Analyzing the transmission dynamics of tuberculosis in Kaduna Metropolis, Nigeria

A mathematical model for the transmission dynamics of tuberculosis in Kaduna metropolis, is formulated and analysed. For the prevalence of the disease, the model was considered in proportions of susceptible, exposed, infectious and recovered compartments. The disease-free equilibrium (DFE) and Endemic Equilibrium (EE) states of the model in proportions were obtained and DFE state was used to compute the basic reproduction number 0, as important threshold whose values allow to establish whether an infection will spread in a population or not. The stability analysis shows that the disease-free equilibrium is locally and globally asymptotically stable whenever the basic reproduction number is less than unity using Routh – Hurwitz stability criterion and Lyapunov function respectively. It is further proved using Routh-Hurwitz that the endemic equilibrium state is locally asymptotically stable whenever the basic reproduction number is greater than unity. The computed results of the basic reproduction number 0 estimated to be 1.0623, as well as the stability analysis revealed that tuberculosis infection will remain endemic (persist) in Kaduna metropolis. Furthermore, effective control measures such as expanded and regular immunization campaign will decrease the infection burden