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Algebraic Moment Closure for Population Dynamics on Discrete Structures

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Abstract

Moment closure on general discrete structures often requires one of the following: (i) an absence of short-closed loops (zero clustering); (ii) existence of a spatial scale; (iii) ad hoc assumptions. Algebraic methods are presented to avoid the use of such assumptions for populations based on clumps and are applied to both SIR and macroparasite disease dynamics. One approach involves a series of approximations that can be derived systematically, and another is exact and based on Lie algebraic methods.

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Acknowledgments

Work funded by the UK Engineering and Physical Sciences Research Council (EPSRC). The author would like to thank Joshua Ross, the editors, and three anonymous reviewers for helpful comments on this manuscript.

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Correspondence to Thomas House.

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House, T. Algebraic Moment Closure for Population Dynamics on Discrete Structures. Bull Math Biol 77, 646–659 (2015). https://doi.org/10.1007/s11538-014-9981-3

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  • DOI: https://doi.org/10.1007/s11538-014-9981-3

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