Dynamic analysis of mother-to-child transmission of HIV and antiretroviral treatment as optimal control

Abstract

Human immunodeficiency virus (HIV) is still an extremely dangerous pandemic and without a prominent cure. And one of the most vulnerable population prone to acquiring the virus can be newborn babies from their HIV positive mothers. It can even turn fatal when an individual gets acquired immunodeficiency syndrome (AIDS) and the disease is left untreated and uncontrolled. One such treatment for suppressing the infections is antiretroviral therapy (ART) treatment. To gain insight of the Indian scenario of the mother to child transmission (MTCT) and the present work of the ARTs strategy in India we shall study a model for HIV infected newborns. Hence, we have formulated a model consisting of newborns born to HIV infected mothers, infected newborns and newborns acquiring AIDS. We have found the equilibrium points and established the local stability of the system. We then considered ARTS as optimal control for the HIV infected newborns and thus, extended our model with the class of newborns going for ARTS. With the help of Pontryagin’s Maximum Principle, we then obtain the optimal ART intensity as part of intervention to control infection among newborns for our optimal control problem. For the numerical simulations we took real time data of India for all parameters along with MTCT rate for the state of Maharashtra. One of our numerical results shows that ART’s as strategy among newborns born to HIV infected mothers decreases the number of HIV infected babies. Thus, the paper highlights the necessary and crucial role of ART programs for babies born to HIV positive mothers in order to suppress the infection for their brighter futures in the epidemic dynamics of India.