Analysis and modelling of the transmission dynamics of tuberculosis in the presence of latent and active populations

Tuberculosis, a chronic infectious disease caused by Mycobacterium tuberculosis, remains a significant global health challenge, particularly in developing countries. This project investigates the dynamic transmission of tuberculosis, focusing on the interplay between latent and active populations. We develop and analyze an (Susceptible, Latent, Infectious, Recovered) compartmental mathematical model to examine key parameters affecting TB transmission dynamics. Our study employs stability and sensitivity analyses to provide critical insights into the basic reproduction number and equilibrium points of the TB transmission model. Through numerical simulations, we explore how various intervention strategies impact the spread of tuberculosis. The model yields an approximate reproduction number of 0.3, suggesting that under the current conditions represented in the model, TB would naturally decline in the population. Key findings emphasize the importance of maintaining a low transmission rate and improving the recovery rate to expedite the elimination of tuberculosis. The model demonstrates the complex interplay between susceptible, infected, latent, and recovered populations over time, highlighting the persistent nature of TB due to factors such as latent activation and loss of immunity in recovered individuals. This project provides a robust foundation for public health strategies aimed at controlling and ultimately eliminating tuberculosis. Our results underscore the need for targeted interventions focusing on reducing transmission, managing latent infections, and enhancing treatment efficacy. These insights can inform policy decisions and resource allocation in TB control programs, contributing to the global effort to combat this persistent disease.