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Immunization strategies in directed networks

Department of Mathematics, Shanghai University, Shanghai 200444, China

Special Issues: Multiscale dynamics of infectious diseases, immune responses and therapeutics

Many complex systems can be modeled as directed networks, which can be regarded as a generalization of undirected networks. In this paper, epidemic dynamics and immunization strategies in directed networks are studied. First, a Susceptible-Infected-Susceptible (SIS) model on a directed network is established employing the mean-field method, and its dynamics and epidemic threshold of the network are studied. Then based on the continuous degree technique, namely, considering the degree of a node as a continuous variable, we propose a method to calculate the epidemic threshold of the immunized network. Besides, some immunization strategies, including optimal immunization, random immunization, combined targeted immunization, and combined acquaintance immunization, and three special networks are considered. Finally, through numerical analysis, all immunization strategies are simulated and compared on different types of networks. We find that the nodes with the largest product of in-degree and out-degree are the most worthy of being immunized.
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Keywords directed network; optimal immunization; random immunization; combined targeted immunization; combined acquaintance immunization

Citation: Junbo Jia, Wei Shi, Pan Yang, Xinchu Fu. Immunization strategies in directed networks. Mathematical Biosciences and Engineering, 2020, 17(4): 3925-3952. doi: 10.3934/mbe.2020218


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