We analyze specific options for the development of the current epidemic situation due to regularly updated SAR-CoV-2 strains and compare methods for modeling the spread of infection. The relevance of the development of scenario modeling methodology is due to the renewed waves of growth in COVID cases in a number of regions in 2024 as an unusual variant of a pulsating epidemic process. The next surges of infections are determined by the activity of the evolutionary branch of the BA.2.86 Pirola strains, which have managed to split, which are better in affinity and antibody avoidance than the previously dominant Omicron EG.5 or XBB.1.5 lines. Strains in 2023 retained sufficient transmissibility with reduced affinity for the ACE2 receptor and a lower replication rate compared to Delta, but the persistence time of the virus increased. In the situation of immunization of the population, the trend of virus evolution has changed with an emphasis on the complication of the phylogenetic tree and with the selection of Spike protein variants that provide balanced characteristics for replication and evasion of antibodies. The potential for variability of coronavirus proteins is clearly not exhausted, and methods for predicting their promising mutations are under development. Methods for computational research of epidemic scenarios based on those modified by expanding the set of statuses of individuals in office “SIR” models are discussed. Variants of systems of equations based on SIR do not describe the resumption of COVID waves, which was already observed in 2020. Status transition schemes based on fundamental aspects are poorly suited for describing nonlinear oscillatory regimes of the epidemic, even when second-order oscillatory equations are included in the linear SIR scheme. The models developed by the author for decaying COVID waves based on equations with delay and with threshold effects were modified to take into account that the new Omicron lines change fluctuation regimes. The changes in oscillation modes that we have identified with an increase in repeated cases are not described only by restructuring the parameters of the equations with damping functions. According to the observed epidemic graphs of COVID waves, the models require a restructuring of regulatory functions. We propose to model aspects of the transition phases of the modern epidemic using special computational tools and based on the nature of nonlinear oscillations. An original method for forming a structure for a hybrid model is substantiated based on a set of right-hand sides of differential equations with heterogeneous delayed regulation parameters that generate relaxation oscillations and are redefined when the criteria for the truth of predicates are violated. It has been shown that changes in the binding affinity of S-protein variants with ACE2 are a key indicator for modeling periods of attenuation and activation of waves associated with the evolution of the virus, as in 2024 for the JN.1 strain. The new hybrid model with evet time describes event-based transformations in the shape of epidemic waves associated with disturbances in the mutational landscape of the coronavirus, which can now be established by monitoring mutations and the frequency of occurrence of strains.
