Solving stochastic epidemiological models using computer algebra

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dc.contributor.authorHincapie, D.
dc.contributor.authorOspina, J.
dc.contributor.departmentUniversidad EAFIT. Departamento de Cienciasspa
dc.contributor.researchgroupLógica y Computaciónspa
dc.creatorHincapie, D.
dc.creatorOspina, J.
dc.date.accessioned2021-03-26T21:35:21Z
dc.date.available2021-03-26T21:35:21Z
dc.date.issued2011-01-01
dc.description.abstractMathematical modeling in Epidemiology is an important tool to understand the ways under which the diseases are transmitted and controlled. The mathematical modeling can be implemented via deterministic or stochastic models. Deterministic models are based on short systems of non-linear ordinary differential equations and the stochastic models are based on very large systems of linear differential equations. Deterministic models admit complete, rigorous and automatic analysis of stability both local and global from which is possible to derive the algebraic expressions for the basic reproductive number and the corresponding epidemic thresholds using computer algebra software. Stochastic models are more difficult to treat and the analysis of their properties requires complicated considerations in statistical mathematics. In this work we propose to use computer algebra software with the aim to solve epidemic stochastic models such as the SIR model and the carrier-borne model. Specifically we use Maple to solve these stochastic models in the case of small groups and we obtain results that do not appear in standard textbooks or in the books updated on stochastic models in epidemiology. From our results we derive expressions which coincide with those obtained in the classical texts using advanced procedures in mathematical statistics. Our algorithms can be extended for other stochastic models in epidemiology and this shows the power of computer algebra software not only for analysis of deterministic models but also for the analysis of stochastic models. We also perform numerical simulations with our algebraic results and we made estimations for the basic parameters as the basic reproductive rate and the stochastic threshold theorem. We claim that our algorithms and results are important tools to control the diseases in a globalized world. © 2011 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).eng
dc.identifierhttps://eafit.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=6791
dc.identifier.doi10.1117/12.883702
dc.identifier.issn0277786X
dc.identifier.issn1996756X
dc.identifier.otherWOS;000295931800007
dc.identifier.otherSCOPUS;2-s2.0-79959814734
dc.identifier.urihttp://hdl.handle.net/10784/27430
dc.language.isoengeng
dc.publisherSPIE-INT SOC OPTICAL ENGINEERING
dc.relation.urihttps://www.scopus.com/inward/record.uri?eid=2-s2.0-79959814734&doi=10.1117%2f12.883702&partnerID=40&md5=24b454dd2ef20117b6561ecff63d410f
dc.rightshttps://v2.sherpa.ac.uk/id/publication/issn/0277-786X
dc.sourceProceedings of SPIE
dc.subject.keywordBasic reproductive numbereng
dc.subject.keywordCarrier-borne modeleng
dc.subject.keywordcontact networkeng
dc.subject.keywordMapleeng
dc.subject.keywordMathematical epidemiologyeng
dc.subject.keywordSAGEeng
dc.subject.keywordSIR modeleng
dc.subject.keywordTutte polynomialeng
dc.subject.keywordAlgebraeng
dc.subject.keywordAlgorithmseng
dc.subject.keywordBiometricseng
dc.subject.keywordComputer simulationeng
dc.subject.keywordComputer softwareeng
dc.subject.keywordDisease controleng
dc.subject.keywordDiseaseseng
dc.subject.keywordEnvironmental engineeringeng
dc.subject.keywordGraph theoryeng
dc.subject.keywordIdentification (control systems)eng
dc.subject.keywordOrdinary differential equationseng
dc.subject.keywordStatisticseng
dc.subject.keywordStochastic systemseng
dc.subject.keywordTechnologyeng
dc.subject.keywordStochastic modelseng
dc.titleSolving stochastic epidemiological models using computer algebraeng
dc.typeinfo:eu-repo/semantics/conferencePapereng
dc.typeconferencePapereng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
dc.type.localDocumento de conferenciaspa

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