A modified Susceptible-Infected-Recovered model for observed under-reported incidence data

PLoS One. 2022 Feb 9;17(2):e0263047. doi: 10.1371/journal.pone.0263047. eCollection 2022.

Abstract

Fitting Susceptible-Infected-Recovered (SIR) models to incidence data is problematic when not all infected individuals are reported. Assuming an underlying SIR model with general but known distribution for the time to recovery, this paper derives the implied differential-integral equations for observed incidence data when a fixed fraction of newly infected individuals are not observed. The parameters of the resulting system of differential equations are identifiable. Using these differential equations, we develop a stochastic model for the conditional distribution of current disease incidence given the entire past history of reported cases. We estimate the model parameters using Bayesian Markov Chain Monte-Carlo sampling of the posterior distribution. We use our model to estimate the transmission rate and fraction of asymptomatic individuals for the current Coronavirus 2019 outbreak in eight American Countries: the United States of America, Brazil, Mexico, Argentina, Chile, Colombia, Peru, and Panama, from January 2020 to May 2021. Our analysis reveals that the fraction of reported cases varies across all countries. For example, the reported incidence fraction for the United States of America varies from 0.3 to 0.6, while for Brazil it varies from 0.2 to 0.4.

Publication types

  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Argentina / epidemiology
  • Bayes Theorem
  • Brazil / epidemiology
  • COVID-19 / epidemiology*
  • Chile / epidemiology
  • Colombia / epidemiology
  • Humans
  • Incidence
  • Markov Chains
  • Mexico / epidemiology
  • Panama / epidemiology
  • Peru / epidemiology
  • Stochastic Processes
  • United States / epidemiology

Grants and funding

Research presented in this article was supported by the Laboratory Directed Research and Development program of Los Alamos National Laboratory, projects 20210709ER and 20210043DR. The content is solely the responsibility of the authors and does not necessarily represent the official views of the sponsors. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Los Alamos National Laboratory is operated by Triad National Security, LLC, for the National Nuclear Security Administration of U.S. Department of Energy (Contract No. 89233218CNA000001).