STUDY OF TUBERCULOSIS TRANSMISSION DYNAMICS USING SIR EPIDEMIC MODEL WITH THREE TYPES OF POPULATION RECRUITMENT RATE

Abstract

This study considers the basic SIR model with three distinct population growth rates to model the tuberculosis transmission dynamics in Kazakhstan. The local stability of disease-free, endemic and extinction equilibrium points of the the models was examined, and the transcritical bifurcation scenario was observed. The effect of growth type on the epidemiological situation in the country was observed through the dynamical analysis and numerical simulations using the data retrieved from the Unified National Electronic Health System (UNEHS). Numerical results reported the basic reproduction number of each of the models to be R0 < 1. Numerical findings support theoretical results. It was revealed that tuberculosis dynamics is approaching its disease-free equilibrium state with R0 < 1, as it was verified by the stability analysis of all three models. SIR model with logistic recruitment rate was proven to give the most favorable results for the epidemic situation in the country.