Abstract
Prior social contagion models consider the spread of either one contagion on interdependent networks or multiple contagions on single layer networks, usually under assumptions of competition. We propose a new threshold model for the diffusion of multiple contagions. Individuals are placed on a multiplex network with a periodic lattice layer and a random-regular-graph layer. On these population structures, we study the interface between two key aspects of the diffusion process: the level of synergy between two contagions, and the rate at which individuals become dormant after adoption. Dormancy is defined as a looser form of immunity that limits active spreading but without conferring resistance. Monte Carlo simulations reveal lower synergy makes contagions more susceptible to percolation, especially those that diffuse on lattices. Faster diffusion of one contagion with dormancy probabilistically blocks the diffusion of the other, in a way similar to ring vaccination. We show that within a band of synergy, bimodal or trimodal branchings occur on the slower contagion on the lattice. We also show complimentary contagions can provide a synergistic boost to help spread contagions that have almost gone dormant.
Highlights
The term ”social contagion” implicitly captures two worlds: the world of social science and the world of epidemiology
There is a desire to understand the diffusion of multiple social contagions under synergistic assumptions and to model the mechanisms for their concurrent, interfering spread
Drawing upon established models within epidemiology and pharmacology, we propose a model which quantifies the amount of synergy between two contagions
Summary
The term ”social contagion” implicitly captures two worlds: the world of social science and the world of epidemiology. The term was initially coined in 1895 by Gustave Le Bon [1] to describe undesirable collective behaviors in crowds, the definition has been stretched to encompass and explain types of collective behavior produced through social contact [2] [3] [4] [5] [6] This broad definition, with advances in statistical physics [7], has led Contagion Theory’s inclusion within many avenues of social science research [8], including marketing [9], innovation diffusion [10], medicine [11], health interventions [12], rumor and information spreading [13] [14] sociology [15] [16], and the spread of emotion [17] [18] [19]. We study the impact of network topology on diffusion, by contrasting short-range connections of lattice graphs and the long-range connections of a multiplex random-regular-graph
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