Estimating Unobservable States in Stochastic Epidemic Models with Partial Information

TL;DR

This paper develops a method to estimate unobservable states in stochastic epidemic models using extended Kalman filtering, aiding in nowcasting and addressing the dark figure problem, with applications to COVID-19.

Contribution

It introduces an extended Kalman filter approach for estimating unobservable epidemic states in stochastic models with partial data, improving nowcasting accuracy.

Findings

Effective estimation of unobservable states demonstrated in COVID-19 simulations

Enhanced nowcasting capabilities for epidemic modeling with partial information

Validation of the method's accuracy through numerical simulations

Abstract

This article investigates stochastic epidemic models with partial information and addresses the estimation of current values of not directly observable states. The latter is also called nowcasting and related to the so-called "dark figure" problem, which concerns, for example, the estimation of unknown numbers of asymptomatic and undetected infections. The study is based on Ouabo Kamkumo et al. (2025), which provides detailed information about stochastic multi-compartment epidemic models with partial information and various examples. Starting point is a description of the state dynamics by a system of nonlinear stochastic recursions resulting from a time-discretization of a diffusion approximation of the underlying counting processes. The state vector is decomposed into an observable and an unobservable component. The latter is estimated from the observations using the extended Kalman filter approach in order to take into account the nonlinearity of the state dynamics. Numerical simulations for a Covid-19 model with partial information are presented to verify the performance and accuracy of the estimation method.