Dynamics of social contagions with limited contact capacity

Abstract

Individuals are always limited by some inelastic resources, such as time and energy, which restrict them to dedicate to social interaction and limit their contact capacities. Contact capacity plays an important role in dynamics of social contagions, which so far has eluded theoretical analysis. In this paper, we first propose a non-Markovian model to understand the effects of contact capacity on social contagions, in which each adopted individual can only contact and transmit the information to a finite number of neighbors. We then develop a heterogeneous edge-based compartmental theory for this model, and a remarkable agreement with simulations is obtained. Through theory and simulations, we find that enlarging the contact capacity makes the network more fragile to behavior spreading. Interestingly, we find that both the continuous and discontinuous dependence of the final adoption size on the information transmission probability can arise. There is a crossover phenomenon between the two types of dependence. More specifically, the crossover phenomenon can be induced by enlarging the contact capacity only when the degree exponent is above a critical degree exponent, while the final behavior adoption size always grows continuously for any contact capacity when degree exponent is below the critical degree exponent.

Unification of theoretical approaches for epidemic spreading on complex networks

“…We explain their main ideas and basic assumptions, and we describe the relationships among them. These approaches have also been widely used in studying the dynamics of social contagions [148][149][150][158][159][160][161][162]. As network science has developed and expanded, many of the existing theoretical approaches have been challenged, and we now must take into consideration numerous intricate mechanisms and network topologies when we build epidemic spreading models.…”

“…Recently these same authors developed the EBC approach for a non-Markovian social contagion and found a transition in which the final adoption size depends on such key parameters as the transmission probability, which can change from discontinuous to continuous [148]. The transition can be triggered by such parameters and structural perturbations to the system as decreasing the adoption threshold of individuals, decreasing the heterogeneity of the adoption threshold, increasing the initial seed size or contact capacity, or enhancing network heterogeneity [148][149][150].…”

Emergence of hysteresis loop in social contagions on complex networks

“…Recently Wang et al . proposed a non-Markovian behavior spreading model to study the effects of social reinforcement and found that the final adoption size versus the transmission probability can change from discontinuous to continuous 22–24 .…”

Social contagions on interdependent lattice networks

“…Our results extend existing studies of interdependent spatial networks and help us understand phase transitions in the social contagion process. The social contagion models including other individual behavior mechanisms, e.g., limited contact ability27 or heterogenous adopted threshold28, should be further explored. Further theoretical studies of our model are very important and full of challenges since the non-Markovian character of our model and non-local-tree like structure of the lattice make it extremely difficult to describe the strong dynamical correlations among the states of neighbors.…”

“…Social contagions252627282930, which include the adoption of social innovations313233, healthy behaviors34, and the diffusion of microfinance35, are another typical dynamical process. Research results show that multiple confirmations of the credibility and legitimacy of a piece of news or a new trend are ubiquitous in social contagions, and the probability that an individual will adopt a new social behavior depends upon previous contacts, i.e., the social reinforcement effect3436373839.…”