A fixed point theorem for a general epidemic model

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:404

Article

Lucas, Adam R.

关键词: Susceptible-Infected-Susceptible epidemic model;    Fixed point theorem;    Epidemic threshold;    Percolation model;   

DOI  :  10.1016/j.jmaa.2013.03.013

来源: Elsevier

【 摘 要 】

Epidemic type models typically undergo a phase transition when the infection rate surpasses the epidemic threshold. However for networks having degree-degree correlations, the epidemic threshold has never formally been defined and there is a shortage of rigorous mathematics describing epidemic phase transitions. In the context of disease spreading on top of a complex network, this paper provides a set of necessary and sufficient conditions for the occurrence of a persistent infected state. As a proof of principle we demonstrate that the percolation and SIS/SIR epidemic models on complex correlated networks satisfy the assumptions necessary for a single phase transition. This paper attempts to highlight commonalities in a variety of different interacting particle systems. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free