The COVID-19 pandemic in 2023 can be divided according to characteristics into groups of regional epidemics. Local processes demonstrate oscillatory dynamics in the form of special forms of oscillations. COVID waves and peaks cannot be considered classic damped relaxation oscillations. Often, the damping amplitude of infection waves formed after the initial outbreak again turns into an extreme peak. The reasons may be effects after crisis events: mass infections and/or an increase in virulence of a new strain that evades vaccine immunity. Using simulation tools, we analyzed a number of variants of epidemic dynamics with sudden changes. We have identified special important epidemic scenarios for the sudden occurrence of a short wave and computationally investigated on the basis of the proposed nonlinear equations with a deviating argument as the most likely development option for a given parametrically simulated situation. Each COVID outbreak is a positive feedback loop: the more infections, the higher the likelihood of further mutations in the virus and strains evading antibodies. At the end of 2023, after a long summer minimum, the incidence rate resumed due to strains of the new Omicron branch of BA.2.xx "Pirola". Keywords: modeling of oscillating epidemic dynamics, attenuation of infection waves, models with destruction of