Reproduction numbers for epidemics with hidden cases, re-infections and newborns

Real-time assessments of the reproduction rates are crucial for timely responses to changes in epidemic dynamics. Known effective reproduction numbers R _t are based on registered (visible) cases despite that asymptomatic and unregistered patients occur in all epidemics and need to be corrected to take into account the number of hidden cases. Since newborns and re-infections significantly affect the dynamics of epidemics, they should also be taken into account in calculations of R _t and recently proposed reproduction rates R _τ - the ratios of the real numbers of infectious persons at different moments of time. The numbers of cases generated by symptomatic and asymptomatic patients were introduced, estimated using a novel mathematical model and compared with the results of classical SIR (Susceptible-Infectious-Removed) model for the COVID-19 pandemic dynamics in Austria. Reproduction rates R _τ were estimated with the use of visible accumulated numbers of COVID-19 cases in Austria and Tanzania (including real-time approach). The proposed methods for calculating reproduction numbers may better reflect the COVID-19 pandemic dynamics than the results listed by John Hopkins University.