Analysis and simulation of mathematical model for the spread of tuberculosis use SEIT type with DOTS strategy

Abstract

Tuberculosis is a contagious disease caused by mycobacterium tuberculosis, which is transmitted through aerosols or droplet nuclei into the air when a person coughs, sneezes, or talks and is then inhaled through the airway. In this study, a mathematical model will be formulated to describe the spread of tuberculosis with the DOTS strategy using the SEIT type epidemic model. Furthermore, the obtained mathematical model will determine the type of stability, look for the basic reproduction number (R0), then simulate the model using MatLab. From the analysis of the model carried out, it was obtained two equilibrium points, namely the disease-free equilibrium point F0=(S0,E0,I0,T0)=(αμ,0,0,0) and the endemic equilibrium point F1 (S*, E*, I*, T*). By using the Routh-Hurwitz criterion, it is obtained that the type of equilibrium from the two equilibrium points is asymptotically stable. The model analysis carried out also produces a basic reproduction number (R0) whereby, R0 > 1 is obtained or the spread of tuberculosis is endemic. Furthermore, the model simulation is carried out using MatLab software with a variation of the parameter value ω (rate of active tuberculosis patients undergoing treatment with the DOTS strategy), the higher the parameter value ω, the less the spread of tuberculosis is.