Integral inflow and outflow model and its applications

Yu. E. Balykina   ; V. V. Zakharov

Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 20 (2024) no. 2, pp. 121-135

Résumé

The article describes a general integral model of the inflow and outflow of a dynamic system, the parameters of which are stochastic in nature. For this type of dynamic systems, the general principle of dynamic balance is formulated, and the concepts of interval dynamic balance of integral volumes of inflow and outflow as well as the concept of dynamic balance characteristic are introduced. The class of stochastic dynamic processes and systems of inflow and outflow that satisfy the principle of dynamic balance is quite wide (the spread of viral epidemics and the dynamics of morbidity in medicine, processes of changes in the size and structure of the population in demography, the dynamics of supply and demand in the economy, etc.). The possibilities of using the proposed model for constructing short-term and long-term forecasts are demonstrated using examples of the spread of the COVID-19 epidemic in Moscow and Saint Petersburg, as well as using the example of forecasting the growth of the Earth population and population of countries. The results of computational experiments on constructing retrospective forecasts of the state of dynamic systems using the method of dynamic trends of stochastic parameters of the integral model and using the classical ARIMA method are presented. A comparative analysis of forecasting accuracy is provided.

Détail

Keywords: dynamic systems of inflow and outflow, principle of dynamic balance, dynamic balance characteristic, mathematical modeling, forecasting.

Bibliographie

[1] 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, 9 (2020), 92–100

[2] 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, 729 (2020), 138883 | DOI

[3] Chaudhry R. M., Hanif A., Chaudhary M., Minhas S. 2$^{nd}$, Mirza K., Ashraf T., Gilani S. A., Kashif M., “Coronavirus disease 2019 (COVID-19): Forecast of an emerging urgency in Pakistan”, Cureus, 12:5 (2020), e8346

[4] Tandon H., Ranjan P., Chakraborty T., Suhag V., “Coronavirus (COVID-19): Arima based time-series analysis to forecast near future and the effect of school reopening in India”, Journal of Health Management, 24:3 (2022), 373–388 | DOI

[5] 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, 5 (2005), 36 | DOI

[6] Li X. J., Kang D. M., Cao J., Wang J. Z., “A time series model in incidence forecasting of hemorrhagic fever with renal syndrome”, Journal of Shandong University (Health Sciences), 46:5 (2008), 547–549

[7] Heisterkamp S. H., Dekkers A. L., Heijne J. C., “Automated detection of infectious disease outbreaks: hierarchical time series models”, Statistics in Medicine, 25:24 (2003), 4179–4196 | DOI | MR

[8] Zhang G. P., “Time series forecasting using a hybrid ARIMA and neural network model”, Neurocomputing, 50 (2003), 159–175 | DOI | Zbl

[9] De Beer J., “Projecting age-specific fertility rates by using time-series methods”, European Journal of Population, 5:4 (1990), 315–346 | DOI

[10] 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 (2022), 17

[11] 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, 16:1 (2021), e0244173 | DOI

[12] 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, 139 (2020), 110086 | DOI | MR

[13] 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, 179 (2021), 524–532 | DOI

[14] Duong N., Phuong Th. L., Nhu Q. D., Binh L., Ai L. C., Hong D. P., “Predicting the pandemic COVID-19 using ARIMA model”, VNU Journal of Science: Mathematics — Physics, 36:4 (2020), 4492 | DOI

[15] Claris S., Peter N., “ARIMA model in predicting of COVID-19 epidemic for the Southern Africa region”, African Journal of Infectious Diseases, 17:1 (2022), 1–9

[16] Zaharov V. V., “Dynamic balance principle of the demographic process and the limits of earth population growth”, Papers of Russian Academy of Sciences, 15 (2023), 108–114 (In Russian) | DOI

[17] Kermack W. O., McKendrick A. G., “A contribution to the mathematical theory of epidemics”, Proceedings of the Royal Society A, 115 (1927), 700–721

[18] Anderson R. M., May R. M., Infectious diseases of humans: Dynamics and control, Oxford University Press, Oxford, 1991, 757 pp.

[19] World Population Prospects 2022: Methodology of the United Nations population estimates and projections, United Nations, Department of Economic and Social Affairs, Population Division, United Nations Publ., New York, 2022, 64 pp.

[20] Zaharov V. V., Ndiaye S. M., “Population growth forecasting and dynamic games against nature”, Mathematical Game Theory and its Applications, 16:1 (2024), 17–37 (In Russian) | MR