Analisis Sensitivitas dan Kestabilan Global Model Pengendalian Tuberkulosis dengan Vaksinasi, Latensi dan Perawatan Infeksi

Abstract

Tuberculosis is an infectious disease caused by the bacterium Mycobacterium tuberculosis which attacks the lungs. Tuberculosis or TB is one of the diseases with the highest mortality rate in the world. In this article, we will examine the sensitivity and global stability analysis of the tuberculosis control model with vaccination, latency and infection treatment. In this model, the population is divided into 5 compartments, namely the immunized population (M), susceptible population (S), infected population with latent TB (L), infected population with active TB (I) and the recovered population (R).  The equilibrium point, local and global stability, basic reproduction number R0 is analyzed along with sensitivity analysis to see the effect of parameter values on the basic reproduction number R0. From the analysis and simulation result, it is found that there are two parameters that have the most influence on the spread of tuberculosis, namely the recovery rate of latent TB and the infection rate of active TB. If the recovery rate of latent TB is higher than the infection rate of active TB infection, then the disease will gradually disappear from the population, whereas if the recovery rate of latent TB is lower than the infection rate of active TB, the disease will spread within the population.