SIMULATION OF DISCRETE-TIME MARKOV CHAIN SUSCEPTIBLE VACCINATED INFECTED RECOVERED SUSCEPTIBLE (DTMC SVIRS) STOCHASTIC EPIDEMIC MODEL ON THE SPREAD OF TUBERCULOSIS DISEASE IN CENTRAL JAVA

Abstract

One of the infectious diseases that is still a public health challenge in Indonesia is tuberculosis (TB). This study is intended to model the spread of TB disease in Central Java using the Discrete-Time Markov Chain Susceptible Vaccinated Infected Recovered Susceptible (DTMC SVIRS) stochastic epidemic model. This model categorizes the population into four groups: susceptible, vaccinated, infected, and recovered. The transition probabilities between these groups are obtained based on transmission, vaccination, vaccine failure, vaccine effectiveness, recovery, and waning immunity rates. Parameter values were estimated using TB data from the Central Java Health Profile. Simulations were performed with different transmission rate treatments to analyze their effect on epidemic dynamics. The results show that the higher transmission rate, the longer it takes to reach the peak of epidemic and the more individuals are infected, which indicates a more serious epidemic. The model predicts that the epidemic will continue timelessly due to waning immunity and remaining susceptibility. The SVIRS model provides an overview of the spread of TB in Central Java.