COVID-19 multiwaves as multiphase percolation: a general N-sigmoidal equation to model the spread

The aim of the current study is to investigate the spread of the COVID-19 pandemic as a multiphase percolation process. Mathematical equations have been developed to describe the time dependence of the number of cumulative infected individuals, $$, and the velocity of the pandemic, $$, as well as to calculate epidemiological characteristics. The study focuses on the use of sigmoidal growth models to investigate multiwave COVID-19. Hill, logistic dose response and sigmoid Boltzmann models fitted successfully a pandemic wave. The sigmoid Boltzmann model and the dose response model were found to be effective in fitting the cumulative number of COVID-19 cases over time 2 waves spread (N = 2). However, for multiwave spread (N > 2), the dose response model was found to be more suitable due to its ability to overcome convergence issues. The spread of N successive waves has also been described as multiphase percolation with a period of pandemic relaxation between two successive waves.