Sliding mode control with stochastic modeling and mobility interaction for managing epidemic spread in high-population regions

Managing infectious disease transmission in high-mobility regions is a critical challenge due to dynamic population interactions and elevated transmission risks. This study develops a stochastic epidemiological model to simulate disease spread between two densely populated provinces in Indonesia, Jakarta and West Java. A robust sliding mode control (SMC) framework is proposed and integrated with an Extended Kalman Filter (EKF) to estimate key epidemiological parameters in real time using limited observable data. The proposed framework functions as a theoretical and simulation-based tool to evaluate the potential effects of vaccination and isolation strategies. Although full-state variables are not directly measurable in practice, the EKF allows for the estimation of unobservable parameters, thereby enabling control analysis under uncertainty. Simulation results demonstrate that the SMC strategy significantly reduces infection levels in both provinces, achieving reductions of 84.45 % and 63.94 % in Jakarta, and 98.83 % and 58.35 % in West Java, for the original and Omicron variants, respectively. By incorporating stochasticity, the model captures natural fluctuations and mismatched uncertainties in epidemic progression. This work contributes a conceptual control framework that integrates EKF and SMC for managing stochastic epidemic systems. While the approach is not directly implementable for real-time policymaking, it offers valuable insight into disease dynamics and the potential impact of control strategies under limited observability. These findings support the use of data-driven control simulations for scenario evaluation and policy guidance in complex, uncertain epidemic settings.