Mathematical modeling and optimal control of tuberculosis spread among smokers with case detection

Cicik Alfiniyah; Wanwha Sonia Putri Artha Soetjianto; Ahmadin; Muhamad Hifzhudin Noor Aziz; Siti Maisharah Sheikh Ghadzi; Cicik Alfiniyah; Wanwha Sonia Putri Artha Soetjianto; Ahmadin; Muhamad Hifzhudin Noor Aziz; Siti Maisharah Sheikh Ghadzi

doi:10.3934/math.20241471

AIMS Mathematics

2024, Volume 9, Issue 11: 30472-30492. doi: 10.3934/math.20241471

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Research article

Mathematical modeling and optimal control of tuberculosis spread among smokers with case detection

1.
Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Indonesia
2.
Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Malaysia
3.
School of Pharmaceutical Sciences, Universiti Sains Malaysia, Malaysia

Received: 18 July 2024 Revised: 17 October 2024 Accepted: 21 October 2024 Published: 25 October 2024
MSC : 34A34, 34A45, 92C60, 92D30, 93C15

Tuberculosis (TB) remains one of deadly infectious diseases worldwide. Smoking habits are a significant factor that can increase TB transmission rates, as smokers are more susceptible to contracting TB than nonsmokers. Therefore, a control strategy that focused on minimizing TB transmission among smokers was essential. The control of TB transmission was evaluated based on the case detection rate. Undetected TB cases often resulted from economic challenges, low awareness, negative stigma toward TB patients, and health system delay (HSD). In this study, we developed a mathematical model that captured the dynamics of TB transmission specifically among smokers, incorporating the effects of case detection. Our innovative approach lied in the integration of smoking behavior as a key factor in TB transmission dynamics, which has been underexplored in previous models. We analyzed the existence and stability of the TB model equilibrium based on the basic reproduction number. Additionally, parameter sensitivity analysis was conducted to identify the most influential factors in the spread of the disease. Furthermore, this study investigated the effectiveness of various control strategies, including social distancing for smokers, TB screening in high-risk populations, and TB treatment in low-income communities. By employing the Pontryagin maximum principle, we solved optimal control problems to determine the most effective combination of interventions. Simulation results demonstrated that a targeted combination of control measures can effectively reduce the number of TB-infected individuals.
- tuberculosis,
- mathematical model,
- sensitivity analysis,
- optimal control,
- smokers,
- case detection rate
Citation: Cicik Alfiniyah, Wanwha Sonia Putri Artha Soetjianto, Ahmadin, Muhamad Hifzhudin Noor Aziz, Siti Maisharah Sheikh Ghadzi. Mathematical modeling and optimal control of tuberculosis spread among smokers with case detection[J]. AIMS Mathematics, 2024, 9(11): 30472-30492. doi: 10.3934/math.20241471

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Abstract

Tuberculosis (TB) remains one of deadly infectious diseases worldwide. Smoking habits are a significant factor that can increase TB transmission rates, as smokers are more susceptible to contracting TB than nonsmokers. Therefore, a control strategy that focused on minimizing TB transmission among smokers was essential. The control of TB transmission was evaluated based on the case detection rate. Undetected TB cases often resulted from economic challenges, low awareness, negative stigma toward TB patients, and health system delay (HSD). In this study, we developed a mathematical model that captured the dynamics of TB transmission specifically among smokers, incorporating the effects of case detection. Our innovative approach lied in the integration of smoking behavior as a key factor in TB transmission dynamics, which has been underexplored in previous models. We analyzed the existence and stability of the TB model equilibrium based on the basic reproduction number. Additionally, parameter sensitivity analysis was conducted to identify the most influential factors in the spread of the disease. Furthermore, this study investigated the effectiveness of various control strategies, including social distancing for smokers, TB screening in high-risk populations, and TB treatment in low-income communities. By employing the Pontryagin maximum principle, we solved optimal control problems to determine the most effective combination of interventions. Simulation results demonstrated that a targeted combination of control measures can effectively reduce the number of TB-infected individuals.

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