Computational aspects of time-lag models of Marchuk type that arise in immunology

Hdl Handle:
http://hdl.handle.net/10034/67630
Title:
Computational aspects of time-lag models of Marchuk type that arise in immunology
Authors:
Baker, Christopher T. H.; Bocharov, Gennady
Abstract:
In his book published in English translation in 1983, Marchuk proposed a set of evolutionary equations incorporating delay-differential equations, and the corresponding initial conditions as a model ('Marchuk's model') for infectious diseases. The parameters in this model (and its subsequent extensions) represent scientifically meaningful characteristics. For a given infection, the parameters can be estimated using observational data on the course of the infection. Sensitivity analysis is an important tool for understanding a particular model; this can be viewed as an issue of stability with respect to structural perturbations in the model. Examining the sensitivity of the models based on delay differential equations leads to systems of neutral delay differential equations. Below we formulate a general set of equations for the sensitivity coefficients for models comprising neutral delay differential equations. We discuss computational approaches to the sensitivity of solutions — (i) sensitivity to the choice of model, in particular, to the lag parameter τ > 0 and (ii) sensitivity to the initial function — of dynamical systems with time lag and illustrate them by considering the sensitivity of solutions of time-lag models of Marchuk type.
Affiliation:
University of Chester ; Institute of Numerical Mathematics, Russian Academy of Sciences
Citation:
Russian Journal of Numerical Analysis and Mathematical Modelling, 2005, 20, pp. 247-262
Publisher:
de Gryuter
Journal:
Russian Journal of Numerical Analysis and Mathematical Modelling
Publication Date:
2005
URI:
http://hdl.handle.net/10034/67630
DOI:
10.1515/1569398054308630
Additional Links:
http://www.reference-global.com/loi/rnam
Type:
Article
Language:
en
Description:
This journal article is not available through ChesterRep.
ISSN:
0927-6467; 1569-3988
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorBaker, Christopher T. H.en
dc.contributor.authorBocharov, Gennadyen
dc.date.accessioned2009-05-08T11:08:43Zen
dc.date.available2009-05-08T11:08:43Zen
dc.date.issued2005en
dc.identifier.citationRussian Journal of Numerical Analysis and Mathematical Modelling, 2005, 20, pp. 247-262en
dc.identifier.issn0927-6467en
dc.identifier.issn1569-3988en
dc.identifier.doi10.1515/1569398054308630en
dc.identifier.urihttp://hdl.handle.net/10034/67630en
dc.descriptionThis journal article is not available through ChesterRep.en
dc.description.abstractIn his book published in English translation in 1983, Marchuk proposed a set of evolutionary equations incorporating delay-differential equations, and the corresponding initial conditions as a model ('Marchuk's model') for infectious diseases. The parameters in this model (and its subsequent extensions) represent scientifically meaningful characteristics. For a given infection, the parameters can be estimated using observational data on the course of the infection. Sensitivity analysis is an important tool for understanding a particular model; this can be viewed as an issue of stability with respect to structural perturbations in the model. Examining the sensitivity of the models based on delay differential equations leads to systems of neutral delay differential equations. Below we formulate a general set of equations for the sensitivity coefficients for models comprising neutral delay differential equations. We discuss computational approaches to the sensitivity of solutions — (i) sensitivity to the choice of model, in particular, to the lag parameter τ > 0 and (ii) sensitivity to the initial function — of dynamical systems with time lag and illustrate them by considering the sensitivity of solutions of time-lag models of Marchuk type.en
dc.language.isoenen
dc.publisherde Gryuteren
dc.relation.urlhttp://www.reference-global.com/loi/rnamen
dc.titleComputational aspects of time-lag models of Marchuk type that arise in immunologyen
dc.typeArticleen
dc.contributor.departmentUniversity of Chester ; Institute of Numerical Mathematics, Russian Academy of Sciencesen
dc.identifier.journalRussian Journal of Numerical Analysis and Mathematical Modellingen
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