Mathematical Analysis of a Model with HIV-1 Mutation in the Midst of a Cellular Immune Response

Many people living with HIV-1/AIDS (PLWH) today can live longer due to potent highly active antiretroviral therapy (HAART). However, another concern has arisen as the HIV virus mutates into drug resistant variants. It is therefore imperative that research be directed to finding out the conditions under which the sensitive variant survives in the presence of mutations. In this study an in-host deterministic model is developed to find out the different states that can exist and the conditions in which the different equilibria can be globally asymptotically stable (GAS). The current model steady states have been established and we have proved their global stability via the construction of suitable Lyapunov functions and invocation of the LaSalle's invariance principle.