Basic Reproduction Number of Tuberculosis Spread Model in Lamongan With DOTS Strategy

Abstract

Tuberculosis (TB) will be a serious threat if not handled quickly and appropriately. The relatively long treatment in time and the high risk of death is a challenge in controlling the spread of this disease. The DOTS (Directly Observed Treatment Short-course) strategy is considered capable of controlling the spread of TB because of the high success rate, reaching 91%. The mathematical model of the spread of TB has been widely studied to determine the potential for the spread of this disease in an area. The purpose of this study is to build a model of tuberculosis spread in Lamongan to determine the rate of its spread and to predict whether it will be endemic or not. Using disease spread mathematical model type SEITR, this research has examined based on 2018 and 2019 data from the Lamongan health office then simulates the result. The research begins with the construction of the model followed by a stability analysis of the model by determining the basic reproduction number ( ), which is simulated after the parameter approach was carried out. From the simulation results, the result shows that means that TB will not endemic in Lamongan. Besides, the results of the effect of parameter ω on I(t) were obtained, which concluded that seeking and treating active TB alone would only reduce infected individuals but not reduce the length of time TB spread. Identification of the effect of parameter φ on I(t) has also been carried out which results in the conclusion that more treatment for susceptible individuals, in addition to reducing the number of infected individuals, will also reduce the length of time TB spreads in that area. This result will be a good suggestion for the government to deal faster with tuberculosis transmission.

Keywords

• tuberculosis model
• dots
• model seitr
• basic reproduction number r_0