Analisis Dinamik Model Penularan Kolera dengan Mempertimbangkan Risiko Individu dan Intervensi Karantina

Abstract

This study develops an SIQRB mathematical model to analyze the transmission dynamics of cholera by incorporating individual risk stratification and quarantine interventions. The model consists of six human compartments, including high- and low-risk susceptible individuals, infected individuals from each risk group, quarantined individuals, and recovered individuals, along with one environmental compartment representing the concentration of Vibrio cholerae. This framework allows a comprehensive analysis of the interaction between human populations and environmental factors in disease transmission. The stability analysis shows that the disease-free equilibrium is locally asymptotically stable when the basic reproduction number (R₀) is less than one (R₀ < 1), and becomes unstable when R₀ exceeds one (R₀ > 1), indicating the potential for endemic conditions. Sensitivity analysis identifies the most influential parameters affecting R₀, namely the immigration rate (Λ), the environmental transmission rate (βb), and the bacterial shedding rate (ξ). These parameters significantly contribute to the increase in disease transmission. Numerical simulations confirm the analytical findings, showing that higher values of these parameters lead to increased numbers of infected individuals and higher environmental bacterial concentrations. Conversely, environmental-based control strategies—such as mobility restrictions, improved sanitation, and water disinfection—are effective in reducing R₀ below one. Therefore, this study highlights the critical importance of environmental interventions in controlling cholera transmission and preventing long-term endemicity.