Identifying the number of unreported cases in SIR epidemic models

Abstract

An SIR epidemic model is analysed with respect to the identification of its parameters and initial values, based upon reported case data from public health sources. The objective of the analysis is to understand the relationship of unreported cases to reported cases. In many epidemic diseases the reported cases are a small fraction of the unreported cases. This fraction can be estimated by the identification of parameters for the model from reported case data. The analysis is applied to the Hong Kong seasonal influenza epidemic in New York City in 1968–1969.

Understanding Unreported Cases in the COVID-19 Epidemic Outbreak in Wuhan, China, and the Importance of Major Public Health Interventions

“…For this epidemic, a modeling approach has been developed in [3], which did not consider unreported cases. Our work continues the investigation in [4,5] of the fundamental problem of parameter identification in mathematical epidemic models. We address the following fundamental issues concerning this epidemic: How will the epidemic evolve in Wuhan with respect to the number of reported cases and unreported cases?…”

Modelling the COVID-19 epidemics in Brasil: Parametric identification and public health measures influence

“…Here, as mentioned in the introduction, we first review an analytical parametric identification described in more details in [4][5][6][7], that from the initial phases of the epidemic evolution allows to explicitly obtain the unknown initial conditions of the model, while offering a reliable estimate for the transmission rate at the onset of the epidemy. Nevertheless, even after these estimates, a few other parameters in the model remain uncertain, either due to the specific characteristics of the physical conditions or reaction to the epidemy in each specific region, or due to lack of epidemiological information on the disease itself.…”

“…As explained in previous works employing this model [4][5][6][7], it is assumed that in the early phase of the epidemic, the cumulative number of reported cases grows approximately exponentially, according to the following functional form:…”

“…After fitting this function to the early stages of the epidemic evolution, one may extract the information on the unknown initial conditions, in the form [4][5][6][7]:…”

“…Here, the SIR-type model in [2][3][4][5][6][7] is implemented for the direct problem formulation of the COVID-19 epidemic evolution, adding a time variable parametrization for the fraction of asymptomatic infectious that become reported symptomatic individuals, a very important parameter in the public health measure associated with massive testing and consequent focused isolation. The same analytical identification procedure is maintained for the required initial conditions, as obtained from the early stages exponential behaviour.…”