Development of Algorithmic and Software Support for Symbolic Computations in Problems of Constructing Controlled Compartmental Models of Dynamic Systems

The analysis of epidemic spreading processes and the development of the corresponding algorithmic and software support for their mathematical modeling are important areas of research. The purpose of this work is to develop tools for symbolic computations in problems of constructing controlled compartmental models of dynamic systems. As a programming language, Julia is used in combination with scientific computing libraries. A software package for compartmental modeling based on schemes of inter-compartment interactions is developed. Several controlled compartmental models—SIRU, SEIRU, and SIDARTHEU—are constructed and investigated. Control is implemented in the form of additional rules with variable transition rates. The developed software complex implements a domain-specific language for compartmental model construction based on interaction schemes. A simulation algorithm for controlled compartmental models is proposed. Computational experiments on controlled simulation of epidemic spreading are carried out, and the trajectory dynamics of the simulation models and corresponding differential models is analyzed. The results can be useful in modeling epidemiological, ecological, physicochemical, and other processes with one-step interactions.