Abstract
Two virus infection models with antibody immune response and chronically infected cells are proposed and analyzed. Bilinear incidence rate is considered in the first model, while the incidence rate is given by a saturated functional response in the second one. One main feature of these models is that it includes both short-lived infected cells and chronically infected cells. The chronically infected cells produce much smaller amounts of virus than the short-lived infected cells and die at a much slower rate. Our mathematical analysis establishes that the global dynamics of the two models are determined by two threshold parametersR0andR1. By constructing Lyapunov functions and using LaSalle's invariance principle, we have established the global asymptotic stability of all steady states of the models. We have proven that, the uninfected steady state is globally asymptotically stable (GAS) ifR0<1, the infected steady state without antibody immune response exists and it is GAS ifR1<1<R0, and the infected steady state with antibody immune response exists and it is GAS ifR1>1. We check our theorems with numerical simulation in the end.
Highlights
In recent years, many mathematical models have been proposed to study the dynamics of viral infections such as the human immunodeficiency virus (HIV), the hepatitis C virus (HCV), and the hepatitis B virus (HBV)
We have proposed two virus infection models with antibody immune response taking into account the chronically infected cells
In the first model we have assumed that the incidence rate of infection is bilinear while in the second model the incidence rate is given by saturation functional response
Summary
Many mathematical models have been proposed to study the dynamics of viral infections such as the human immunodeficiency virus (HIV), the hepatitis C virus (HCV), and the hepatitis B virus (HBV) (see, e.g., [1–17]). Where T, T∗, C∗, and V are the concentration of the uninfected cells, short-lived infected cells, chronically infected cells, and free virus particles, respectively. Δ and a are the death rate constants of the short-lived infected cells and chronically infected cells, respectively. The chronically infected cells produce much smaller amounts of virus than the short-lived infected cells and die at a much slower rate (i.e., NT > NC and δ > a). We propose two virus infection models with antibody immune response and chronically infected cells. If R0 ≤ 1, the infection-free equilibrium is globally asymptotically stable (GAS), if R1 ≤ 1 < R0, the infected equilibrium without antibody immune response exists and it is GAS, and if R1 > 1 the infected equilibrium with antibody immune response exists and it is GAS
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
