Order reprints

Heterogeneous population dynamics and scaling laws near epidemic outbreaks

Andreas Widder Christian Kuehn

*Corresponding author:  


In this paper, we focus on the influence of heterogeneity and stochasticity of the population on thedynamical structure of a basic susceptible-infected-susceptible (SIS) model. Firstwe prove that, upon a suitable mathematical reformulation of the basic reproduction number, thehomogeneous system and the heterogeneous system exhibit a completely analogous globalbehaviour. Then we consider noise terms to incorporate the fluctuation effects and therandom import of the disease into the population and analyse the influence of heterogeneityon warning signs for critical transitions (or tipping points). This theory shows that one maybe able to anticipate whether a bifurcation point is close before it happens. We use numericalsimulations of a stochastic fast-slow heterogeneous population SIS model and show various aspectsof heterogeneity have crucial influences on the scaling laws that are used as early-warningsigns for the homogeneous system. Thus, although the basic structural qualitative dynamicalproperties are the same for both systems, the quantitative features for epidemic predictionare expected to change and care has to be taken to interpret potential warning signs for diseaseoutbreaks correctly.

Please supply your name and a valid email address you yourself

Fields marked*are required

Article URL   http://www.aimspress.com/MBE/article/2249.html
Article ID   1551-0018_2016_5_1093
Editorial Email  
Your Name *
Your Email *
Quantity *

Copyright © AIMS Press All Rights Reserved