Modeling of aleatoric uncertainty phenomena in biosystems based on perturbed equations with delay

Title	Modeling of aleatoric uncertainty phenomena in biosystems based on perturbed equations with delay
Authors	A. Y. Perevaryukha¹ ¹National Research Mordovia State University
Annotation	The report considers an approach to modeling phenomena with a probabilistic component in biosystems, which we define as situations under aleatoric uncertainty. Randomness plays a role at certain stages of their development. The situations under study arise in changing biophysical processes, when the choice from a possible set of development options is not predetermined in the initial state. Thus, during the spread of COVID-19, the course of the infectious disease, the rate and spectrum of immune response production, and the duration of immunity after the disease turned out to be very different in one subpopulation. For reasons that are still unclear, long-lived immune memory cells are formed in some vaccinated people, but not in others. The evolution of the coronavirus and the launch of new waves of COVID-19 infection are affected by random factors, but these are not stochastic processes and are not described by including white noise in the perturbation equations. In the paper, aspects of interval-bounded uncertainty in the dynamics of situations are modeled based on equations with perturbed delay that generate transient oscillatory modes.
Keywords	delay equations, epidemic waves, local uncertainty, probabilistic component of processes.
Citation	Perevaryukha A. Y. ''Modeling of aleatoric uncertainty phenomena in biosystems based on perturbed equations with delay'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 29-31, 2025). Saransk: SVMO Publ, 2025. - pp. 212-216. Available at: https://conf.svmo.ru/files/2025/papers/paper42.pdf. - Date of access: 30.08.2025.

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Modeling of aleatoric uncertainty phenomena in biosystems based on perturbed equations with delay

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