Mathematical modeling of HIV/AIDS with optimal control: A case study in Ethiopia
Tigabu Kasie Ayele, Emile Franc Doungmo Goufo, Stella Mugisha
Abstract
In this paper, we developed HIV/AIDS mathematical model which comprises important compartments such as individuals with aware and unaware susceptible, undiagnosed HIV infections, diagnosed HIV infectious with and without AIDS symptom, and treated from the disease. This model considers the rate of becoming aware and unaware as a function of media campaign, whereas screening and treatments rates are constants. The effective reproduction number, equilibria and their nature of stability were formulated. The bifurcation also occurred when the effective reproduction number is equal to unity. This model extended to a new model which incorporates interventions such as preventive, screening, and treatment strategies. In this model the optimal control problem is formulated and solved analytically. In addition to this the optimality system is derived and solved numerically using the forward-backward sweep method (FBSM). Finally the cost-effectiveness of these combination controlling strategies is derived.