SIR Model Analysis of Tuberculosis, Leprosy, HIV, Dengue, and COVID-19 Transmission in Madura

Infectious diseases pose a significant public health challenge in the Madura region, necessitating a clear understanding of their transmission dynamics for effective control strategies. This study aims to apply the Susceptible-Infected-Removed (SIR) model to comparatively analyze the transmission dynamics of five major infectious diseases in Madura-Tuberculosis (TB), Leprosy, HIV, Dengue Fever, and COVID-19 using 2023 case data. A quantitative, comparative modeling approach was employed using data from 18 sub-districts, involving descriptive/spatial analysis, inter-disease correlation, and dynamic SIR modeling to estimate epidemiological parameters (transmission rate , recovery rate $\gamma$) and the Basic Reproduction Number (R0). Intervention scenarios were also simulated for TB. The results identified Tuberculosis as the predominant health burden (1,641 total cases), spatially concentrated in hotspots like Bangkalan sub-district (249 cases). All five diseases showed epidemic potential (R0 > 1), with HIV exhibiting the highest R0 (10.0) due to its extremely low recovery rate (  =0.01$), followed by TB and Leprosy (R0=4.0) COVID-19 (R0=3.33), and Dengue Fever (R0=1.50). A strong positive correlation (0.84) was found between TB and HIV cases at the sub-district level. Intervention simulations for TB demonstrated that a 50% reduction in the transmission rate ( ) could reduce the peak infection load by over 60%. This study concludes that while TB is the largest case burden, HIV has the highest epidemic potential, and their strong correlation necessitates integrated, spatially-targeted (sub-district level) control strategies.