Including the Indicator of the S-Protein Binding Affinity of SAR-CoV-2 Strains in Modeling New COVID-19 Waves

Based on analysis of the spread of new convergent SAR-CoV-2 strains, an original method for modeling scenarios for the spread of infection in the form of new COVID waves after the long-term activity minima has been proposed. Specific variants of the development of the current epidemic situation due to regularly updated strains have been modeled as versions of the pulsating epidemic process. The relevance of the development of a modeling technique with the inclusion of the virion binding indicator is related to the emergence of a series of convergent strains as a coronavirus evolutionary trend in 2025. It has been noted that the indicator of affinity of new strains fluctuates, which determines the COVID growth waves in several regions. The infection waves in the spring of 2024 were determined by the activity of the evolutionary branch of BA.2.86 strains, which had time to split and were successful in binding affinity and in avoiding antibodies. The JN lineage displaced the Omicron lines that dominated in 2023. The Pirоla branch strains were transmissible with reduced affinity for the ACE2 receptor and a lower replication rate. The advantage of the Pirоla coronavirus branch was the increased virus persistence time. In the fall of 2024, the virus evolution trend changed with an emphasis on the complication of the phylogenetic tree. The convergent XEC and XDC variants appeared which seemed dangerous. Unexpectedly, in the winter of 2025, the variants spread more slowly than predicted and turned out to be inefficient. In 2025, a selection of the Spike protein variants providing balanced characteristics for replication and evasion from antibodies occurs. The potential for variability of coronavirus proteins has not been exhausted. We have proposed a method for computational study of epidemic scenarios based on the modification of hybrid equations rebuilt on the basis of tracking the virion affinity and fusogenicity indicators. The decaying COVID wave models developed by the author on the basis of equations with the delay and threshold effects have been modified to take into account that fluctuations in the binding affinity of strains change the dynamics of COVID waves. The identified changes in the infection oscillation modes have been described within the model by the algorithmic rearrangement in the right-hand sides of the equations with damping functions. According to the available epidemic curves of COVID waves, the models require rearrangement of the regulation functions, which follows the evolutionary trend of convergent strains. It has been proposed to model aspects of the epidemic stage in 2025 using special computing tools. An original method for forming a structure for the hybrid model has been substantiated based on a set of the right-hand sides of differential equations with the heterogeneous parameters of delayed regulation that generate relaxation oscillations and are redefined when the truth criteria for predicates are violated. It has been shown that a change in the binding affinity of the S-protein variants with ACE2 is a key indicator for modeling the wave attenuation and activation periods associated with the virus evolution. The hybrid model describes event-driven transformations in the forms of epidemic waves that follow disturbances in the coronavirus mutational landscape, which is implemented by monitoring the mutations, frequency of occurrence of strains, their affinity, and fusogenicity. The LB.8 strain turned out to be not as aggressive in evolution in 2025 as expected.