Analysis of Tuberculosis (TB) Case Patterns Using the Hurst Exponent Fractal Dimension Method in North Sumatra

Abstract

Tuberculosis is a chronic infectious disease caused by Mycobacterium tuberculosis. This bacteria is commonly known as Acid Resistant Bacilli (BTA). The Hurst Exponent Fractal Dimension method was used in this work to identify the properties of time series data and fractal patterns in tuberculosis (TB) patients. The Hurst exponent method is calculated by the smallest prime factor that divides the data (pi). This fractal dimension's value is calculated using the Hurst exponent value. Time series data is classified into three groups depending on computation results: random, anti-persistence, and persistence. In the study, three data ranges (n) were obtained from the observed data, namely tuberculosis (TB) patients from July to December 2023 (174, 87, and 29). The value of the Hurst exponent obtained was 0,475 (0<H<0,5) and the value of the fractal dimension obtained was 1,525 (1,5<H<2). Based at the Hurst exponent value and fractal dimension fee, it indicates that the records is anti-persistence. Anti-persistence means that the time series data of cases of tuberculosis (TB) patients which if the data increases at one time, it tends to decrease at the next time and if the data decreases at one time, it tends to increase at the next time.