  While understanding of periodic recurrent waves of Covid-19 epidemics would
aid to combat the pandemics, quantitative analysis of data over a two years
period from the outbreak, is lacking. The complexity of Covid-19 recurrent
waves is related with the concurrent role of i) the containment measures
enforced to mitigate the epidemics spreading ii) the rate of viral gene
mutations, and iii) the variable immune response of the host implemented by
vaccination. This work focuses on the effect of massive vaccination and gene
variants on the recurrent waves in a representative case of countries enforcing
mitigation and vaccination strategy. The spreading rate is measured by the
ratio between the reproductive number Rt(t) and the doubling time Td(t) called
RIC-index and the daily fatalities number. The dynamics of the Covid-19
epidemics has been studied by wavelet analysis and represented by a non-linear
helicoid vortex in a 3D space where both RIC-index and fatalities change with
time. The onset of periodic recurrent waves has been identified by the
transition from convergent to divergent trajectories on the helicoid vortex. We
report a main period of recurrent waves of 120 days and the elongation of this
period after the vaccination campaign
