Algebraic moment closure for population dynamics on discrete structures

TL;DR

This paper introduces algebraic methods for moment closure in population dynamics on discrete structures, avoiding common assumptions and applying to disease models with systematic and exact approaches.

Contribution

It presents algebraic techniques, including Lie algebraic methods, to achieve moment closure without typical assumptions in population models on discrete networks.

Findings

Systematic approximation methods for moment closure.

Exact algebraic closure using Lie algebraic techniques.

Application to SIR and macroparasite disease models.

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.