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Dynamics analysis of SIR epidemic model with correlation coefficients and clustering coefficient in networks
Juping Zhang1, Chan Yang1, Zhen Jin1
1Complex 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.
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.
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