An optimal combination of antiretroviral treatment and immunotherapy for controlling HIV infection

Antiretroviral (ART) drugs have been used to treat HIV patients over last two decades. But, the daily use of these drugs in order to control HIV load in patients' body results different side effects and high cost over long period of time. Motivated by these, researchers have been trying to find other treatment strategy whose combination with antiretroviral treatments can control HIV without use of large quantities of drugs. Immunotherapy is one of such treatment which assist natural immune system of patients in order to get control over viral infection. Administration of immunotherapy in combination with antiretroviral drugs has been found safe and effective after different clinical trials on humans and other animals. In this paper, we propose a mathematical model to describe HIV dynamics under antiretroviral treatment and immunotherapy combination. We find that our model is biologically feasible and the findings of the clinical trials support the dynamics of our model. The stability analyses of HIV-free equilibrium point are performed and found the basic reproduction number as a threshold parameter. Also, we calculate a critical efficacy for overall antiretroviral treatment such that when the efficacy of overall treatment exceeds this value HIV will be completely removed. Also, we have found that critical drug efficacy for antiretroviral drugs decreases with increasing immunotherapy, which indicates combination of immunotherapy with antiretroviral treatments minimize the quantity of antiretroviral drugs for HIV eradication, hence minimize the side effects and cost of antiretroviral drugs. Numerical simulations are carried out to substantiate the analytical results and to illustrate different drug administration scenarios. Moreover, an optimal combination of drugs which can control HIV with lower costs and side effects, is obtained by solving an optimal control problem numerically.