Heterogeneous Susceptibles-Infectives model: Mechanistic derivation of the power law transmission function
Abstract
Description
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.
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
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