Интегральная модель притока и оттока и ее приложения
DOI:
https://doi.org/10.21638/spbu10.2024.201Аннотация
Описана общая интегральная модель притока и оттока динамической системы, параметры которой имеют стохастический характер. Для такого типа динамических систем формулируется общий принцип динамического баланса, а также вводятся понятия интервальной динамической сбалансированности интегральных объемов притока и оттока и характеристики динамического баланса. Класс стохастических динамических процессов и систем притока и оттока, удовлетворяющих принципу динамического баланса, достаточно широк (распространение эпидемий вирусов и динамика заболеваемости в медицине, процессы изменения численности и структуры населения в демографии, динамика спроса-предложения в экономике и т. д.). Возможности применения предлагаемой модели для построения кратко- и долгосрочных прогнозов демонстрируются на примерах распространения эпидемии COVID-19 в Москве и Санкт-Петербурге, а также прогнозирования роста населения Земли и отдельных стран. Приводятся результаты вычислительных экспериментов по построению ретроспективных прогнозов состояния динамических систем с использованием метода динамических трендов стохастических параметров интегральной модели и классического метода ARIMA. Проводится сравнительный анализ точности прогнозирования.
Ключевые слова:
динамические системы притока и оттока, принцип динамического баланса, характеристика динамического баланса, математическое моделирование, прогнозирование
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Библиографические ссылки
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References
Moftakhar L., Seif M., Safe M. S. Exponentially increasing trend of infected patients with COVID-19 in Iran: a comparison of neural network and ARIMA forecasting models. Iran Journal of Public Health, 2020, vol. 9, pp. 92–100.
Ahmar A. S., del Val E. B. SutteARIMA: short-term forecasting method, a case: COVID-19 and stock market in Spain. Science of the Total Environment, 2020, vol. 729, art. no. 138883.
Chaudhry R. M., Hanif A., Chaudhary M., Minhas S. 2nd, Mirza K., Ashraf T., Gilani S. A., Kashif M. Coronavirus Disease 2019 (COVID-19): Forecast of an Emerging urgency in Pakistan. Cureus, 2020, vol. 12, iss. 5, art. no. e8346.
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Earnest A., Chen M. I., Ng D., Leo Y. S. Using autoregressive integrated moving average (ARIMA) models to predict and monitor the number of beds occupied during a SARS outbreak in a tertiary hospital in Singapore. BMC Health Services Research, 2005, vol. 5, art. no. 36.
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Heisterkamp S. H., Dekkers A. L., Heijne J. C. Automated detection of infectious disease outbreaks: hierarchical time series models. Statistics in Medicine, 2003, vol. 25, no. 24, pp. 4179–96.
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De Beer J. Projecting age-specific fertility rates by using time-series methods. European Journal of Population, 1990, vol. 5, no. 4, pp. 315–346.
Abonazel M., Darwish N. Forecasting confirmed and recovered COVID-19 cases and deaths in Egypt after the genetic mutation of the virus: ARIMA Box-Jenkins approach. Communications in Mathematical Biology and Neuroscience, 2022, vol. 2022, art. no. 17.
Gecili E., Ziady A., Szczesniak R. D. Forecasting COVID-19 confirmed cases, deaths and recoveries: revisiting established time series modeling through novel applications for the USA and Italy. PLoS One, 2021, vol. 16, no. 1, art. no. e0244173.
Singh S., Parmar K. S., Makkhan S. J. S., Kaur J., Peshoria S., Kumar J. Study of ARIMA and least square support vector machine (LS-SVM) models for the prediction of SARS-CoV-2 confirmed cases in the most affected countries. Chaos, Solitons and Fractals, 2020, vol. 139, art. no. 110086.
Aditya S. C. B., Darmawan W., Nadia B. U., Hanafiah N. Time series analysis and forecasting of coronavirus disease in Indonesia using ARIMA model and PROPHET. Procedia Computer Science, 2021, vol. 179, pp. 524–532.
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Статьи журнала «Вестник Санкт-Петербургского университета. Прикладная математика. Информатика. Процессы управления» находятся в открытом доступе и распространяются в соответствии с условиями Лицензионного Договора с Санкт-Петербургским государственным университетом, который бесплатно предоставляет авторам неограниченное распространение и самостоятельное архивирование.
