On stable parameter estimation and short-term forecasting with quantified uncertainty with application to COVID-19 transmission

Abstract

A novel optimization algorithm for stable parameter estimation and forecasting from limited incidence data for an emerging outbreak is proposed. The algorithm combines a compartmental model of disease progression with iteratively regularized predictor-corrector numerical scheme aimed at the reconstruction of case reporting ratio, transmission rate, and effective reproduction number. The algorithm is illustrated with real data on COVID-19 pandemic in the states of Georgia and New York, USA. The techniques of functional data analysis are applied for uncertainty quantification in extracted parameters and in future projections of new cases.

Reconstruction of incidence reporting rate for SARS-CoV-2 Delta variant of COVID-19 pandemic in the US

“…8 ). This confirms earlier accounts on considerable under-reporting of COVID-19 cases due to the impact of silent transmissions, resulting from a combination of presymptomatic and asymptomatic infections, and the limitations of testing ( Luo et al., 2023 ; Smirnova et al., 2022 ; Tuncer et al., 2022 ). An important goal for our future research is to design a regularized numerical procedure with observation operators connected to a stochastic compartmental model.…”

“…3 . In our numerical simulations with both synthetic and real data, shifted Legendre polynomials are used to project transmission rate, β ( t ), onto a finite dimensional subspace with m = 10 ( Smirnova et al., 2022 ).

Fig.

…”

“…The transmission dynamics of the disease within and between these compartments are then modeled through the implementation of mathematical equations thus helping scholars and decision-makers to mitigate and control emerging epidemics. Over the years, compartmental models have been extensively utilized to study the transmission of infectious diseases such as HIV, influenza, cholera, COVID-19, and others ( He, Peng, & Sun, 2020 ; Kudryashov, Chmykhov, & Vigdorowitsch, 2021 ; Smirnova et al., 2020 , 2022 ). Their ability to quantify the diffusion of diseases and the related intricate systems was instrumental in guiding high-stakes recommendations on public health policies and interventions.…”

“…When COVID-19 spread all over the world ( Li et al., 2020 ), compartmental models came to light as a valuable tool in forecasting of future incidence cases, especially under diverse circumstances involving immunization campaigns, social distancing measures, and the emergence of novel virus strains ( Patalon et al., 2022 ; Smirnova et al., 2022 ). At the onset of COVID-19, when little was know about the disease transmission, a simple SI compartmental model ( Kosmidis & Macheras, 2020 ) was proposed to explain the dynamics of the virus.…”