How re-infections and newborns can change the visible and hidden epidemic dynamics?

A recently proposed model for visible and hidden epidemic dynamics has been generalized to account for the effects of re-infections and newborns. The set of five differential equations and initial conditions contain 13 unknown parameters. The analysis of the equilibrium points, the examples of numerical solutions and comparisons with dynamics of real epidemics are provided. It was shown that equilibriums exist when the influence of re-infections or newborns can be neglected. A stable quasi-equilibrium for the particular case of almost completely hidden epidemics was 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. The newborns can cause repeating epidemic waves even without re-infections. In particular, numerical simulations of the pertussis epidemic in England in 2023 and 2024 demonstrated that the next epidemic peak is expected in 2031. The proposed model can be recommended for calculations and predictions of visible and hidden numbers of cases, infectious and removed patients. With the use of effective algorithms for parameter identification, the accuracy of method could be rather high.