{"title":"Generalized Hamiltonian and Lagrangian aspects of a model for virus–tumor interaction in oncolytic virotherapy","authors":"Partha Guha, Anindya Ghose-Choudhury","doi":"10.1002/mma.10538","DOIUrl":null,"url":null,"abstract":"<p>We analyze the generalized Hamiltonian structure of a system of first-order ordinary differential equations for the Jenner et al. system (<i>Letters in Biomathematics</i> 5 (2018), no. S1, S117–S136). The system of equations is used for modeling the interaction of an oncolytic virus with a tumor cell population. Our analysis is based on the existence of a Jacobi last multiplier and a time-dependent first integral. Suitable conditions on the model parameters allow for the reduction of the problem to a planar system of equations, and the time-dependent Hamiltonian flows are described. The geometry of the Hamiltonian flows is also investigated using the symplectic and cosymplectic methods.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"4173-4184"},"PeriodicalIF":1.8000,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10538","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.10538","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
We analyze the generalized Hamiltonian structure of a system of first-order ordinary differential equations for the Jenner et al. system (Letters in Biomathematics 5 (2018), no. S1, S117–S136). The system of equations is used for modeling the interaction of an oncolytic virus with a tumor cell population. Our analysis is based on the existence of a Jacobi last multiplier and a time-dependent first integral. Suitable conditions on the model parameters allow for the reduction of the problem to a planar system of equations, and the time-dependent Hamiltonian flows are described. The geometry of the Hamiltonian flows is also investigated using the symplectic and cosymplectic methods.
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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