Abstract <p>Methods for computational modeling of effects of the threshold development of extreme social and biophysical processes on the basis of the principle of physical analogies are discussed. Epidemic processes involve the trigger interaction of biophysical, social, and informational factors. Their intersections sometimes give rise to the development of critical scenarios, similar to an uncontrolled chain reaction. The intensity of social communication is a key factor in the spread of infection at the early stages of an epidemic. Not all measures help reduce the average intensity of contacts within groups and break infection chains. For example, before the announcement of lockdowns in megacities, panicked crowds of people formed in stores. Interconnected processes with feedback loops arise in the social environment, where information is transformed into behavior that influences infection dynamics. Crisis and stress affect the informational projection of the situation created on social networks, activating simultaneous mass actions. During epidemic waves, disturbances in the information environment, which determine the collective behavior of social groups, are important for crisis situations. The effect of panic and hoarding, in turn, critically influences the development of the situation. A distorted information projection of the real situation obtained by decision-makers, based on a set of statistical characteristics, determines the forecast of a future trend. The development of unnecessary countermeasures against the epidemic has harmful economic consequences. The problem of modeling scenarios with threshold effects on social behavior is relevant for both monitoring epidemic outbreaks and analyzing the collapses in stock markets. Differences in the COVID-19 epidemic course in different regions, even within the same country (the United States, India, and Brazil), in 2020 were very significant, which cannot be explained by immunological differences. The rates of growth of daily cases and mortality after the initial introduction of the new virus into the population vary significantly. According to our hypothesis, the factor of social rigidity or adaptability determines the divergence of local forms of the epidemic dynamics in neighboring states. The history of epidemics suggests that there exist several possible bifurcation scenarios for the initiation and termination of a rapid outbreak. Significant differences in the local dynamics emerge during the initial peak of the coronavirus epidemic. We identified qualitatively different scenarios for the COVID-19 spread and highlighted the differences between two scenarios with repeated outbreaks in 2020. We proposed a phenomenological model for a scenario of sequentially attenuating epidemic outbreaks based on delay equations that take into account countermeasures against the epidemic process. In many regions, the epidemics in 2025 are oscillatory with repeated incidence growth and decline phases. A scenario for the wave-like dynamics in the number of cases can be presented as a result of a balance of factors inhibiting the spread of infection, limiting the maximum possible infection rate. An alternative modification of the regulation form in the equation demonstrates the possibility of a sudden increase in amplitude, since the maximum of a repeated outbreak is higher. The evolution changes the epidemic situation. We proposed to build a model by logically selecting equations from a set of forms. Waves of hype in the information society influence the frequency of epidemic peaks.</p>