On regime changes of COVID-19 outbreak.

The COVID-19 pandemic has had a very serious impact on societies and caused large-scale economic changes and death toll worldwide. The first cases were detected in China, but soon the virus spread quickly worldwide and the intensity of newly reported infections grew high during this initial period almost everywhere. Later, despite all imposed measures, the intensity shifted abruptly multiple times during the two-year period between 2020 and 2022 causing waves of too high infection rates in almost every part of the world.

Models induced from critical birth-death process with random initial conditions.

In this work, we study a linear birth-death process starting from random initial conditions. First, we consider these initial conditions as a random number of particles following different standard probabilistic distributions - Negative-Binomial and its closest Geometric, Poisson or Pólya-Aeppli distributions. It is proved analytically and numerically that in these cases the random number of particles alive at any positive time follows the same probability law like the initial condition, but with different parameters depending on time.