To demonstrate the dynamics of the Mycobacterium tuberculosis disease population, a mathematical model was presented. The model has five compartments, and the resulting equations were resolved. While multiple cases of illness transmission were simulated using the compartmental model of infectious disease spread for a structured population model, the fundamental reproduction number was found using the next-generation matrix. Based on the results of the simulations, the system’s disease-free and endemic equilibrium was created by presenting, analyzing, and graphing the various subpopulations across time. The Homotopy Perturbation Method (HPM) analytical technique was then used to resolve the model.