A model for interactions between immune cells and HIV considering drug treatments

In this work, we analyze the capacity of the human body to combat HIV. The model here treated takes into consideration four types of defense of an organism infected by HIV: susceptible defense cells, the infected immune cells, killer T cells, and the HIV-specific killer T cells. This model, therefore, analyzes the interactions between the responses of killer T cells and HIV infections, evidencing how the immune system is attacked and how it defends. An optimal control problem is proposed to derive an optimal sequence of dosages in the standard drug treatment, in such a way as to minimize the side effects