D. Lestari, A. Dhoruri, E.R. Sari
Recently, researchers in the health field are very interesting. The spread of disease begins from the susceptible population become infected population or from infected population become recovered population is necessary to be observed. Tuberculosis is one diseases that can be represented by mathematical model. The transmission is described by using mathematical models as a form of the nonlinear differential equation system. The stages are forming the mathematical model, determining equilibrium point, determining the basic reproduction number (Ro) with Next Generation Matrix method, analysing the stability of equilibrium points by Routh Hurwitz Criteria method, and perform numerical simulation using MAPLE Program based on data from health profile in Yogyakarta area. Based on data of tuberculosis sufferers in Yogyakarta region is still considered to need attention. Vaccines to prevent tuberculosis infection have been given, but there needs to be an optimal vaccine control strategy. So that the number of infected population related to the percentage of vaccine should be given to vulnerable populations affect the spread of disease will not occur. Mathematically, if basic reproduction number less than one, the disease free equilibrium point is local asymptotically stable. It means the disease does not spread. Meanwhile, if the basic reproduction number more than one then the endemic equilibrium point is local asymptotically stable. It means the disease is persisting in the population. Furthermore, the value of the basic reproduction number is influenced by contact rate and vaccination parameter. The greater the rate of contact with the percentage of fixed vaccines, the more the TB infected population. The greater the percentage of the vaccinated population with fixed contact rate parameters, the more decreasing the number of infected populations. © Published under licence by IOP Publishing Ltd.
Department of Mathematics Education, Yogyakarta State University, Indonesia
