Sensitivity Analysis and Optimization of Stochastic Epidemic Models under Parameter Uncertainty

2026-07-01

AI Summary

This study addresses sensitivity analysis and intervention optimization for discrete-time stochastic epidemic models under parameter uncertainty. The authors propose an unbiased gradient estimator tailored to posterior parameter distributions obtained via Bayesian calibration, enabling quantification of how vaccination coverage and contact rates influence the total number of infections over a finite time horizon. By integrating stochastic simulation with gradient estimation, the method achieves low variance—particularly outperforming finite-difference approaches in estimating derivatives with respect to contact rates—and reveals substantial discrepancies in sensitivity between the stochastic model and its deterministic limit. The findings indicate that parameter uncertainty attenuates indirect effects such as herd immunity, leading to more conservative optimal intervention strategies and an overall reduction in sensitivity.

Abstract

To address sensitivity analysis and optimization for a discrete-time stochastic epidemic model, we derive unbiased gradient estimators that accommodate uncertainties represented as distributions over the parameters of interest, such as those arising from Bayesian calibration. Specifically, we estimate the sensitivity of total infections over a finite time horizon with respect to the proportion immunized ($v$) and the contact rate ($β$). Comparing the proposed estimators with deterministic limit approximations based on large populations reveals differences due to the finite population and time horizon. The estimators exhibit lower variance than finite-difference estimators for the derivative with respect to $β$, but higher variance for the derivative with respect to $v$. Simulation experiments indicate parameter uncertainty reduces sensitivity to the parameters of interest. In particular, indirect effects of vaccination, such as herd immunity, are less pronounced compared to when parameters are known. For optimization problems balancing intervention and infection costs, incorporating parametric uncertainty leads to more conservative policies.

Problem

• sensitivity analysis
• stochastic epidemic models
• parameter uncertainty
• optimization
• vaccination

Innovation

• stochastic epidemic model
• sensitivity analysis
• gradient estimation
• parameter uncertainty
• optimization under uncertainty