*Result*: Modeling of the Epidemic and Pulsating Biophysical Wave Processes Based on Hybrid Computing Structures.

*A method for computational modeling of rapidly developing biophysical processes on the basis of physical analogies and the transient damped oscillation theory has been developed. The relevant phenomena, including invasions of aggressive species, have been discussed and epidemics in the form of a series of peaks in the pathogen activity have been compared. The spread of COVID waves in regions turned out to be difficult to predict using conventional systems of equations of the Kermack–McKendrick theory. A new method for forming modeling structures with the included logic that sets the conditions for redefining the system of equations has been developed. It has been proposed to identify key events for changing the right-hand sides of the system of equations on the basis of tracking the changing evolutionary characteristics and transforming parameters of the interaction between the aggressive agent and the environment. Continuous evolution causes the wave-like dynamics; therefore, repeated virus activity outbreaks have been observed. To model the evolving biophysical processes, several wave equations at once should be used, since the properties of oscillations are not preserved. A hybrid model of wave differential equations has been built from a set of redefined activation and damping functions of oscillations selected according to specified conditions, while the oscillation minima remain positive and the wave maxima do not increase indefinitely. Using a new original method, consequences of the event-driven pathogen evolution has been simulated, which is especially reflected on the characteristics of a new series of COVID wave oscillations. Based on the algorithmic implementation of the structure of transitions between behavioral modes in a series of simulation scenarios for the development of epidemic waves in regions depending on immunization factors and estimated efficiency of anti-epidemic measures, scenarios for the development of the epidemic situation with a change in the dominant strains of coronavirus in five regions have been obtained. The method for organizing hybrid models from variable sets of wave equation forms can be applied to the scenario modeling of many stage oscillatory transient modes that arise both during the formation of new neural connections and in electrical circuits with feedback and trigger switching. The physical, biophysical, and social wave processes have a surprisingly large number of common dynamic aspects. Pulse and rapidly damping phenomena similar to epidemic waves are observed, for example, when waves of negative reactions spread in indignant social networks to information with the deliberate dissemination of shocking content. In social networks, there are groups that actively spread the impact and slow down this indignation, as in physics. The main problem in 2005 is the activity of the group of chronic "Long COVID" spreaders. [ABSTRACT FROM AUTHOR]

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