Dynamics analysis of SIR epidemic model with correlation coefficients and clustering coefficient in networks

Juping Zhang; Chan Yang; Zhen Jin; Jia Li

doi:10.1016/j.jtbi.2018.04.007

Dynamics analysis of SIR epidemic model with correlation coefficients and clustering coefficient in networks

J Theor Biol. 2018 Jul 14:449:1-13. doi: 10.1016/j.jtbi.2018.04.007. Epub 2018 Apr 10.

Authors

Juping Zhang¹, Chan Yang¹, Zhen Jin², Jia Li³

Affiliations

¹ Complex Systems Research Center, Shanxi University, Taiyuan 030006, China; Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease, Control and Prevention, Shanxi University, Taiyuan 030006, China.
² Complex Systems Research Center, Shanxi University, Taiyuan 030006, China; Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease, Control and Prevention, Shanxi University, Taiyuan 030006, China. Electronic address: jinzhn@263.net.
³ Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899, USA.

PMID: 29649430
DOI: 10.1016/j.jtbi.2018.04.007

Abstract

In this paper, the correlation coefficients between nodes in states are used as dynamic variables, and we construct SIR epidemic dynamic models with correlation coefficients by using the pair approximation method in static networks and dynamic networks, respectively. Considering the clustering coefficient of the network, we analytically investigate the existence and the local asymptotic stability of each equilibrium of these models and derive threshold values for the prevalence of diseases. Additionally, we obtain two equivalent epidemic thresholds in dynamic networks, which are compared with the results of the mean field equations.

Keywords: Basic reproduction number; Clustering coefficient; Correlation coefficients; Pair approximation; Stability.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Communicable Diseases / epidemiology*
Computer Simulation*
Humans
Models, Biological*