New reproduction numbers for epidemics with the hidden cases, re-infections, and newborns

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