Mathematical Model of Pulmonary Tuberculosis Disease Spread

This study presents the development of a mathematical framework to model the spread of pulmonary tuberculosis. The analysis includes determining equilibrium points, calculating the basic reproduction number, and examining the local stability of the formulated model. Additionally, a sensitivity assessment and numerical simulations are conducted using the fourth-order Runge–Kutta approach. The constructed SEIRI (Susceptible–ExposedInfected–Recovered–Infected) epidemic model incorporates the recurrence rate into its formulation. Under this framework, equilibrium points for both disease-free and endemic scenarios are identified for each model variation. The basic reproduction number is computed through the Next Generation Matrix technique. Furthermore, based on the eigenvalues of the Jacobian matrix, the stability classification of each equilibrium point is established, with certain cases being locally asymptotically stable. Sensitivity analysis indicates that the transmission rate and recovery rate are the most influential parameters affecting changes in the basic reproduction number, exhibiting direct and inverse proportionality, respectively. Higher relapse rates tend to accelerate transitions in the susceptible and exposed compartments, while maintaining higher proportions in the infected group. These findings, supported by numerical simulations, strengthen the stability and sensitivity conclusions obtained in this research.