Multilayer networks are widely used to characterize the dynamic behavior of complex systems. The study of epidemic spreading dynamics on multilayer networks has become a hot topic in network science. Although many models have been proposed to explore epidemic spreading across different networks, there is still a lack of models to study the spreading of diseases in the process of evolution on multilayer homogeneous networks. In the present work, we propose an epidemic spreading dynamic model of homogeneous evolving networks that can be used to analyze and simulate the spreading of epidemics on such networks. We determine the global epidemic threshold. We make the interesting discovery that increasing the epidemic threshold of a single network layer is conducive to mitigating the spreading of an epidemic. We find that the initial average degree of a network and the evolutionary parameters determine the changes in the epidemic threshold and the spreading process. An approach for calculating the falling and rising threshold zones is presented. Our work provides a good strategy to control epidemic spreading. Generally, controlling or changing the threshold in a single network layer is easier than trying to directly change the threshold in all network layers. Numerical simulations of small-world and random networks further support and enrich our conclusions. Published under license by AIP Publishing.
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