The temporal evolution of second and subsequent waves of the Covid-19 pandemic is investigated. Analytic expressions for the peak time and asymptotic behaviors, early doubling time, late half decay time, and a half-early peak law, characterizing the dynamical evolution of number of cases and fatalities are derived, where the pandemic evolution exhibiting multiple waves is described by the semi-time SIR model. The asymmetry of the epidemic wave and its exponential tail are affected by the initial conditions; a feature that has no analogue in the all-time SIR model. Our analysis reveals that the immunity is very strongly increasing during the 2nd wave. Wave-specific SIR parameters describing infection and recovery rates we find to behave in a similar fashion. Still, an apparently moderate change of their ratio can have significant consequences. As we show, the probability for an additional wave is however low in several countries due to the fraction of immune inhabitants at the end of the 2nd wave, irrespective the currently ongoing vaccination efforts. We compare with alternate approaches and data available at the time of submission. Most recent data serves to demonstrate the successful forecast and high accuracy of the SIR-model in predicting the evolution of pandemic outbreaks.

Measured data has been collected from the open source stated in the manuscript and processed using in-house perl and python scripts. The enclosed data contains all the numbers that were used to create figures. Each line contains the x and y coordinates of a data point. Datasets are named after the figure and subfigure.