  Nowcasting and forecasting of epidemic spreading rely on incidence series of
reported cases to derive the fundamental epidemiological parameters for a given
pathogen. Two relevant drawbacks for predictions are the unknown fractions of
undocumented cases and levels of nonpharmacological interventions, which span
highly heterogeneously across different places and times. We describe a simple
data-driven approach using a compartmental model including asymptomatic and
presymptomatic contagions that allows to estimate both the level of
undocumented infections and the value of effective reproductive number R t from
time series of reported cases, deaths, and epidemiological parameters. The
method was applied to epidemic series for COVID-19 across different
municipalities in Brazil allowing to estimate the heterogeneity level of
under-reporting across different places. The reproductive number derived within
the current framework is little sensitive to both diagnosis and infection rates
during the asymptomatic states. The methods described here can be extended to
more general cases if data is available and adapted to other epidemiological
approaches and surveillance data.
