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

Temesgen Debas  Awoke; Semu Mityiku Kassa

doi:10.3390/pr6050048

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

Temesgen Debas Awoke, Semu Mityiku Kassa

Mathematics & Statistical Sciences

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

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.

Original language	English
Journal	Processes
Volume	6
Issue number	5
DOIs	https://doi.org/10.3390/pr6050048
Publication status	Published - 2018

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

abstract = "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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AU - Awoke, Temesgen Debas

AU - Kassa, Semu Mityiku

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N2 - 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.

AB - 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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DO - 10.3390/pr6050048

M3 - Article

SN - 2227-9717

VL - 6

JO - Processes

JF - Processes

IS - 5

ER -

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

Abstract

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