An application of the ensemble Kalman filter in epidemiological modelling.

Rajnesh Lal,Weidong Huang,Zhenquan Li,Andrea Zanini

doi:10.1371/journal.pone.0256227

Rajnesh Lal, Weidong Huang + Show 2 more

Open Access

https://doi.org/10.1371/journal.pone.0256227

Copy DOI

Abstract

Since the novel coronavirus (COVID-19) outbreak in China, and due to the open accessibility of COVID-19 data, several researchers and modellers revisited the classical epidemiological models to evaluate their practical applicability. While mathematical compartmental models can predict various contagious viruses’ dynamics, their efficiency depends on the model parameters. Recently, several parameter estimation methods have been proposed for different models. In this study, we evaluated the Ensemble Kalman filter’s performance (EnKF) in the estimation of time-varying model parameters with synthetic data and the real COVID-19 data of Hubei province, China. Contrary to the previous works, in the current study, the effect of damping factors on an augmented EnKF is studied. An augmented EnKF algorithm is provided, and we present how the filter performs in estimating models using uncertain observational (reported) data. Results obtained confirm that the augumented-EnKF approach can provide reliable model parameter estimates. Additionally, there was a good fit of profiles between model simulation and the reported COVID-19 data confirming the possibility of using the augmented-EnKF approach for reliable model parameter estimation.

Highlights

The outbreak of the novel coronavirus disease (COVID-19) in early December 2019 in Wuhan, China, attracted many researchers to evaluate the dynamics of infectious COVID-19 virus using various mathematical models [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]
Li et al [11] used an SEIR model based on deterministic assumptions and applied the Ensemble Adjustment Kalman Filter (EAKF) to estimate model parameters using the data of China
We evaluated an augmented Ensemble Kalman Filter’s capability to estimate time-varying model parameters using two types of observational data, i.e., synthetic data and with COVID-19 data of Hubei province, China

Summary

Introduction

The outbreak of the novel coronavirus disease (COVID-19) in early December 2019 in Wuhan, China, attracted many researchers to evaluate the dynamics of infectious COVID-19 virus using various mathematical models [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] Mathematical compartmental models, such as SIR (Susceptible—Infectious—Recovered) [18, 19], in epidemiology, are generally expressed by a system of ordinary differential equations (ODE). Recent studies on COVID-19 modelling includes using the basic SIR model [12, 18, 19] or its extension (modified) versions such as SEIR (Susceptible—Exposed—Infectious—Recovered) [7, 10, 11, 19,20,21], SIRD (Susceptible— Infectious—Recovered—Dead) [1,2,3,4, 16, 17, 22] and SEIRD (Susceptible—Exposed—Infected —Recovered—Dead) [13,14,15].

Methods

Findings

Discussion

Conclusion