Efficient calibration for imperfect epidemic models with applications to the analysis of COVID-19

TL;DR

This paper introduces an efficient, asymptotically consistent estimator for calibrating imperfect epidemic models, improving parameter estimation accuracy for COVID-19 analysis across multiple countries.

Contribution

A novel estimator that outperforms least squares in efficiency and variance, specifically designed for imperfect epidemic models like SEIR used in COVID-19 analysis.

Findings

The new estimator achieves semiparametric efficiency.

Application to COVID-19 data reveals key epidemiological parameters.

Improved parameter estimates inform public health strategies.

Abstract

The estimation of unknown parameters in simulations, also known as calibration, is crucial for practical management of epidemics and prediction of pandemic risk. A simple yet widely used approach is to estimate the parameters by minimizing the sum of the squared distances between actual observations and simulation outputs. It is shown in this paper that this method is inefficient, particularly when the epidemic models are developed based on certain simplifications of reality, also known as imperfect models which are commonly used in practice. To address this issue, a new estimator is introduced that is asymptotically consistent, has a smaller estimation variance than the least squares estimator, and achieves the semiparametric efficiency. Numerical studies are performed to examine the finite sample performance. The proposed method is applied to the analysis of the COVID-19 pandemic for 20 countries based on the SEIR (Susceptible-Exposed-Infectious-Recovered) model with both deterministic and stochastic simulations. The estimation of the parameters, including the basic reproduction number and the average incubation period, reveal the risk of disease outbreaks in each country and provide insights to the design of public health interventions.