Reinforcement-driven spread of innovations and fads

Abstract

Abstract. We investigate how social reinforcement drives the spread of permanent innovations and transient fads. We account for social reinforcement by endowing each individual with M + 1 possible awareness states 0, 1, 2, . . . , M , with state M corresponding to adopting an innovation. An individual with awareness k < M increases to k + 1 by interacting with an adopter. Starting with a single adopter, the time for an initially unaware population that consists of N individuals to adopt an innovation grows as ln N for M = 1, and as N 1−1/M for M > 1. When individuals can abandon the innovation at rate λ, the population fraction that remains clueless about the fad undergoes a phase transition at λ c ; this transition is second order for M = 1 and first order for M > 1, with macroscopic fluctuations accompanying the latter. The time for the fad to disappear has an intriguing non-monotonic dependence on λ.

Effects of variable-state neighborhoods for spreading synergystic processes on lattices

“…Without lost of generality, we restrict the analysis to functions A(t) satisfying 1 0 A(t)dt = 1 in order for Eq. (11) and thus all the equations derived in Sec. III A for general ρ(t j ) to hold.…”

“…Several theoretical models have been developed to incorporate synergistic effects in the description of spreading processes [2,[7][8][9][10][11][12][13]. In particular, the effects of constructive and destructive synergy caused by the nearest neighbors of the pair of hosts transmitting infection in between were considered for SIR process in Ref.…”

The dynamics of two-stage contagion

“…An equivalent model is introduced in [9], as a way to describe co-infection with two pathogens, under some symmetry assumptions. A similar model was introduced in [33], with the aim of describing innovations (with permanent adoption) and fads (with temporary adoption), and including an arbitrary number of stages, though without direct movement of naive individuals into the adopter class. The models above do not include demographic turnover, so that there is no mechanism for the renewal of the naive population, and they therefore generate transient epidemics rather than endemic states (except for the permanent adoption model of [33], in which the entire population eventually adopts).…”

“…To incorporate the idea of stages of contagion into mathematical models, one can divide the population into classes, each of which consists of individuals at a certain stage in the adoption process, with movement among the classes due to contact with adopters. Models of this type have been proposed studied in several works [4,10,11,13,14,22,27,28,33], and in section 1.2 we will briefly describe and compare these with the model studied here.…”

A new rumor propagation model on SNS structure

“…More information is spreading in the online social networks, such as fads, news, opinions, rumor, and so on [20,21,22]. In our opinion, we should pay close attention to rumor propagation (in this paper, rumor is defined as false news).…”