Periodic Travelling Waves of COVID-19 Epidemics and Vaccination Campaign

While understanding of periodic travelling waves (PTW) 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 PTW 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 PTW 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 travelling waves has been identified by the transition from convergent to divergent trajectories on the helicoid vortex. We report a main period of PTW of 120 days and the elongation of the periods of epidemic travelling waves due to the vaccination campaign.