A simple model for the analysis of epidemics based on hospitalization data

Abstract

An epidemiological model with a minimal number of parameters is introduced and its structural and practical identifiabity is investigated both analytically and numerically. The model is useful when a high percentage of unreported cases is suspected, hence only hospitalization data are used to fit the model parameters and calculate the basic reproductive number $R_0$ and the effective reproductive number $R_e$. As a case study, the model is used to study the initial surge and the Omicron wave of the COVID-19 epidemic in Belgium. It was found that the reported cases largely underestimate the actual cases, and the estimated values of $R_0$ are consistent with other studies. The exact number of people initially in each epidemiological class is also considered unknown and was estimated directly and not considered as additional parameters to be fitted. Furthermore, the parameter fitting was performed with two different available data sets, in order to improve confidence. The methodology presented here can be easily modified to study outbreaks of diseases for which little information on confirmed cases is known a priori or when the available information is largely unreliable.