Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China

In this paper we develop a mathematical model for the spread of the coronavirus disease 2019 (COVID-19). We use a compartmental model (but not a SIR, SEIR or other general purpose model) and take into account the known special characteristics of this disease, as the existence of infectious undetected cases. We study the particular case of China (including Chinese Mainland, Macao, Hong-Kong and Taiwan, as done by the World Health Organization in its reports about COVID-19), the country spreading the disease, and use its reported data to identify the modelparameters, which can be of interest for estimating the spread of COVID-19 in other countries. The model is also able to estimate the needs of beds in hospitals for intensive care units. Finally, we also study the behavior of the outputs returned by our model when considering incomplete data (by truncating them at some dates before and after the peak of daily reported cases). By comparing those results with real observation we can estimate the error produced by the model when identifying the parameters at early stages of the epidemic