R. Campoamor-Stursberg, Eduardo Fernández-Saiz, F. J. Herranz
{"title":"具有随机波动的时变SIS流行病模型的hamilton系统的精确解和叠加规则","authors":"R. Campoamor-Stursberg, Eduardo Fernández-Saiz, F. J. Herranz","doi":"10.3934/math.20231225","DOIUrl":null,"url":null,"abstract":"Using the theory of Lie-Hamilton systems, formal generalized time-dependent Hamiltonian systems that extend a recently proposed SIS epidemic model with a variable infection rate are considered. It is shown that, independently on the particular interpretation of the time-dependent coefficients, these systems generally admit an exact solution, up to the case of the maximal extension within the classification of Lie-Hamilton systems, for which a superposition rule is constructed. The method provides the algebraic frame to which any SIS epidemic model that preserves the above-mentioned properties is subjected. In particular, we obtain exact solutions for generalized SIS Hamiltonian models based on the book and oscillator algebras, denoted by $ \\mathfrak{b}_2 $ and $ \\mathfrak{h}_4 $, respectively. The last generalization corresponds to an SIS system possessing the so-called two-photon algebra symmetry $ \\mathfrak{h}_6 $, according to the embedding chain $ \\mathfrak{b}_2\\subset \\mathfrak{h}_4\\subset \\mathfrak{h}_6 $, for which an exact solution cannot generally be found but a nonlinear superposition rule is explicitly given.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":" ","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2023-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Exact solutions and superposition rules for Hamiltonian systems generalizing time-dependent SIS epidemic models with stochastic fluctuations\",\"authors\":\"R. Campoamor-Stursberg, Eduardo Fernández-Saiz, F. J. Herranz\",\"doi\":\"10.3934/math.20231225\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Using the theory of Lie-Hamilton systems, formal generalized time-dependent Hamiltonian systems that extend a recently proposed SIS epidemic model with a variable infection rate are considered. It is shown that, independently on the particular interpretation of the time-dependent coefficients, these systems generally admit an exact solution, up to the case of the maximal extension within the classification of Lie-Hamilton systems, for which a superposition rule is constructed. The method provides the algebraic frame to which any SIS epidemic model that preserves the above-mentioned properties is subjected. In particular, we obtain exact solutions for generalized SIS Hamiltonian models based on the book and oscillator algebras, denoted by $ \\\\mathfrak{b}_2 $ and $ \\\\mathfrak{h}_4 $, respectively. The last generalization corresponds to an SIS system possessing the so-called two-photon algebra symmetry $ \\\\mathfrak{h}_6 $, according to the embedding chain $ \\\\mathfrak{b}_2\\\\subset \\\\mathfrak{h}_4\\\\subset \\\\mathfrak{h}_6 $, for which an exact solution cannot generally be found but a nonlinear superposition rule is explicitly given.\",\"PeriodicalId\":48562,\"journal\":{\"name\":\"AIMS Mathematics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2023-04-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"AIMS Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3934/math.20231225\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"AIMS Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/math.20231225","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Exact solutions and superposition rules for Hamiltonian systems generalizing time-dependent SIS epidemic models with stochastic fluctuations
Using the theory of Lie-Hamilton systems, formal generalized time-dependent Hamiltonian systems that extend a recently proposed SIS epidemic model with a variable infection rate are considered. It is shown that, independently on the particular interpretation of the time-dependent coefficients, these systems generally admit an exact solution, up to the case of the maximal extension within the classification of Lie-Hamilton systems, for which a superposition rule is constructed. The method provides the algebraic frame to which any SIS epidemic model that preserves the above-mentioned properties is subjected. In particular, we obtain exact solutions for generalized SIS Hamiltonian models based on the book and oscillator algebras, denoted by $ \mathfrak{b}_2 $ and $ \mathfrak{h}_4 $, respectively. The last generalization corresponds to an SIS system possessing the so-called two-photon algebra symmetry $ \mathfrak{h}_6 $, according to the embedding chain $ \mathfrak{b}_2\subset \mathfrak{h}_4\subset \mathfrak{h}_6 $, for which an exact solution cannot generally be found but a nonlinear superposition rule is explicitly given.
期刊介绍:
AIMS Mathematics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in all fields of mathematics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports.