Investigating Tuberculosis Dynamics Under Various Control Strategies: A Comprehensive Analysis Using Real Statistical Data - Al‐Hdaibat, Bashir; DarAssi, Mahmoud H.; Ahmad, Irfan; Altaf Khan, Muhammad; Algethamie, Reem (Mathematical methods in the applied sciences, 2025)
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.