A simple modification to the classical SIR model to estimate the proportion of under-reported infections using case studies in flu and COVID-19  

作　　者：Leonid Kalachev Jon Graham Erin L.Landguth 

机构地区：[1]Mathematical Sciences,University of Montana,Missoula,USA [2]Center for Population Health Research,School of Public and Community Health Sciences,University of Montana,Missoula,USA

出　　处：《Infectious Disease Modelling》2024年第4期1147-1162,共16页传染病建模（英文）

基　　金：supported by National Institute of General Medical Sciences of the National Institutes of Health,United States(Award numbers P20GM130418 and U54GM104944).

摘　　要：Background:Under-reporting and,thus,uncertainty around the true incidence of health events is common in all public health reporting systems.While the problem of underreporting is acknowledged in epidemiology,the guidance and methods available for assessing and correcting the resulting bias are obscure.Objective:We aim to design a simple modification to the Susceptible e Infected e Removed(SIR)model for estimating the fraction or proportion of reported infection cases.Methods:The suggested modification involves rescaling of the classical SIR model producing its mathematically equivalent version with explicit dependence on the reporting parameter(true proportion of cases reported).We justify the rescaling using the phase plane analysis of the SIR model system and show how this rescaling parameter can be estimated from the data along with the other model parameters.Results:We demonstrate how the proposed method is cross-validated using simulated data with known disease cases and then apply it to two empirical reported data sets to estimate the fraction of reported cases in Missoula County,Montana,USA,using:(1)flu data for 2016e2017 and(2)COVID-19 data for fall of 2020.Conclusions:We establish with the simulated and COVID-19 data that when most of the disease cases are presumed reported,the value of the additional reporting parameter in the modified SIR model is close or equal to one,so that the original SIR model is appropriate for data analysis.Conversely,the flu example shows that when the reporting parameter is close to zero,the original SIR model is not accurately estimating the usual rate parameters,and the re-scaled SIR model should be used.This research demonstrates the role of under-reporting of disease data and the importance of accounting for underreporting when modeling simulated,endemic,and pandemic disease data.Correctly reporting the“true”number of disease cases will have downstream impacts on predictions of disease dynamics.A simple parameter adjustment to the SIR modeling framework can help allev

关 键 词：Modeling of epidemics SIR type models flu and COVID-19 Under-reporting parameter Proportion of reported disease cases 

分 类 号：R563.1[医药卫生—呼吸系统]