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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 R0 is less than or equal unity, then the uninfected steady state is globally asymptotically stable (GAS), and if the humoral immune response reproduction number R1 is less than or equal unity and R0 > 1, then the infected steady state without humoral immune response exists and it is GAS, and if R1 > 1, then the infected steady state with humoral immune response exists and it is GAS. Numerical simulations have been carried out with a specific form of the incidence rate function. We have shown that, both the numerical and theoretical results are consistent. 2010 Mathematics Subject Classification: 34D20; 34D23; 37N25; 92D30

Stability of humoral immunity virus infection model with general incidence rate and distributed delays