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Chin. Phys. B, 2022, Vol. 31(6): 068906    DOI: 10.1088/1674-1056/ac4e04

Effects of heterogeneous adoption thresholds on contact-limited social contagions

Dan-Dan Zhao(赵丹丹)1, Wang-Xin Peng(彭王鑫)2, Hao Peng(彭浩)1,3, and Wei Wang(王伟)4,†
1 College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China;
2 College of Information, Zhejiang Guangsha Vocational and Technical University of Construction, Dongyang 322100, China;
3 Shanghai Key Laboratory of Integrated Administration Technologies for Information Security, Shanghai 200240, China;
4 School of Public Health and Management, Chongqing Medical University, Chongqing 400016, China
Abstract  Limited contact capacity and heterogeneous adoption thresholds have been proven to be two essential characteristics of individuals in natural complex social systems, and their impacts on social contagions exhibit complex nature. With this in mind, a heterogeneous contact-limited threshold model is proposed, which adopts one of four threshold distributions, namely Gaussian distribution, log-normal distribution, exponential distribution and power-law distribution. The heterogeneous edge-based compartmental theory is developed for theoretical analysis, and the calculation methods of the final adoption size and outbreak threshold are given theoretically. Many numerical simulations are performed on the Erdös-Rényi and scale-free networks to study the impact of different forms of the threshold distribution on hierarchical spreading process, the final adoption size, the outbreak threshold and the phase transition in contact-limited propagation networks. We find that the spreading process of social contagions is divided into three distinct stages. Moreover, different threshold distributions cause different spreading processes, especially for some threshold distributions, there is a change from a discontinuous first-order phase transition to a continuous second-order phase transition. Further, we find that changing the standard deviation of different threshold distributions will cause the final adoption size and outbreak threshold to change, and finally tend to be stable with the increase of standard deviation.
Keywords:  social contagions      threshold distribution      heterogeneous adoption thresholds      limited contact  
Received:  06 October 2021      Revised:  29 December 2021      Accepted manuscript online:  24 January 2022
PACS:  89.75.Hc (Networks and genealogical trees)  
  87.19.X- (Diseases)  
  87.23.Ge (Dynamics of social systems)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 62072412, 61902359, 61672467, and 61672468), the Social Development Project of Zhejiang Provincial Public Technology Research (Grant No. 2016C33168), Zhejiang Provincial Natural Science Foundation of China (Grant No. LQ19F030010), and the Opening Project of Shanghai Key Laboratory of Integrated Administration Technologies for Information Security (Grant No. AGK2018001).
Corresponding Authors:  Wei Wang     E-mail:,

Cite this article: 

Dan-Dan Zhao(赵丹丹), Wang-Xin Peng(彭王鑫), Hao Peng(彭浩), and Wei Wang(王伟) Effects of heterogeneous adoption thresholds on contact-limited social contagions 2022 Chin. Phys. B 31 068906

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