An Alternative to Moment Closure

An Alternative to Moment Closure 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of Mathematical Biology Springer Journals

An Alternative to Moment Closure

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Publisher
Springer US
Copyright
Copyright © 2017 by Society for Mathematical Biology
Subject
Mathematics; Mathematical and Computational Biology; Life Sciences, general; Cell Biology
ISSN
0092-8240
eISSN
1522-9602
D.O.I.
10.1007/s11538-017-0321-2
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Bulletin of Mathematical BiologySpringer Journals

Published: Jul 18, 2017

References

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