Abstract
In this paper, we discuss virus dynamics that helps to understand the dynamics of human immunodeficiency virus (HIV), hepatitis B virus (HCB), hepatitis C virus (HCV), and some other viruses. We also discussed the model with the immune system of the hepatitis B virus model with Cytotoxic T Lymphocyte (CTL) immune responses. We obtained the basic reproduction number R0 in all models which can be used to establish the conditions for stability of the equilibrium state. Analyzing the model, we show that if the basic reproductive number of viruses is less than one then the virus-free equilibrium is asymptotically stable and if the basic reproductive ratio is greater than one then the endemic equilibrium is locally asymptotically stable. Mathematical analysis and numerical simulations show that the CTL immune responses play a significant role in eradication of the disease. Ams subject classification 201037N25.34C23.49J15.92D30.
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