MMN-1083
Stability of humoral immunity virus infection model with general incidence rate and distributed delays
Ahmed Elaiw; A. Alhejelan; A. M. Shehata;Abstract
In this paper, we investigate the global stability of a virus infection model with humoral immune response and distributed intracellular delays. The incidence rate of infection is given by general functional response. The model
has two types of distributed time delays which describe the time needed for infection of uninfected cell and virus replication. Lyapunov functionals are constructed and LaSalle's invariance principle is used to establish the global asymptotic stability of all steady states of the model. We have proven that, if the basic reproduction number $R_{0}$ is less than or equal unity, then the uninfected steady state is globally asymptotically stable (GAS), and if the humoral immune response reproduction number $R_{1}$ is less than or equal unity and $R_{0}>1$, then the infected steady state without humoral immune response exists and it is GAS, and if $R_{1}>1$, then the infected steady
state with humoral immune response exists and it is GAS.
Vol. 17 (2016), No. 1, pp. 209-230
DOI: 10.18514/MMN.2016.1083