Impact of Immunization Strategies on the Dynamics of Social Contagions

Hao Peng,Zhonglong Zheng,Dandan Zhao,Wangxin Peng,Zhaolong Hu,Jianmin Han

doi:10.1155/2020/5284348

Hao Peng, Zhonglong Zheng + Show 4 more

Open Access

https://doi.org/10.1155/2020/5284348

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Abstract

Immunization strategies on complex networks are effective methods to control the spreading dynamics on complex networks, which change the topology and connectivity of the underlying network, thereby affecting the dynamics process of propagation. Here, we use a non-Markovian threshold model to study the impact of immunization strategies on social contagions, in which the immune index greater than (or equal to) 0 corresponds to targeted (random) immunization, and when the immune index is less than 0, the probability of an individual being immunized is inversely related to the degree of the individual. A generalized edge-based compartmental theory is developed to analyze the dynamics of social contagions under immunization, and theoretical predictions are very consistent with simulation results. We find that increasing the immune index or increasing the immune ratio will reduce the final adoption size and increase the outbreak threshold, in other words, make the residual network after immunization not conducive to social contagions. Interestingly, enhancing the network heterogeneity is proved to help improve the immune efficiency of targeted immunization. Besides, the dependence of the outbreak threshold on the network heterogeneity is correlated with the immune ratio and immune index.

Highlights

In many fields, such as sociology and biology, the diffusion mechanisms of some real spreading processes can be essentially described as the spreading dynamics on complex networks [1,2,3,4,5,6]
In this paper, we have systematically studied the effects of degree-based immunization strategies on the dynamics of social contagions
Using a non-Markovian SAR threshold model, we described the dynamics of social contagions under immunization, in which the adoption threshold of all individuals is the same, and the immune probability of each individual is related to its degree and the immune index. e type of immunization strategy depends on the size of the immune index

Summary

Introduction

In many fields, such as sociology and biology, the diffusion mechanisms of some real spreading processes can be essentially described as the spreading dynamics on complex networks [1,2,3,4,5,6]. There is still a lack of systematic theoretical and numerical simulations to address how immunization strategies affect the dynamics of social contagions For this purpose, we use the non-Markovian susceptible-adoptedrecovered (SAR) threshold model to study the effects of different immunization strategies on social contagions, in which we select different types of immunization strategies by adjusting the value of the immune index α. En, a proportion ρ0 of valid individuals are selected randomly as the adopted individuals for triggering social contagion, and the remaining valid individuals are susceptible individuals and have not obtained any behavioral information. In the residual network, each adopted individual j can transmit the behavioral information to its susceptible neighbors with probability λ in a nonredundant transmission way (i.e., a piece of information can only be passed once through an edge). If there are no adopted individuals in the residual network after immunization, the social contagion ends

Theoretical Analysis

Numerical Simulations and Analysis

Conclusions