Predicative Computing Structures and Hybrid Automates in Modeling Invasive Processes and Epidemic COVID Waves

Rapid processes in the area of cell biophysics, invasions, or epidemiology are distinguished by the variety of their variants; therefore, they require original methods of mathematical description for long-term prediction of the state of biophysical systems. Without building predictions of the dynamics of biophysical interaction, it is impossible to improve the technology of industrial exploitation of natural objects. Classical models based on systems of differential equations do not describe the dynamics of real processes that are observed during aggressive invasions of alien species. Known models of “predator/prey” systems assumed the cyclical dynamics of two rival species, but in reality, the oscillatory solution of the model’s equations is only a mathematical hypothesis. In real biosystems, the variants for the development of scenarios after the introduction of an aggressive predator or parasite are more complicated. Dynamics during invasions becomes extreme. In laboratory experiments with ciliates, instead of asynchronous oscillations with the prey, the infused predator after a rapid outbreak completely destroyed the entire population of prey. Processes with abrupt metamorphoses are extremely relevant, for example, the development of an immune response during the presentation of antigens of new strains of coronavirus and the activation of specific T-lymphocytes of immune memory killer cells to destroy infected cells. Modeling of extreme development in our works is based on the aspects of eventfulness and variability of choice during abrupt changes in the stages of the process under study, for example, adaptation of a parasite against a breeding invader, which is an important way to combat invasions. For rapidly changing biophysical processes, we proposed to expand the models in differential equations with the components of eventfulness, delay, trigger switching, and the logic of switching stages of development. Previously, we proposed an original formalization of the event hierarchy for continuous-discrete time in a hybrid model. In the article, we will present a method for including predicates in the model, i.e., logical functions that allow us to calculate the sequence of changes in the behavior of the invasive process. Our predictive logic approach is important for computational modeling with transformations in dangerous and fast invasive processes and waves of the COVID-19 epidemic based on a comparative analysis of scenarios. Based on the predicative choice of the behavior of a hybrid automaton defined for a set of right-hand sides of systems of differential equations, we also formalize the decision-making logic in scenarios with a controlled impact on biosystems. Post-COVID immunodeficiency is the most complex legacy of the pandemic.