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.
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 mode is proposed, which adopts one of four threshold distribution, 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 ER and SF networks to study the impact of different forms of 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.
The promotion system in Chinese universities has been undergoing a reform since 2017. This study employed an online survey validated by confirmatory factor analysis with 372 Chinese teachers to investigate the extent to which they were empowered by the two practices of participation in decision-making and professional growth in the reform and level of their appraisal of and behavioral intentions toward the new promotion system. Structural equation modeling was used to measure how the two empowerment practices influenced the teachers' appraisal of and behavioral intentions toward the new system. The findings suggest that the Chinese teachers had low participation in decision-making and medium institutional support for professional growth, relatively low nonmonetary cost-benefit appraisal and medium practicality and fairness appraisal of the new system, and relatively high behavioral intentions to increase efforts according to the new system. Besides, participation in decision-making had a significantly direct effect on practicality and nonmonetary cost-benefit appraisal. Professional growth had a significantly direct effect on practicality, fairness, and nonmonetary cost-benefit appraisal and behavioral intentions. Nonmonetary cost-benefit appraisal had a significantly direct effect on behavioral intentions. The implications are that, in promotion system reforms, the two empowerment strategies of shared decision-making and professional growth can help establish a new promotion system with high nonmonetary cost-benefits for teachers and raise teachers' behavioral intentions to develop and pursue promotion. They can also contribute to the formulation of a new promotion system that effectively evaluates individual teacher's achievements according to the characteristics of the specific university, teacher type, and discipline. This study had the limitations of using convenience sampling, collecting cross-sectional data through self-administered questionnaires, and reporting only teachers' side of the story. Therefore, it is recommended that future studies target both teachers and administrators, employ a mixed-method design, collect quantitative data through random sampling, and take a longitudinal view.
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