Estimation of Time-Dependent Transmission Rate for COVID-19 SVIRD Model Using Predictor–Corrector Algorithm

Abstract

Stable parameter estimation is an ongoing challenge within biomathematics, especially in epidemiology. Oftentimes epidemiological models are composed of large numbers of equations and parameters. Due to high dimensionality, classic parameter estimation approaches, such as least square fitting, are computationally expensive. Additionally, the presence of observational noise and reporting errors that accompany real-time data can make these parameter estimation problems ill-posed and unstable. The recent COVID-19 pandemic highlighted the need for efficient parameter estimation tools. In this chapter, we develop a modified version of a regularized predictor–corrector algorithm aimed at stable low-cost reconstruction of infectious disease parameters. This method is applied to a new compartmental model describing COVID-19 dynamics, which accounts for vaccination and immunity loss (from vaccinated and recovered populations). Numerical simulations are carried out with synthetic and real data for COVID-19 pandemic. Based on the reconstructed disease transmission rates (and known mitigation measures), observations on historical trends of COVID-19 in the states of Georgia and California are presented. Such observations can be used to provide insights into future COVID policies.