Phenomenological models of three scenarios of local coronavirus epidemics

The COVID-19 pandemic did not end in the summer of 2023, but moved into the stage of a dynamic confrontation between a mutating pathogen and herd immunity (natural and vaccine). Pandemic influenza strains were guaranteed to die out after three waves. SARS-COV-2 is able to maintain variability in its E and S proteins. The diversity of SARS-COV-2 strains is increasing impulsively (XBB.x in India, XBC in Philippines). Most strains drop out of distribution, but the remaining ones give rise to new branches like BA.2.86 «Pirola». The evolution is reflected by the pulsation in the number of recorded infections, but the frequency and amplitude of the peaks differ in the regions. Regional epidemic scenarios are emerging, and some of them are unusual. Not only the property of the variability of the antigens of the virus leads, after the attenuation of the oscillations in the number of infections, to new repeated outbreaks. For a phenomenological model description of scenarios for the emergence of new waves, we proposed equations with delay as a flexible tool for analyzing complex forms of oscillatory dynamics. The equations were supplemented with special threshold damping functions. In the models, it was possible to obtain scenarios of both collapsing and damping oscillations with the possibility of a new outbreak, which describes the effect of a single extreme wave after increase in length of active infection chains in New York with the sharp J-shaped peak with oscillatory attenuation that stands out sharply among the morbidity oscillations. The wave scenario in Brazil differs significantly from both the primary outbreak in 2020 and the special Japan epidemic scenario in 2022-23 in the form of a series of eight consecutive short peaks with increasing wave amplitude. Since the coronavirus successfully counteracts the immune system, there is an increase in severe cases of reinfection with COVID-19 in a group that is particularly susceptible. An important factor for slowing down the evolution of the virus is heterogeneity of population immunity, when activated T-lymphocytes and produced antibodies in the population are able to respond to a wide range of epitopes from different conservative regions of proteins.