Dynamical analysis of HIV/AIDS and HBV co-infection model with drug-related kidney disease using optimal control theory

HIV/AIDS and HBV co-infection with drug-related kidney disease is a common health problem throughout the world. The main objective of this study is to develop and analyze a novel HIV/AIDS and HBV co-infection with drug-related kidney disease model with optimal control theory. The theoretical analysis of the model computed disease-free equilibrium points, basic reproduction numbers and endemic equilibrium points of the HIV sub-model, the HBV sub-model, HIV/AIDS and HBV co-infection and the HIV/AIDS and HBV co-infection with drug-related kidney disease model, and we have examined equilibrium points local stabilities using Routh-Hurwitz criteria respectively. By aapplying Pontryagin's Maximum Principle, a novel HIV/AIDS and HBV co-infection with drug-related kidney disease optimal control problem incorporating seven time-dependent control measures is formulated and analyzed. The study carried out sensitivity analysis of the model parameters and verified that the disease spreading rates and treatment rates are the most influential parameters that shall be considered to reduce and control the diseases spreading dynamics. Using the parameter values and MATLAB ode45 solver with fourth-order Runge-Kutta numerical methods we performed numerical simulations for the HIV/AIDS and HBV co-infection with drug-related kidney disease optimal control problem dynamical system. Furthermore, since the proposed model considered the acute and chronic drug-related kidney disease stages which indicates the novelty the study seeks to explore the most effective protective and enhancement strategies to reduce and manage the HIV/AIDS and HBV co-infection with drug-related kidney disease spreading impact within the community. Eventually, the numerical simulation results show that implementing Strategy 15(that is implementing the protection strategies (c1,c2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${c}_{1}, {c}_{2}$$\end{document} and c3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${c}_{3}$$\end{document}) combined with the three therapy strategies (c4,c6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${c}_{4}, {c}_{6}$$\end{document}, andc7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${c}_{7}$$\end{document}) simultaneously emerges as the most dominant and impactful approach shall be used to reduce and control the HIV/AIDS and HBV co-infection with drug-related kidney disease spreading dynamics in the community.