{"title":"基于Ornstein-Uhlenbeck过程的新冠肺炎大流行模拟研究","authors":"P. Nabati","doi":"10.22034/CMDE.2021.43961.1864","DOIUrl":null,"url":null,"abstract":"The rapid spread of coronavirus disease (COVID-19) has increased the attention to the mathematical modeling of spreading the disease in the world. The behavior of spreading is not deterministic in the last year. The purpose of this paper is to presents a stochastic differential equation for modeling the data sets of the COVID-19 involving infected, recovered, and death cases. At first, the time series of the covid-19 is modeling with the Ornstein-Uhlenbeck process and then using the Ito lemma and Euler approximation the analytical and numerical simulations for the stochastic differential equation are achieved. Parameters estimation is done using the maximum likelihood estimator. Finally, numerical simulations are performed using reported data by the world health organization for case studies of Italy and Iran. The numerical simulations and root mean square error criteria confirm the accuracy and efficiency of the findings of the present study.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2021-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A simulation study of the COVID-19 pandemic based on the Ornstein-Uhlenbeck processes\",\"authors\":\"P. Nabati\",\"doi\":\"10.22034/CMDE.2021.43961.1864\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The rapid spread of coronavirus disease (COVID-19) has increased the attention to the mathematical modeling of spreading the disease in the world. The behavior of spreading is not deterministic in the last year. The purpose of this paper is to presents a stochastic differential equation for modeling the data sets of the COVID-19 involving infected, recovered, and death cases. At first, the time series of the covid-19 is modeling with the Ornstein-Uhlenbeck process and then using the Ito lemma and Euler approximation the analytical and numerical simulations for the stochastic differential equation are achieved. Parameters estimation is done using the maximum likelihood estimator. Finally, numerical simulations are performed using reported data by the world health organization for case studies of Italy and Iran. The numerical simulations and root mean square error criteria confirm the accuracy and efficiency of the findings of the present study.\",\"PeriodicalId\":44352,\"journal\":{\"name\":\"Computational Methods for Differential Equations\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2021-06-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational Methods for Differential Equations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22034/CMDE.2021.43961.1864\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Methods for Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22034/CMDE.2021.43961.1864","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
A simulation study of the COVID-19 pandemic based on the Ornstein-Uhlenbeck processes
The rapid spread of coronavirus disease (COVID-19) has increased the attention to the mathematical modeling of spreading the disease in the world. The behavior of spreading is not deterministic in the last year. The purpose of this paper is to presents a stochastic differential equation for modeling the data sets of the COVID-19 involving infected, recovered, and death cases. At first, the time series of the covid-19 is modeling with the Ornstein-Uhlenbeck process and then using the Ito lemma and Euler approximation the analytical and numerical simulations for the stochastic differential equation are achieved. Parameters estimation is done using the maximum likelihood estimator. Finally, numerical simulations are performed using reported data by the world health organization for case studies of Italy and Iran. The numerical simulations and root mean square error criteria confirm the accuracy and efficiency of the findings of the present study.
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