Analysis of Regional Scenarios of New Epidemic Waves of SARS-CoV-2 Coronavirus Based on Equations with a Deviating Argument and Damping Functions

The methods we develop within the framework of transient technical process modeling are adaptable to the tasks of biophysics—both to the prediction of invasions of aggressive species and to the analysis of the dynamics of epidemics. The practical application of modeling results to predict the development of the modern pandemic in 2020 has shown the fundamental limitations of the basic methods of model building. Based on an analysis of the properties of the deterministic SIRS model, it has not been possible to present the variety of forms that the regional dynamics of coronavirus spread has taken. The characteristics of the epidemic process do not remain constant, as a variable pathogen evolves competitively. The phenomena since the outbreak of COVID-19 have proven to be much more complex than the naturally fading waves of pandemic influenza strains as immunity accumulates. The development of a scenario approach to the analysis of individual epidemic situations is promising, taking into account the logic of the evolution of the pathogen and adaptation to the peculiarities of its spread in local populations. We performed an analysis of the available data in terms of oscillation forms to get an idea of the real qualitative diversity of local wavelike dynamics of the epidemic of coronavirus strains and identify some special development scenarios described as a catastrophic cycle breakdown on the basis of the known phase-portrait transformations. Applying a bifurcation approach to the epidemic data, we were able to identify features of local forms of oscillatory epidemic processes. We classified the observed phenomena of outbreaks and attenuation of coronavirus infection waves by correlating the dynamics of epidemics with nonlinear effects. We derived scenarios for a number of epidemic situations (in Brazil, New York, and Japan) using lagged equations. It is shown on the basis of comparison of specific situations that the dynamics of epidemics evolve diversely and variably at the current stage according to the internal unpredictable logic of the confrontation process, which is determined by the rate of change in the joint evolution of the virus and population immunity, including the previously formed T-cell immunity. We were able to analyze variants of COVID-wave transformations in lagged equations using the idea of distinguishing bifurcation-inducing parameters. It is substantiated that all nonlinear effects and transformations of oscillatory modes, isolated by epidemic plots, cannot in principle be obtained within a single model. Comparative scenario analysis supports the hypothesis that epidemic processes are primarily influenced by population immunity and contact density. Vaccination has failed to complete the emergence of new waves of infections, but clearly affects the properties of local oscillatory regimes of disease incidence. Experience with new outbreaks of COVID-19 in 2023 in Sweden, New Zealand, Japan, and South India with fundamentally different coping strategies showed that sustained population immunity blocking coronavirus transmission could not be achieved over the long term. Our assumed scenario for the end of the pandemic is the formation of four stable strains whose sporadic circulation in the regions is controlled by CD8+ T-cell immunity.