On the Estimation of the Time-Dependent Transmission Rate in Epidemiological Models

TL;DR

This paper develops a nonparametric SEIR model with a time-varying transmission rate, employing inverse problem regularization to accurately estimate disease spread dynamics from data, including COVID-19.

Contribution

It introduces a novel inverse problem framework for nonparametric SEIR models with time-dependent parameters, proving theoretical properties and demonstrating practical estimation accuracy.

Findings

Model accurately estimates time-varying transmission rates.

The inverse problem approach ensures solution stability.

Numerical examples validate the model's effectiveness.

Abstract

The COVID-19 pandemic highlighted the need to improve the modeling, estimation, and prediction of how infectious diseases spread. SEIR-like models have been particularly successful in providing accurate short-term predictions. This study fills a notable literature gap by exploring the following question: Is it possible to incorporate a nonparametric susceptible-exposed-infected-removed (SEIR) COVID-19 model into the inverse-problem regularization framework when the transmission coefficient varies over time? Our positive response considers varying degrees of disease severity, vaccination, and other time-dependent parameters. In addition, we demonstrate the continuity, differentiability, and injectivity of the operator that link the transmission parameter to the observed infection numbers. By employing Tikhonov-type regularization to the corresponding inverse problem, we establish the existence and stability of regularized solutions. Numerical examples using both synthetic and real data illustrate the model's estimation accuracy and its ability to fit the data effectively.