ANALYSIS OF TUBERCULOSIS DISEASE SPREAD MODEL WITH SATURATED INFECTION RATE AND THE TREATMENT EFFECT

Abstract

This paper deals with analysis of tuberculosis disease spread model with saturated infection rate and the treatment effect. It analyzes the dynamical behavior of the model to see the local stability equilibrium. The Routh-Hurwitz Theorem is used to analyze the local stability equilibrium in free disease equilibrium point and the Transcritical Bifurcation principle is used to prove the endemic equilibrium for the local stability of the constructed model. The local stability equilibrium state exists depending on the basic reproduction number R0 which is generated by the next generation matrix (NGM). When R0 is less than 1, it means that non-endemic equilibrium point is locally asymptotically stable, while R0 exceed 1, it means the endemic equilibrium point is locally asymptotically stable. The numeric simulation is presented to describe the evolution of the dynamical behavior and also to understand the treatment effectiveness for the tuberculosis disease of the population. Keywords: Tuberculosis, Saturated Incidence Rate, Routh-Hurwitz Criteria, Transcritical Bifurcation.