Hybrid Models of Evolutionary Transformations of SAR-CoV-2 Epidemic Waves

Abstract

The specific variants of the development of the current epidemic situation due to regularly updated SAR-CoV-2 strains are analyzed and methods for modeling special scenarios of the spread of this infection are compared. The relevance of the development of the modeling methodology is due to the renewed growth of waves of COVID cases in a number of regions in 2024 as an unusual variant of the pulsating epidemic process. The latest outbreaks of infections are determined by the activity of the BA.2.86 Pirola strain evolutionary branch, which has managed to split and is more effective in terms of affinity and antibody avoidance than the previously dominant Omicron EG.5 and XBB.1.5 lines. In 2024, the strains maintained sufficient transmissibility with reduced affinity for the ACE2 receptor and a lower replication rate compared to Delta, and at the same time, the virus persistence time increased. In the situation of population immunization, the trend of virus evolution has changed with an emphasis on complicating the phylogenetic tree and selecting Spike protein variants that provide balanced characteristics for replication and antibody avoidance. The potential of variability in coronavirus proteins is clearly not exhausted, and methods for predicting their promising mutations are under development. Methods of computational study of epidemic scenarios based on modified by expanding the set of statuses of individuals in office “SIR models” are discussed. Variants of SIR-based systems of equations do not describe the resumption of COVID waves, which was observed as early as 2020. Status transition schemes are in principle poorly suited for describing nonlinear oscillatory modes of an epidemic, even when second-order oscillatory equations are included in a linear SIR scheme. The models developed by the author for attenuating COVID waves based on equations with delay and threshold effects have been modified to take into account that the new Omicron lines change the modes of oscillations. The changes in oscillation modes that we have identified with an increase in repeated cases are not described only by rearranging the parameters of the equations with damping functions. According to the observed epidemic schedules of COVID waves, a restructuring of regulatory functions is required in the models. It is proposed to model aspects of the transitional phases of the modern epidemic by special computational means, based on the nature of nonlinear oscillations. An original method of forming a structure for a hybrid model based on a set of right-hand sides of differential equations with heterogeneous parameters of delayed regulation generating relaxation oscillations and redefined predicates in violation of the criterion of truth is substantiated. It has been shown that the change in the binding affinity of S protein variants with ACE2 is a key indicator for modeling the periods of attenuation and activation of waves associated with the evolution of the virus, as observed in 2024 in strain JN.1. The hybrid model describes the event-driven transformations of the form of epidemic waves associated with the disturbance of the coronavirus mutation landscape, which can now be established by monitoring mutations and the frequency of occurrence of strains.