How Re-Infections and Newborns Can Impact Visible and Hidden Epidemic Dynamics?

Mathematical modeling allows taking into account registered and hidden infections to make correct predictions of epidemic dynamics and develop recommendations that can reduce the negative impact on public health and the economy. A model for visible and hidden epidemic dynamics (published by the author in February 2025) has been generalized to account for the effects of re-infection and newborns. An analysis of the equilibrium points, examples of numerical solutions, and comparisons with the dynamics of real epidemics are provided. A stable quasi-equilibrium for the particular case of almost completely hidden epidemics was also revealed. Numerical results and comparisons with the COVID-19 epidemic dynamics in Austria and South Korea showed that re-infections, newborns, and hidden cases make epidemics endless. Newborns can cause repeated epidemic waves even without re-infections. In particular, the next epidemic peak of pertussis in England is expected to occur in 2031. With the use of effective algorithms for parameter identification, the proposed approach can ensure effective predictions of visible and hidden numbers of cases and infectious and removed patients.