Global dynamics of virus infection model with humoral immune response and distributed delays

摘要

In this paper, we investigate the global dynamics of virus infection model with humoral immune response and distributed intracellular delays. The model is 4-dimensional nonlinear delay differential equations that describe the interaction of the virus with target cells, taking into account the humoral immune system response. The model has two types of distributed time delays which describe the time needed for infection of target cell and virus replication. Lyapunov functionals are constructed to establish the global asymptotic stability of the steady states of the model. We have proven that if the basic reproduction number Ro is less than or equal unity then the uninfected steady state is globally asymptotically stable (GAS), and if the antibody immune response reproduction number Ri is less than or equal unity and Ro > 1, then the infected steady state without immune response exists and it is GAS; if R_1 > 1 then the infected steady state with immune response exists and it is GAS.