A Method for Modeling the Transformation of Epidemic Scenarios during the Propagation of Waves of Convergent SARS-CoV-2 Variants

The study of the epidemic waves of mutating coronavirus involves an analysis of the forms of transient oscillatory modes. Similar phase portraits of oscillators are known in physical problems, but the physical parameters in experiments are constant or controlled. The adaptation of SARS-CoV-2 proteins is unpredictable. Apart from our intuition, there are no methods at present to predict actual mutations in the next season. Renewed virus has returned once again after victory over the infection was declared and the properties of the new COVID wave need to be investigated. The problems of adequacy of modifications of сompartmental models at the current stage of the mutant virus epidemic are in their extensible rather than threshold-change adaptive structure of equations. We classified in our studies the scenarios of COVID-19 epidemics according to the characteristic features of their nonlinear dynamics and forms of oscillation transformations in the physical perspective. We show that the SARS-CoV-2 dynamics since 2020 spring has already changed the mode of autonomous oscillations of infections twice after Omicron BA.1 during spring 2022 and in the autumn 2023. Local epidemics are asynchronous after the global BA.2.86/JN.1 wave in both wave formation and attenuation. The wave epidemic variants were qualitatively different in some countries, such as Japan and Australia. We studied these situations in specific models. Frequent short waves of large amplitude developed in countries previously isolated from the 2020 pandemic wave. In November 2024, we see signs of another qualitative change with a disproportionate increase in the percentage of fatalities without a clear increase in the number of infections. Two strains with signs of convergent mutations appeared synchronously combining adjacent evolutionary branches of the coronavirus. Only the alarming XEC strain, the most evasive to accumulated immunity, began to spread widely. The frequency of XEC infections varies considerably between regions. There is no global epidemic trend at the end of 2024. The number of cases in the new autumn wave of infections was lower than in the past seasons, but the COVID case fatality rate is unexpectedly increasing. It tripled in a month in several countries, which indicates that the epidemic is entering a new stage. We propose a method for modeling the abrupt development of the virus spread based on equations with threshold regulation functions describing variants of infection outbreaks and with situational damping functions determining the form of oscillatory decay for the number of infection cases. A computational experiment simulated the variant of extreme peak development after the stage of local epidemic wave attenuation as a bifurcation scenario. The regional wave with unusual properties is due to the effect of a single mass infection at the appearance of the convergent variant. The declining trend after the primary COVID wave is interrupted in the model during wave reactivation by a mass contagion event that induces an outbreak of SARS-CoV-2 infections and then a fluctuation declining mode, new in characteristics. The main parameter for the rearrangement of the model equations is the fluctuation in the binding affinity of emerging virions to cellular receptors. An important feature of the model is the estimation of the evasion of new strains from antibodies prevailing in the populations. The third indicator analyzed for switching modes of the model was the efficacy of remaining T cell immunity in local populations. These three indicators vary not gradually in sync, but in pulses. The new variants are not as virulent as Gamma and Delta. The evolution of convergent strains may give rise to a variant of Spike protein capable of causing a global wave, which binds much better to ACE2 in our cells and is quite different from both the basic variants and Omicron BA.2.