Optimal Control Strategy for TB-HIV/AIDS Co-Infection Model in the Presence of Behaviour Modification

Processes - Tập 6 Số 5 - Trang 48
Temesgen Debas Awoke1, Semu Mitiku Kassa2,3
1Department of Mathematics, Kotebe Metropolitan University, P.O. Box 31248, Addis Ababa, Ethiopia;
2Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology (BIUST), P/Bag 16, Palapye, Botswana
3Department of Mathematics, Addis Ababa University, P.O. Box 1176, Addis Ababa, Ethiopia

Tóm tắt

A mathematical model for a transmission of TB-HIV/AIDS co-infection that incorporates prevalence dependent behaviour change in the population and treatment for the infected (and infectious) class is formulated and analyzed. The two sub-models, when each of the two diseases are considered separately are mathematically analyzed. The theory of optimal control analysis is applied to the full model with the objective of minimizing the aggregate cost of the infections and the control efforts. In the numerical simulation section, various combinations of the controls are also presented and it has been shown in this part that the optimal combination of both prevention and treatment controls will suppress the prevalence of both HIV and TB to below 3% within 10 years. Moreover, it is found that the treatment control is more effective than the preventive controls.

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