Dynamics of social contagions with limited contact capacity

TL;DR

This paper investigates how limited contact capacity influences social contagion dynamics, revealing that increasing contact capacity can make networks more susceptible to behavior spreading and can lead to different types of adoption size dependence.

Contribution

It introduces a non-Markovian model incorporating contact capacity and develops a heterogeneous edge-based theory, providing new insights into social contagion behaviors.

Findings

Enlarging contact capacity increases network fragility.

Both continuous and discontinuous adoption size dependence are observed.

A crossover phenomenon depends on the degree exponent.

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 capacity. 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 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. And 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 the final behavior adoption size always grows continuously for any contact capacity when degree exponent is below the critical degree exponent.