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Author Novozhilov, Artem S.
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2008-09-09
Language English
Subject Domain (in DDC) Natural sciences & mathematics ♦ Life sciences; biology
Subject Keyword Quantitative Biology - Populations and Evolution ♦ q-bio
Abstract In many epidemiological models a nonlinear transmission function is used in the form of power law relationship. It is constantly argued that such form reflects population heterogeneities including differences in the mixing pattern, susceptibility, and spatial patchiness, although the function itself is considered phenomenological. Comparison with large-scale simulations show that models with this transmission function accurately approximate data from highly heterogeneous sources. In this note we provide a mechanistic derivation of the power law transmission function, starting with a simple heterogeneous susceptibles--infectives (SI) model, which is based on a standard mass action assumption. We also consider the simplest SI model with separable mixing and compare our results with known results from the literature.
Description Comment: 14 pages, 1 figure. This is an extended version of the manuscript accepted for the publication in Proceedings of the 6th International Conference Differential Equations and Dynamical Systems, Baltimore, USA, 2008
Educational Use Research
Learning Resource Type Article
Page Count 14


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