Parameter estimation and analysis on SIS-SEIS types model of tuberculosis transmission in East Java Indonesia

Abstract

In this work, the parameter estimation of the SIS-SEIS types of Tuberculosis (TB) model is considered based on the data of TB-infected cases in East Java Province, Indonesia. We utilize the combination of the performance index approach in the optimal control theory and genetic algorithm to estimate the TB model parameters. Two basic reproduction numbers were also determined as well. The sensitivity analysis is performed to establish the most significant parameters on the TB model transmission dynamics. Based on the parameter estimation results of the SIS-SEIS types TB models, the basic reproduction numbers for both models are greater than one which means that, TB disease will persist in the province. Furthermore, the simulation of the TB model is carried out using the parameter estimation results which confirms that the spread of TB is ongoing in East Java Indonesia, and is yet to reach its endemicity.