2518-1092Научный результат. Информационные технологии2518-109210.18413/2518-1092-2024-9-3-0-13555ИНФОРМАЦИОННЫЕ СИСТЕМЫ И ТЕХНОЛОГИИ<strong>МАТЕМАТИЧЕСКИЙ АНАЛИЗ МОДЕЛИ SIR С УЧЕТОМ ПЕРИОДА ИНКУБАЦИИ</strong><strong>MATHEMATICAL ANALYSIS OF SIR MODEL WITH INCUBATION PERIOD</strong>КонстантиновИгорь СергеевичKonstantinovIgor Sergeyevichkonstantinov@bsu.edu.ruТахаАсраа ТарикTahaAsraa Tariq20249300

Модель SIR является фундаментальным инструментом для моделирования эпидемической динамики, но у нее есть ограничения в точном представлении реальных сценариев. В данной статье представлено всестороннее обзорное и математическое аналитическое исследование модели SIR при включении инкубационного периода инфекционных заболеваний. Мы обсуждаем значимость инкубационного периода в динамике передачи заболевания и исследуем модификации, внесенные в модель SIR для интеграции этого параметра. Анализируя математические уравнения, определяющие измененную модель SIR, мы демонстрируем ее улучшенную точность в прогнозировании паттернов распространения болезни и ее влияние на меры общественного здравоохранения. Наши результаты подчеркивают важность включения инкубационного периода в эпидемические модели.

The SIP model is a fundamental tool for simulating epidemic dynamics, but it has limitations in accurately representing real-world scenarios. This paper presents a comprehensive review and mathematical analysis of the SIR model when incorporating the incubation period of infectious diseases. We discuss the significance of the incubation period in disease transmission dynamics and explore the modifications made to the SIR model to integrate this parameter. By analyzing the mathematical equations governing the modified SIR model, we demonstrate its enhanced accuracy in predicting disease spread patterns and its implications for public health interventions. Our findings evaluated the importance of incorporating the incubation period into epidemic models.

модель SIRинкубационный периодэпидемическая динамикапередача заболеванияматематическое моделированиеSIR modelincubation periodepidemic dynamicsdisease transmissionmathematical modelingСписок литературыChatterjee S., Zehmakan A.N. (2023). Effective Vaccination Strategies in Network-based SIR Model. http://arxiv.org/abs/2305.16458Hansson J., Govaert A., Pates R., Tegling E., Soltesz K. (2022). Limitations of time-delayed case isolation in heterogeneous SIR models. https://doi.org/10.23919/ACC53348.2022.9867465Kahn R., Peak C.M., Fern&aacute;ndez-Gracia J., Hill A., Int H., Jambai A., Ganda L., Castro M.C., Buckee&nbsp;C.O., Edu C.H. (n.d.). Incubation periods impact the spatial predictability of outbreaks: analysis of cholera and Ebola outbreaks in Sierra Leone. https://doi.org/10.1101/19003525Kahn R., Peak C.M., Fern&aacute;ndez-Gracia J., Hill A., Jambai A., Ganda L., Castro M. C., Buckee C.O. (n.d.). World Health Organization, CH-1211 Geneva 27, Switzerland; d Disease Control and Prevention, Sierra Leone Ministry of Health and Sanitation. https://doi.org/10.1073/pnas.1913052117/-/DCSupplementalLiu J., Tian B., Wu J. 2023. Temporal Analysis of Infectious Diseases: A Case Study on COVID-19. Acadlore Transactions on Applied Mathematics and Statistics, 1(1), 1&ndash;9. https://doi.org/10.56578/atams010101Liu T., Huang J., He Z., Zhang Y., Yan N., Zhang C.J.P., Ming W.K. (2023a). A real-world data validation of the value of early-stage SIR modelling to public health. Scientific Reports, 13(1). https://doi.org/10.1038/s41598-023-36386-9Liu T., Huang J., He Z., Zhang Y., Yan N., Zhang C..JP., Ming W.K. (2023b). A real-world data validation of the value of early-stage SIR modelling to public health. Scientific Reports, 13(1). https://doi.org/10.1038/s41598-023-36386-9Mckeigue P.M., Wood S.N. (2022). Limitations of models for guiding policy in the COVID-19 pandemic. https://doi.org/10.1101/2022.06.30.22277091Melikechi O., Young A. L., Tang T., Bowman T., Dunson D., Johndrow J. (2022). Limits of epidemic prediction using SIR models. Journal of Mathematical Biology, 85(4). https://doi.org/10.1007/s00285-022-01804-5Owen L., Hoseana, J., &amp; Yong B. (2023). Codimension-Two Bifurcations of an SIR-Type Model for COVID-19 and Their Epidemiological Implications. http://arxiv.org/abs/2307.08892Salman A.M., Hafiz Mohd M., Ahmad N.A., Musa I., Ahmed I., Alqahtani Z. (2022). An Optimal Control of SIRS Model with Limited Medical Resources and Reinfection Problems. In Malaysian Journal of Fundamental and Applied Sciences (Vol. 18).Sharbayta S.S., Buonomo B., d&rsquo;Onofrio A., Abdi T. (2022). &lsquo;Period doubling&rsquo; induced by optimal control in a behavioral SIR epidemic model. Chaos, Solitons &amp; Fractals, 161, 112347.Shatz I. (2023). Assumption-checking rather than (just) testing: The importance of visualization and effect size in statistical diagnostics. Behavior Research Methods. https://doi.org/10.3758/s13428-023-02072-xSingh R.P. (2022). Bifurcation and Stability Analysis of Delayed SIR Model. Journal of Physics: Conference Series, 2267(1). https://doi.org/10.1088/1742-6596/2267/1/012011SUN X. (2023). Sensitivity analysis: Advancing the effectiveness of global sensitivity analysis. Bulletin of the Australian Mathematical Society, 107(2), 351&ndash;352.Taib N.A.A., Labadin J. (2022). Sensitivity Analysis of the Effective Reproduction Number in a Sarawak Rabies Epidemic Model. 2022 International Conference on Future Trends in Smart Communities, ICFTSC 2022, 194&ndash;198. https://doi.org/10.1109/ICFTSC57269.2022.10039940Varghese A., Lacap Jr. E.M., Sajath I., Kumar M.K., Kolamban S. (2022). Controlling Epidemics with Mathematical and Machine Learning Models. IGI Global.Oxford University Department for Continuing Education. (2021). &quot;Pandemic Dynamics series: Dr. Tom Crawford&quot;. URL: https://www.conted.ox.ac.uk/profiles/tom-crawfordOur World in Data. (2023). &quot;COVID-19 Data Explorer.&quot; Accessed December 29, 2023. URL: https://ourworldindata.org/covid-cases