Global Dynamics of Virus Infection Model with Antibody Immune Response and Distributed Delays

• Published in: Discrete Dynamics in Nature and Society Vol. 2013; no. 2013; pp. 854 - 862-200
• Main Authors: Elaiw, A. M., Alhejelan, A., Alghamdi, Mohammad Ali
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Limiteds 01.01.2013; Hindawi Puplishing Corporation; Hindawi Publishing Corporation; John Wiley & Sons, Inc; Hindawi Limited
• Subjects: Analysis; Antibodies; Disease transmission; Health aspects; Immune response; Immunological research; Viral antibodies; Virus diseases; Virus research; China
• ISSN: 1026-0226; 1607-887X
• DOI: 10.1155/2013/781407

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 number R0 and antibody immune response reproduction number R1. We have proven that if R0≤1, then the uninfected steady state is globally asymptotically stable (GAS), if R1≤1<R0, then the infected steady state without antibody immune response is GAS, and if R1>1, then the infected steady state with antibody immune response is GAS.