Population demography can change the network structure, which further plays an important role in the spreading of infectious disease. In this paper, we study the epidemic dynamics in temporal clustered networks where the local-world structure and clustering are incorporated into the attachment mechanism of new nodes. It is found that increasing the local-world size of new nodes has little influence on the clustering coefficient but increases the degree heterogeneity of networks. Besides, when the network evolves faster, increasing the local-world size of new nodes leads to a faster initial growth rate and a larger steady density of infectious nodes, while it has small impacts on the steady density of infectious disease when the network evolves slowly. Furthermore, if the average degree is fixed, increasing the probability of triad formation p enlarges the clustering coefficient of a network, which reduces the initial growth rate and steady density of infectious nodes in the network. This work could provide a theoretical foundation for the control of infectious disease.
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