Dynamics analysis of SIR epidemic model with correlation coefficients and clustering coefficient in networks. (14th July 2018)

• Record Type: Journal Article
• Authors: Zhang, Juping; Yang, Chan; Jin, Zhen; Li, Jia
• Is Part Of: Journal of theoretical biology. Volume 449(2018)
• Page Start: 1
• Page End: 13
• Publication Date: 2018-07-14
• Subjects: Correlation coefficients -- Clustering coefficient -- Pair approximation -- Stability -- Basic reproduction number; Biology -- Periodicals; Biological Science Disciplines -- Periodicals; Biology -- Periodicals; Biologie -- Périodiques; Theoretische biologie; Biology; Periodicals; 571.05
• DOI: 10.1016/j.jtbi.2018.04.007
• Languages: English
• ISSNs: 0022-5193

Abstract

Highlights: The SIR epidemic dynamic models with correlation coefficients are proposed. The correlation coefficients between individuals are used as dynamic variables. More complex dynamics are generated. Two equivalent epidemic thresholds are given in the dynamic networks. 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.