A class of delayed viral infection models with general incidence rate and adaptive immune response

To model the role of the adaptive immune response in viral infection, take account the time needed for infected cells to produce new virions after viral entry and the time necessary for the newly produced virions to become mature and infectious, we propose three generalized models that describe the interactions between virus, host cells, antibodies and cytotoxic T lymphocytes (CTL) cells. The incidence rate of the infection into three models is given by a general function which includes many special cases and depends on the uninfected cells, infected cells and virus. Our main results show that the global dynamics of the three models under certain hypotheses on the incidence function is fully determined by five threshold parameters called the reproduction numbers for viral infection, for antibody immune response, for CTL immune response, for antibody immune competition and for CTL immune competition. Several viral infection models with discrete, finite and infinite distributed delays existing in other previous studies are extended and generalized. Furthermore, we give some biological findings of our analytical results. © 2015, Springer-Verlag Berlin Heidelberg.