title: Systematization of a set of closure techniques.
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.
authors.affiliation: Faculty of Social Sciences, University of Stavanger, N-4036 Stavanger, Norway. kjell.hausken@uis.no
authors.forename: Kjell
authors.initials: K
authors.lastname: Hausken
authors.forename: John F
authors.initials: JF
authors.lastname: Moxnes
mesh_terms: D020342:Finite Element Analysis; D008962:Models, Theoretical; D009010:Monte Carlo Method; D011336:Probability