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