Stability analysis of MSEITR model on the spread of tuberculosis disease using treatment with DOTS strategy
Tuberculosis (TB) is an infectious disease that can cause death. Indoneisa is the third country with the highest number of TB patients in the world after India and China. This study discusses the MSEITR mathematical model on the spread of TB disease with the DOTS strategy. The purpose of this research is to form a mathematical model, find the equilibrium point and basic reproduction number, analyze the stability, and simulate the model with maple. The analysis resulted in a DFE and endemic equilibrium point and . From these results it is obtained theorem 1 if then there is only a positive DFE point which is positive and if then there is a DFE and endemic equilibrium point which has a positive value and theorem 2 is obtained which is a DFE point is locally asymptotically stable if and the endemic equilibrium point is locally asymptotically stable if . Furthemore, simulation the model using maple obtained several facts, is the smaller the value of the rate of decline in passive immunity and the probability of individuals infected with TB and the greater the value of the increase in the rate of passive immunity , the rate of latent TB individuals and the rate of active TB individuals undergoing DOTS treatment will accelerate the individual growth rate in each stable subpopulation at the DFE point, menaing that TB disease will disappear faster from the population.