Analisis Kestabilan Model Penyebaran Penyakit Tuberkulosis Dengan Laju Infeksi Tersaturasi (Stability Analysis of Tubercolosis Spread Diseases Model Considering Saturated Infection Rate)

Abstract

This paper deals with the analysis of tuberculosis disease spread model with saturated infection rate and the treatment effect. We analyze the dynamical behavior of the model to observe the stability peroperty of the model’s equilibrium points. The Routh-Hurwitz Theorem is used to analyze the local stability peroperty of the free disease equilibrium point whereas Transcritical Bifurcation principle is used to analyze the local stability property of the endemic equilibrium pont. The result show that the local stability property of the equilibrium points is depending on the basic reproduction number value calculated by the next generation matrix (NGM). When the basic reproduction number is less than 1, the free disease equilibrium point is locally asymptotically stable, and when it is greater than 1, the endemic equilibrium point is locally asymptotically stable. Numeric simulation results were presented to describe the evolution of the dynamical behavior and to understand the treatment effectiveness for the tuberculosis disease of the population. From the simulation results, it was derived that the treatment in the infected subpopulation had a better result than the one in latent.