Computational Modeling of Transformations of Epidemic Waves of BA.2.86/JN.1 SAR-COV-2 Coronavirus Variants on the Basis of Hybrid Oscillators

Abstract

Abstract—

We are developing a modeling method for oscillating processes in biophysics with discontinuous nonlinearities on the basis of logic of impulse perturbations and equations with a deviating argument. We compared specific variants of development of the epidemic situation in different countries due to regularly updated SAR-CoV-2 strains and discuss methods for modeling specific scenarios for the spread of this infection. The relevance of the development of modeling methods is due to the renewed waves of growth in COVID-19 cases in different regions in 2024 as an unusual variant of a pulsating epidemic process. The next surges of infections in New Zealand are determined by the long hidden presence of strains of the evolutionary leader branch BA.2.86/JN, which managed to split, which surpassed in their binding affinity to cells all the previously dominant Omicron sublines (B.1.1.529, XBB.2.3), and now JN.1 effectively evades vaccine antibodies. Earlier in 2023, XBB strains retained sufficient infectivity with reduced affinity for the ACE2 receptor and a lower replication rate compared to Gamma, but the persistence time of the virus increased. Due to 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 variability potential in coronavirus proteins is high. Our method for predicting its prospecting mutations in a computational study of epidemic scenarios is necessary for species modified by expanding the set of statuses of individuals in compartmental models. Variants of systems of equations based on SIRS did not describe the resumption of COVID waves in Iran in 2020. Schemes for status transitions are not suitable in fundamental aspects for describing nonlinear oscillatory modes of the epidemic even after including second-order oscillatory equations in the linear SIR scheme. The equations with delay and with threshold effects during bifurcations of cycle generation, developed by the author for decaying COVID waves, take into account that new Omicron lines change the fluctuation modes. The real changes that we revealed in oscillation modes with an increase in repeated cases cannot be described only by restructuring the parameters of the equations with attenuation functions. According to the hospitalization graphs shown to us, in Finland, Wales, and Nepal, it is necessary to restructure the attenuation functions of the COVID waves. We described the aspects of the transitional phases of the modern COVID epidemic using special computational tools based on the nature of their nonlinear oscillations. Our original method for forming a structure for a hybrid model was substantiated on the basis of the choice from a set of right-hand sides of differential equations with heterogeneous delayed control parameters that generate relaxation oscillations. The equations will be redefined if the criterion for the truth of predicates is violated when measuring the binding affinity of S-protein variants with the ACE2 receptor, which play a key role in restructuring the model of periods of attenuation and activation caused by the evolution of the S-protein. A hybrid model with the logic of changing the right-hand side will describe event transformations in the form of epidemic waves caused by mutations in SAR-CoV-2. According to mutation monitoring, the next increase in binding affinity of the viral S protein to ACE2 will occur in November 2024. In June local outbreaks of the KP.3 strain suddenly occurred.