Global dynamics of humoral and cellular immune responses to virus infection

We study the global stability of a model of virus dynamics with consideration of humoral and cellular immune responses. We use a Lyapunov direct method to obtain sufficient conditions for the global stability of virus free and viruspresence equilibriums. First, we analyze the model without an immune response and found that if the reproductive number of the virus is less than or equal to one, the virus-free equilibrium is globally asymptotically stable. However, for the virus-presence equilibrium, global stability is obtained if the virus entrance rate into the target cells is less than one. We analyze the model with humoral and cellular immune responses and found similar results. The difference is that in the reproductive number of the virus and in the virus entrance rate into the target cells appear parameters of humoral and cellular immune responses, which means that the adaptive immune response will cease or control the rise of the infection.