Are the SIR and SEIR models suitable to estimate the basic reproduction number for the CoViD-19 epidemic?

The transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) becomes pandemic but presents different incidences in the world. Mathematical models were formulated to describe the coronavirus disease 2019 (CoViD-19) epidemic in each country or region. At the beginning of the pandemic, many authors used the SIR (susceptible, infectious, and recovered compartments) and SEIR (including exposed compartment) models to estimate the basic reproduction number R ₀ for the CoViD-19 epidemic. These simple deterministic models assumed that the only available collection of the severe CoViD-19 cases transmitted the SARS-CoV-2 and estimated lower values for R ₀ , ranging from 1.5 to 3.0. However, the major flaw in the estimation of R ₀ provided by the SIR and SEIR models was that the severe CoViD-19 patients were hospitalized, and, consequently, not transmitting. Hence, we proposed a more elaborate model considering the natural history of CoViD-19: the inclusion of asymptomatic, pre-symptomatic, mild and severe CoViD-19 compartments. The model also encompassed the fatality rate depending on age. This SEAPMDR model estimated R ₀ using the severe CoViD-19 data from São Paulo State (Brazil) and Spain, yielding higher values for R ₀ , that is, 6.54 and 5.88, respectively. It is worth stressing that this model assumed that severe CoViD-19 cases were not participating in the SARS-CoV-2 transmission chain. Therefore, the SIR and SEIR models are not suitable to estimate R ₀ at the beginning of the epidemic by considering the isolated severe CoViD-19 data as transmitters.