Abstract
We present qualitative behavior of virus infection model with antibody immune response. The incidence rate of infection is given by saturation functional response. Two types of distributed delays are incorporated into the model to account for the time delay between the time when uninfected cells are contacted by the virus particle and the time when emission of infectious (matures) virus particles. Using the method of Lyapunov functional, we have established that the global stability of the steady states of the model is determined by two threshold numbers, the basic reproduction numberR0and antibody immune response reproduction numberR1. We have proven that ifR0≤1, then the uninfected steady state is globally asymptotically stable (GAS), ifR1≤1<R0, then the infected steady state without antibody immune response is GAS, and ifR1>1, then the infected steady state with antibody immune response is GAS.
Highlights
In the past ten years there has been a growing interest in modeling viral infections for the study and characterization of host infection dynamics
We prove that the global dynamics of this model is determined by the basic reproduction number R0 and antibody immune response reproduction number R1
We have proposed a virus infection model which describes the interaction of the virus with the uninfected and infected cells taking into account the antibody immune response
Summary
In the past ten years there has been a growing interest in modeling viral infections for the study and characterization of host infection dynamics. Mathematical models for virus dynamics with the antibody immune response have been developed in [20,21,22,23,24,25,26]. Model (1) is based on the assumption that the infection could occur and that the viruses are produced from infected cells instantaneously, once the Discrete Dynamics in Nature and Society uninfected cells are contacted by the virus particles. In [25, 28], global stability of viral infection models with antibody immune response and discrete delays has been studied. In [26], a virus infection model with antibody immune response and with saturation incidence rate has been considered. If R0 ≤ 1, the uninfected steady state is globally asymptotically stable (GAS), if R1 ≤ 1 < R0, the infected steady state without antibody immune response is GAS, and if R1 > 1, the infected steady state with antibody immune response is GAS
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