Investigating Tuberculosis Dynamics Under Various Control Strategies: A Comprehensive Analysis Using Real Statistical Data
In the present investigation, a mathematical model with vaccination, treatment, and environmental impact under real data is presented. Initially, we present the model without any interventions, followed by an examination of its equilibrium points. The stability analysis indicates the confirmation of...
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| Veröffentlicht in: | Mathematical methods in the applied sciences |
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17.02.2025
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| Abstract | In the present investigation, a mathematical model with vaccination, treatment, and environmental impact under real data is presented. Initially, we present the model without any interventions, followed by an examination of its equilibrium points. The stability analysis indicates the confirmation of the local asymptotical stability of the disease‐free equilibrium (DFE), , whenever . Moreover, we demonstrate the global asymptotical stability of for . We also investigate the endemic equilibria and show that there exists a unique endemic equilibrium, , which confirms that the model does not exhibit the backward bifurcation. Utilizing real TB data from Pakistan (Khyber Pakhtunkhwa) over a specific timeframe, we parameterize the model accordingly. We perform sensitivity analysis to assess the impact of model parameters on , with the results depicted graphically. Subsequently, we extend the model to include vaccination and an optimal control framework, deriving the relevant outcomes. The numerical solutions for the optimal control model are presented under various control strategies, demonstrating that simultaneous activation of all four controls yields effective results in managing TB. The impact of four control strategies on TB management through a numerical optimal control framework is shown. The results reveal that all four controls, vaccination, awareness, screening, and pathogens clearance, simultaneously yield the most effective reduction in both exposed and infected cases, highlighting the necessity for an integrated approach to TB prevention and control. |
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| AbstractList | In the present investigation, a mathematical model with vaccination, treatment, and environmental impact under real data is presented. Initially, we present the model without any interventions, followed by an examination of its equilibrium points. The stability analysis indicates the confirmation of the local asymptotical stability of the disease‐free equilibrium (DFE), , whenever . Moreover, we demonstrate the global asymptotical stability of for . We also investigate the endemic equilibria and show that there exists a unique endemic equilibrium, , which confirms that the model does not exhibit the backward bifurcation. Utilizing real TB data from Pakistan (Khyber Pakhtunkhwa) over a specific timeframe, we parameterize the model accordingly. We perform sensitivity analysis to assess the impact of model parameters on , with the results depicted graphically. Subsequently, we extend the model to include vaccination and an optimal control framework, deriving the relevant outcomes. The numerical solutions for the optimal control model are presented under various control strategies, demonstrating that simultaneous activation of all four controls yields effective results in managing TB. The impact of four control strategies on TB management through a numerical optimal control framework is shown. The results reveal that all four controls, vaccination, awareness, screening, and pathogens clearance, simultaneously yield the most effective reduction in both exposed and infected cases, highlighting the necessity for an integrated approach to TB prevention and control. |
| Author | Algethamie, Reem Altaf Khan, Muhammad DarAssi, Mahmoud H. Al‐Hdaibat, Bashir Ahmad, Irfan |
| Author_xml | – sequence: 1 givenname: Bashir surname: Al‐Hdaibat fullname: Al‐Hdaibat, Bashir organization: Department of Mathematics, Faculty of science The Hashemite University Zarqa Jordan – sequence: 2 givenname: Mahmoud H. orcidid: 0000-0003-1993-7859 surname: DarAssi fullname: DarAssi, Mahmoud H. organization: Department of Basic Sciences Princess Sumaya University for Technology Amman Jordan – sequence: 3 givenname: Irfan surname: Ahmad fullname: Ahmad, Irfan organization: Department of Clinical Laboratory Sciences, College of Applied Medical Science King Khalid University Abha Saudi Arabia – sequence: 4 givenname: Muhammad orcidid: 0000-0002-4483-7879 surname: Altaf Khan fullname: Altaf Khan, Muhammad organization: Faculty of Natural and Agricultural Sciences University of the Free State Bleomfontein South Africa, School of Health and Environmental Science Korea University Seoul South Korea – sequence: 5 givenname: Reem surname: Algethamie fullname: Algethamie, Reem organization: Department of Mathematics, Faculty of science Al‐Baha university Alaqiq Saudi Arabia |
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| Title | Investigating Tuberculosis Dynamics Under Various Control Strategies: A Comprehensive Analysis Using Real Statistical Data |
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