Analytical and Computational Analysis of the HIV/AIDS Ordinary Differential Equations Model with Optimal Controls
O. A. Odebiyi *
Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso, Nigeria.
A.W. Ayanrinola
Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso, Nigeria.
A.O. Adeboye
Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso, Nigeria.
O.A. Olajide
Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso, Nigeria.
E.O. Elijah
Department of Mathematics, Federal University of Technology, Minna, Niger State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The global fight against Human Immune Deficiency Syndrome (HIV/AIDS) has been ongoing for decades, with significant progress made in understanding the virus, improving treatment options, and expanding access to care. Mathematical modelling has played a crucial role in understanding the dynamics of HIV/AIDS transmission and informing effective control strategies. Previous HIV transmission has not fully explored the existence and optimal control strategies for minimising the spread of HIV. Therefore, this study aims to identify effective interventions that can be tailored to specific contexts, thereby contributing to global efforts to combat HIV/AIDS and improve health outcomes. The study extends the HIV/AIDS model, investigating the existence and Optimal control of the Human Immunodeficiency Virus (HIV) and Acquired Immune Deficiency Syndrome (AIDS). This study formulates a deterministic mathematical model incorporating three time-dependent optimal control strategies. A comparative analysis of three control strategies was incorporated, namely: awareness campaigns, treatment with ART, and targeted outreach programs. Using Pontryagin's Maximum principle, the study characterises the optimal control strategies and proves the existence of solutions. Numerical simulations using MATLAB software illustrate the effectiveness of the proposed control strategies, highlighting the importance of tailored interventions and sustained investment in HIV/AIDS control programs. The results show that combined implementation of awareness campaigns, treatment with ART, and targeted outreach significantly reduces AIDS cases and suppresses AIDS-related outcomes, while treatment and targeted outreach effectively manage the disease. Overall, the findings provide valuable insights into HIV/AIDS dynamics and optimal intervention strategies, offering important guidance for public health policy, resource allocation, and the design of effective HIV prevention and control programs.
Keywords: Mathematical modelling, HIV/AIDS dynamics, optimal control, strategies