Optimal control of cardiovascular diseases among HIV infected

Abstract

In this article, we formulated a new model of cardiovascular diseases as a complication of HIV infection and its HAART treatment with optimal control strategies. The stability of the equilibrium point for the model without control is established via the Routh Hurwitz criterion. In addition, our model is linked to three control measures, including the organization of programs to prevent HIV infection, awareness of the infected about the impact of HIV and HAART, and regular diagnosis and monitoring of risk factors of cardiovascular diseases in HIV-positive people. The objective function of optimal control problem aims to minimize the number of complications and associated costs. Then, we characterized the optimal controls by applying Pontryagin’s Maximum Principle after having proven its existence. We used Gauss Siedel’s iterative approaches to solve the resulting system. We used HIV data from Burundi to estimate fixed and adjusted parameters, to be able to provide numerical simulations to illustrate our theoretical results. Ultimately, the controls reduce the risk of cardiovascular diseases and improve public health.