Cost Effective Analysis on Mathematical Modelling of HIV/AIDS with Optimal Control Strategy
Eshetu Dadi Gurmu *
Department of Mathematics, Wollega University, Nekemte, Ethiopia.
Boka Kumsa Bole
Department of Mathematics, Wollega University, Nekemte, Ethiopia.
Purnachandra Rao Koya
Department of Mathematics, Wollega University, Nekemte, Ethiopia.
*Author to whom correspondence should be addressed.
Abstract
In this paper, a deterministic model of the Human Immunodeficiency Virus has been formulated to describe the transmission dynamics of the disease. The good posedness of the model equations was proved and the equilibrium points of the model have been identified. Basic reproduction numbers were used to establish both local and global stability of the disease-free and endemic equilibrium points of the model equation. The analysis reveals that if the basic reproduction is smaller than one, the solution converges to the disease-free steady-state, which is locally asymptotically stable. If the fundamental reproduction number is more than one, the solution converges to the endemic equilibrium point, which is locally asymptotically stable., sensitivity analysis of the model equation was performed on the key parameters to find out their relative significance and potential impact on the transmission dynamics of the Human Immunodeficiency Virus. The results of the simulation show that treatment minimizes the risk of Human Immunodeficiency Virus transmission from the community and the stability of disease-free equilibrium is achievable when basic reproduction is less. The findings from the analysis of cost-effectiveness revealed that a combination of prevention and screening is the most effective strategy to eradicate the disease from the community.
Keywords: Model, stability, optimal control, simulation