PARAMETERS ESTIMATION OF DISCRETE TIME MARKOV CHAIN SUSCEPTIBLE INFECTED RECOVERED (DTMC SIR) EPIDEMIC MODEL CASE STUDY : THE SPREAD OF TUBERCULOSIS IN INDONESIA

Abstract

An epidemic is the rapid spread of disease that arises in several individuals in region at a certain time. A susceptible infected recovered (SIR) epidemic model describes the pattern of spread of disease with characteristics susceptible individuals who interact with infected individuals can be infected by a particular disease, and after recovery they will have permanent immunity. A SIR epidemic model that studies changes in the number of infected individuals in discrete time is called a discrete time Markov chain susceptible infected recovered (DTMC SIR) epidemic model. This study aims to estimate the parameters of the discrete time Markov chain susceptible infected recovered (DTMC SIR) epidemic model using the maximum likelihood method and to apply to the case of tuberculosis transmission in Indonesia. The method used in this research is estimate the parameters of the discrete time Markov chain susceptible infected recovered (DTMC SIR) epidemic model by study theoretical references that is relevant then to apply to the case of tuberculosis transmission in Indonesia. The result of this study describes that tuberculosis in Indonesia has contact rate β = 0, 1614 and recovery rate γ = 0, 1377. Based on result tuberculosis will continue to exist and epidemic has not over until 2039.