Modelling the Impact of Control Measures on Tuberculosis Transmission

Tuberculosis (TB) is a global health pandemic which spreads through the air and is caused by Mycobacterium tuberculosis (MTB) which is a major contributor of illness and death worldwide. The ease of Tuberculosis transmission in closed environments makes it exposure becomes difficult to prevent, which do result in cases of Infection with and without symptoms. Moreso, Inadequate treatment of Tuberculosis cases often leads to antibiotic resistance, resulting in relapses even after apparent recovery. This study introduces a modified (????,????,????1,????2,????,????) model which analyze Tuberculosis transmission and optimal control strategies. Four key intervention strategies were examined: awareness-based interventions, tuberculosis examinations, provision of essential treatments and tuberculosis diagnosis with treatment. Qualitative analysis and optimal control analysis were conducted to validate the model. The model's system of differential equations was solved numerically using finite difference methods and simulated in MATLAB. Optimal control analysis using Pontryagin’s Maximum Principle demonstrated how gradual control strategies reduce infections and flatten the transmission curve. Results from the study showed that combination of the strategies are most effective for controlling Tuberculosis. These findings can guide policymakers in developing comprehensive and evidence-based decision to combat Tuberculosis spread.