, but the immune response delay can destabilize the equilibrium, leading to Hopf bifurcations. Numerical simulations are given to verify the analytical results. This can provide a possible interpretation for the viral oscillation observed in chronic hepatitis B virus (HBV) and human immunodeficiency virus (HIV) infected patients.

Keywords:  Time delay, stability, virus infection, immune response, general incidence rate.
Mathematics Subject Classification:  Primary: 34K20, 34K25; Secondary: 92D30.

Received: February 2015;      Revised: April 2015;      Available Online: November 2015.

 References