New Reproduction Numbers for Epidemics with the Hidden Cases, Re-Infections, and Newborns
Article In Press | Published on: March 28, 2026
Volume: 3, Issue: 1
1. Institute of Hydromechanics, National Academy of Sciences of Ukraine, Kyiv, Ukraine. Isaac Newton Institute for Mathematical Sciences, Cambridge, UK.
Corresponding Author: Igor Nesteruk, Institute of Hydromechanics, National Academy of Sciences of Ukraine, Kyiv, Ukraine. Isaac Newton Institute for Mathematical Sciences, Cambridge, UK.
Citation: I. Nesteruk. (2026). New Reproduction Numbers for Epidemics with the Hidden Cases, Re-Infections, and Newborns. Journal of Bio-Med and Clinical Research. RPC Publishers. 3(1),
Copyright: © 2026 Igor Nesteruk, this is an open-Access article distributed under the Terms of the Creative Commons Attribution License, which permits unrestricted use, Distribution, and reproduction in any medium, provided the original author and source are credited.
Abstract
Real-time assessments of reproduction numbers are crucial for timely responses to the changes in epidemic dynamics. Known effective reproduction numbers Rt 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 Rt 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.
Keywords
reproduction numbers mathematical modeling of infectious diseases SIR model COVID-19 pandemic COVID-19 in Austria COVID-19 in Tanzania real-time estimationsReferences
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