Immunization strategies in directed networks

Junbo Jia; Wei Shi; Pan Yang; Xinchu Fu; Junbo Jia; Wei Shi; Pan Yang; Xinchu Fu

doi:10.3934/mbe.2020218

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 4: 3925-3952. doi: 10.3934/mbe.2020218

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Research article Special Issues

Immunization strategies in directed networks

Department of Mathematics, Shanghai University, Shanghai 200444, China

Received: 12 March 2020 Accepted: 20 May 2020 Published: 28 May 2020

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.
- 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[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 3925-3952. doi: 10.3934/mbe.2020218

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Abstract

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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