Modeling the cytotoxic immune response effects on human immunodeficiency virus

The immune system is responsible for the body defense against strange organisms. This type of control is performed by molecules and cells in an organized way. The proposed model consists in a system of ordinary deferential equations intended to resemble the interaction between HIV and the immune response when considering cytotoxic cells. Standard local stability analysis at the virus free equilibrium is carried out to determine the theoretical conditions that avoid infection. Simulations were run to obtain results for particular immunological conditions and also to describe the dynamics of the system when facing infection states