Effect of humoral immunity on HIV 1 dynamics with virus to target and infected to target infections
We consider an HIV 1 dynamics model by incorporating (i) two routes of infection via, respectively, binding of a virus to a receptor on the surface of a target cell to start genetic reactions (virus to target infection) and the direct transmission from infected cells to uninfected cells through the concept of virological synapse in vivo (infected to target infection) (ii) two types of distributed time delays to describe the time between the virus or infected cell contacts an uninfected CD4+ T cell and the emission of new active viruses; (iii) humoral immune response, where the HIV 1 particles are attacked by the antibodies that are produced from the B lymphocytes. The existence and stability of all steady states are completely established by two bifurcation parameters, R0 (the basic reproduction number) and R1 (the viral reproduction number at the chronic infection steady state without humoral immune response) By constructing Lyapunov functionals and using LaSalle's invariance principle, we have proven.