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Systematization of a set of closure techniques

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  • Hausken, Kjell
  • Moxnes, John F.

Abstract

Approximations in population dynamics are gaining popularity since stochastic models in large populations are time consuming even on a computer. Stochastic modeling causes an infinite set of ordinary differential equations for the moments. Closure models are useful since they recast this infinite set into a finite set of ordinary differential equations. This paper systematizes a set of closure approximations. We develop a system, which we call a power p closure of n moments, where 0≤p≤n. Keeling’s (2000a,b) approximation with third order moments is shown to be an instantiation of this system which we call a power 3 closure of 3 moments. We present an epidemiological example and evaluate the system for third and fourth moments compared with Monte Carlo simulations.

Suggested Citation

  • Hausken, Kjell & Moxnes, John F., 2011. "Systematization of a set of closure techniques," Theoretical Population Biology, Elsevier, vol. 80(3), pages 175-184.
    • Handle: RePEc:eee:thpobi:v:80:y:2011:i:3:p:175-184
    DOI: 10.1016/j.tpb.2011.07.001
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    References listed on IDEAS

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    1. Kjell Hausken & John F. Moxnes, 2005. "The Dynamics Of Multilateral Exchange," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 16(04), pages 607-631.
    2. Kjell Hausken & John F. Moxnes, 2010. "A closure approximation technique for epidemic models," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 16(6), pages 555-574, May.
    3. Cornell, Stephen J. & Ovaskainen, Otso, 2008. "Exact asymptotic analysis for metapopulation dynamics on correlated dynamic landscapes," Theoretical Population Biology, Elsevier, vol. 74(3), pages 209-225.
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