Prediction of Corona Lockdowns Using a Semi-Markov Poisson-Weibull-Wiener Framework (SILENT-COVID Model)

Abstract

Background: COVID-19 lockdowns occurred intermittently and unpredictably, reflecting stochastic epidemic shocks and healthcare pressures. Traditional epidemic models inadequately capture such intervention dynamics. Aim: To develop and validate the SILENT-COVID model, a novel statistical framework using Poisson shocks, Weibull durations, and semi-Markov processes to predict the initiation and duration of COVID-19 lockdowns. Methods: Synthetic epidemic data were generated with covariates including mobility, holiday gatherings, and ICU load. Lockdown initiation was modeled as a Poisson shock process with covariate-dependent intensity, while durations followed a Weibull distribution linked to ICU stress. Daily cases were simulated using state-dependent Negative Binomial emissions. Parameters were estimated through an Expectation-Maximization algorithm with explicit-duration Forward-Backward recursion. Results: The model closely recovered true parameter values for initiation hazards, duration distributions, and emission means. Mobility and holiday effects significantly increased the hazard of lockdown initiation, and higher ICU load prolonged lockdown durations. Forecasting yielded a 41% probability of at least one lockdown start within 21 days. Conclusion: SILENT-COVID offers a robust and interpretable statistical framework for forecasting lockdown initiation and duration. By combining stochastic initiation, covariate-linked duration modeling, and realistic epidemic emission structures, it provides decision-makers with probabilistic forecasts to balance epidemiological needs and socio-economic costs.