{"title":"Stochastic Gompertzian Model for Parathyroid Tumor Growth","authors":"Tugcem Partal, Mustafa Bayram","doi":"10.1002/mma.10715","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we study on the behavior and growth of parathyroid tumor in the human body. We investigate the change of parathyroid cancer cell with respect to time, obtained from the deterministic Gompertz model through 41 actual patients in the literature. Then we describe the stochastic Gompertz model based on deterministic Gompertz law and obtain the diffusion coefficient for our stochastic model, using the data taken from the patients. We compare the stochastic and deterministic results at the same graph. Also, we numerically solve the defined stochastic differential using the Euler–Maruyama, Milstein, stochastic Runge–Kutta, and Taylor methods. Finally, we demonstrate the effectiveness of each of these methods using graphs and error table.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6788-6798"},"PeriodicalIF":2.1000,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.10715","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we study on the behavior and growth of parathyroid tumor in the human body. We investigate the change of parathyroid cancer cell with respect to time, obtained from the deterministic Gompertz model through 41 actual patients in the literature. Then we describe the stochastic Gompertz model based on deterministic Gompertz law and obtain the diffusion coefficient for our stochastic model, using the data taken from the patients. We compare the stochastic and deterministic results at the same graph. Also, we numerically solve the defined stochastic differential using the Euler–Maruyama, Milstein, stochastic Runge–Kutta, and Taylor methods. Finally, we demonstrate the effectiveness of each of these methods using graphs and error table.
期刊介绍：
Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome.
Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted.
Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.
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