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An Alternative to Moment Closure
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2017 (English)In: Bulletin of Mathematical Biology, ISSN 0092-8240, E-ISSN 1522-9602, Vol. 79, no 9, p. 2088-2108Article in journal (Refereed) Published
Abstract [en]

Moment closure methods are widely used to analyze mathematical models. They are specifically geared toward derivation of approximations of moments of stochastic models, and of similar quantities in other models. The methods possess several weaknesses: Conditions for validity of the approximations are not known, magnitudes of approximation errors are not easily evaluated, spurious solutions can be generated that require large efforts to eliminate, and expressions for the approximations are in many cases too complex to be useful. We describe an alternative method that provides improvements in these regards. The new method leads to asymptotic approximations of the first few cumulants that are explicit in the model's parameters. We analyze the univariate stochastic logistic Verhulst model and a bivariate stochastic epidemic SIR model with the new method. Errors that were made in early applications of moment closure to the Verhulst model are explained and corrected.

Place, publisher, year, edition, pages
Springer-Verlag New York, 2017. Vol. 79, no 9, p. 2088-2108
Keywords [en]
Asymptotic approximations, Quasi-stationarity, Verhulst model
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-215388DOI: 10.1007/s11538-017-0321-2ISI: 000410478100007Scopus ID: 2-s2.0-85024485320OAI: oai:DiVA.org:kth-215388DiVA, id: diva2:1147851
Note

QC 20171009

Available from: 2017-10-09 Created: 2017-10-09 Last updated: 2017-10-09Bibliographically approved

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  • apa
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  • de-DE
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  • nn-NB
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  • Other locale
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  • asciidoc
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