Modelling and optimal control of HIV/AIDS prevention through PrEP and limited treatment

Epidemic outbreak is one of the primary issue that induce behavioural changes in healthy individuals to avoid contracting infection. We here propose a compartmental model for the transmission of HIV/AIDS including treatment and Pre-exposure prophylaxis (PrEP). It accounts for the effect of individual's behavioural response due to information of PrEP also. Taking PrEP by uninfected individuals actually can prevent the acquisition of HIV infection. Model analysis has been performed as well as the local and global stability of equilibrium points is established. Further, an optimal control problem has been formulated to minimize the cost and disease fatality by choosing the treatment and the effect of information regarding PrEP as control variables. Numerical analysis gives that if only control via information regarding PrEP is used, then it will be economical for early phase of the time period whereas treatment works well for long term control. Moreover, simultaneous use of both the control interventions is more useful than any single applied control policy and it reduces the number of infective individuals and also minimizes the economic cost generated from disease burden and controls. In the model it can be observed how uptake of PrEP can effect in the population by reducing the number of HIV infections. Moreover the combined effect of both the control policies is found to be more economical during the entire epidemic period whereas the implementation of a single policy is comparatively found less economical viable. (C) 2018 Elsevier B.V. All rights reserved.