Spread and Control of Tuberculosis in the Case of Chiro Town: A Mathematical Model Analysis

In this work, will be studied tuberculosis transmission using Susceptible-Exposed-Infected-Carrier-Recovered-Susceptible (SEIRS) Mathematical model analysis on the spread and control of tuberculosis of Chiro town population. We found that the dynamical system exhibit two equilibrium points (EPs) namely, disease free equilibrium point (DFEP) and endemic equilibrium point (EEP). Their stabilities were analyzed by the Routh-Hurwitz stability criterion. Thus we found that the DFEP is stable and the EEP is unstable. We also found that the basic reproduction number of the dynamical system is 0 = (+)(++) which depends on seven parameters. Using the real data collected from study area's population the numerical value of reproduction number is 0 = 0.4964. That is 0 < 1 which implies that the TB disease is not spread. Numerical simulations are performed to validate the theoretical results of our study. The control parameter that can help us to control the spread of the TB disease is transmission rate , with numerical value = 0.4732 . To control the spread of the TB disease and possibly eradicate the disease from the community, the transmission rate needs to be less than 0.4732.