COMPUTER MODELING OF EPIDEMIC SPREAD BASED ON CELLULAR AUTOMATA

Abstract

The paper provides a comprehensive analysis of modern methodological approaches to the computer modeling of infectious disease spread processes, with the mathematical apparatus of cellular automata serving as the pivotal tool. The author substantiates the scientific expediency of transitioning from classical analytical models of the SIR type, characterized by a certain level of abstraction and simplification, to more flexible discrete-spatial models. Such models allow for a significantly more adequate reproduction of the complex and non-linear spatio-temporal dynamics of epidemic processes, taking into account the structural heterogeneity of the environment and the stochastic nature of interpersonal contacts within a population. Within the framework of the conducted research, a comparative review of existing scientific paradigms was carried out, specifically multi-agent modeling concepts, which enabled a clear definition of the advantages of the cellular automata approach in tasks involving the mapping of local interactions, diffusion processes, and the direct impact of physical spatial constraints on pathogen transmission. The primary scientific result of the work is the development and full-featured software implementation of an interactive model of infection spread, which provides high-quality visualization of the epidemic process dynamics in real-time, supporting the functionality for operational changes in simulation parameters. The model architecture is based on a two-dimensional state matrix structure, where each individual cell is identified as an autonomous agent and can reside in one of the predefined epidemic states: susceptible, infected, immune (recovered/removed), deceased, or a stationary barrier. Transition rules between states are formalized based on developed probabilistic mechanisms of infection transmission and temporal characteristics of the disease course, ensuring high flexibility in adapting the model to various scenarios for both viral and bacterial outbreaks. The software implementation of the model was performed using the Python programming language, employing specialized NumPy libraries for optimizing matrix calculations and Pygame for implementing the graphical user interface and interactive visualization. During the study, a series of complex computational experiments were conducted, including varying the initial vaccination levels, changing the intensity of social contacts, and modeling the implementation of quarantine restrictions of various degrees of severity. The obtained empirical results confirm the adequacy of the developed model, particularly its ability to accurately reproduce characteristic wave-like epidemic dynamics, outbreak localization effects, and the formation of herd immunity. It has been established that the synergetic combination of high preventive immunization levels and timely restrictive measures is the most effective factor in containing an epidemic threat. The practical significance of the developed software complex lies in the possibility of its wide application as a tool for fundamental scientific research, short-term forecasting, and for educational purposes for specialists in relevant profiles. Prospects for further investigation in this direction are associated with the deep integration of the cellular automata model with modern machine learning methods and Big Data analysis to increase predictive accuracy based on real statistical indicators of urban mobility.