Interplay between exogenous triggers and endogenous behavioral changes in contagion processes on social networks

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arXiv:2210.15286v1 [physics.soc-ph] 27 Oct 2022

Interplay between exogenous triggers and endogenous

behavioral changes in contagion processes on social

networks

Clara Eminentea,∗, Oriol Artimeb, Manlio De Domenicoa,c

aDepartment of Physics and Astronomy ‘Galileo Galilei’, University of Padua, Padova,

Veneto, Italy

bCHuB Lab, Fondazione Bruno Kessler, Via Sommarive 18, Povo, TN 38123, Italy

cPadua Center for Network Medicine, University of Padua, Padova, Veneto, Italy

Abstract

In recent years, statistical physics’ methodologies have proven extremely suc-

cessful in oﬀering insights into the mechanisms that govern social interac-

tions. However, the question of whether these models are able to capture

trends observed in real-world datasets is hardly addressed in the current lit-

erature. With this work we aim at bridging the gap between theoretical mod-

eling and validation with data. In particular, we propose a model for opinion

dynamics on a social network in the presence of external triggers, framing

the interpretation of the model in the context of misbehavior spreading. We

divide our population in aware, unaware and zealot/educated agents. Indi-

viduals change their status according to two competing dynamics, referred

to as behavioral dynamics and broadcasting. The former accounts for infor-

mation spreading through contact among individuals whereas broadcasting

plays the role of an external agent, modeling the eﬀect of mainstream media

∗Corresponding Author

Email address: clara.eminente@gmail.com (Clara Eminente)

Preprint submitted to Elsevier October 28, 2022

outlets. Through both simulations and analytical computations we ﬁnd that

the stationary distribution of the fraction of unaware agents in the system

undergoes a phase transition when an all-to-all approximation is considered.

Surprisingly, such a phase transition disappears in the presence of a min-

imum fraction of educated agents. Finally, we validate our model using

data collected from the public discussion on Twitter, including millions of

posts, about the potential adverse eﬀects of the AstraZeneca vaccine against

COVID-19. We show that the intervention of external agents, as accounted

for in our model, is able to reproduce some key features that are found in

this real-world dataset.

Keywords: complex networks, noisy opinion dynamics, covid-19

https://doi.org/10.1016/j.chaos.2022.112759

1. Introduction

The eﬀects that external, often traumatic events have on collective at-

tention and public opinion are of utmost importance due to their societal,

economical and political impact and, accordingly, have been studied from

diﬀerent points of view in various disciplines [1, 2, 3]. The role played by

mainstream media in disseminating information is particularly crucial dur-

ing periods of crisis [4], as citizens’ perception of the news can alter the

way they process and share information, ultimately leading to behavioral

changes that might be harmful from both the individual and the collective

viewpoints. This inevitably entangles the role of mainstream media with

another increasingly important phenomenon: the unprecedented speed and

reach of content spreading, such as rumors and fake news, on online social

networks [5]. However, recent studies have shown that often mainstream

media fail to bridge the public discourse with the accurate and objective

representation of external events [6], calling for a study of the eﬀects of their

inﬂuence: do mainstream media inﬂuence online discussion both in terms of

topics (what is discussed online) and sentiment (how is it addressed)? Can

the way media report an event be more relevant in shaping public discussion

than the occurrence of the event itself? Providing solid and convincing an-

swers to this type of questions would be an important step toward a more

eﬃcient, reliable and democratic information ecosystem.

Previous works have already investigated the role of mainstream media

from a mechanistic perspective. For example, Quattrociocchi et al. [7] high-

lighted how diﬀerent communication strategies can determine the reach of

consensus in the population; Gonz´alez-Avella et al. [8] linked the cultural

diversity of a society with the inﬂuence strength of the broadcasted mes-

sages by the media; Brooks et al. [9] proposed a model that incorporates

mainstream media as part of the social media network, analyzing how to

maximize their inﬂuence. Moreover, by analyzing real-world data, it has

been found that mainstream media agenda and online discussion tend to

align, especially in periods of crises [10]. Finally, Pires et al. [11] showed

how the sentiment towards a topic (vaccination) can indeed have disruptive

eﬀects when coupled to another dynamical process (disease spreading). The

strands of research can be roughly divided between those works that propose

simple models where isolated socially-inspired mechanisms are tested in order

to establish cause-eﬀect relations that go beyond statistical correlations [12]

(see, e.g., [13, 14] for good reviews), and those works that aim at giving in-

sights directly from the data analysis [15, 16], that sometimes are oriented

toward accurate future predictions, e.g., via machine learning algorithms. Of

course, the frontier is blurry and there is a continuous spectrum of works

that lie between these two approaches [17], even though they are still scarce

in number.

With the aim of bridging the two aforementioned strands in the context of

information spreading and mass media inﬂuence, here we study a variation of

one of these statistical mechanics ﬂavoured models -the so-called Kirman [18]

or noisy voter model [19]- and evaluate its performance at reproducing the

onset of the online debate in Twitter about the AstraZeneca vaccine ban in

the late winter of 2021. Hence, from a theoretical and modeling standpoint,

we address how exogenous events inﬂuence the behavioral dynamics on a

social network via a model that, with an appropriate ﬁtting procedure, is

able to reproduce some trends observed in a real event.

The article is organized as follows. In the ﬁrst section we introduce our

proposed model, explaining how we account for both social interactions and

the external drive of mainstream media. We provide a summary of results,

highlighting diﬀerent regimes of the dynamics using agent-based simulations

and oﬀering a description of the model analytically in its all-to-all approxima-

tion. We next move to the comparison of the model to a real-world scenario.

To close, we oﬀer the conclusions.

2. Modeling the role of broadcasters in a social contagion process

The phenomenon we are investigating lies at the intersection between

opinion and information (e.g., rumors) spreading [13]. We refer to the spread-

ing phenomenon taking place on the social network as behavioral dynam-

ics. This accounts for standard communication between individuals via their

social contacts. On top of that, we consider an additional process that, in

ﬁrst approximation, is not bounded by the topology. This, what we call

broadcasting dynamics, is related to the role played by the mainstream

media outlets, such as newspapers, television and radio, whose direct inﬂu-

ence disregards social connections. Last but not least, we want to take into

account those individuals with a strong moral, who would never engage in

the misbehavior. They can also be interpreted as a fraction of “uninter-

ested” individuals, who might, in general, be connected to individuals with

certain interests (e.g. the discussion around vaccines) but that decide to not

take part in a particular discussion (e.g. hesitancy toward the AstraZeneca

vaccine).

2.1. Mathematical modeling of behavioral and broadcasting dynamics

Let us consider a population of Nindividual, also called agents, each

one endowed with a binary variable: Uand A. In the framework of mis-

conduct dynamics, Ustands for unaware, whereas Astands for aware of

the misconduct. The unaware population is split, in turn, into two types

of agents U(t) = ˜

U+U0(t), such that 0 ≤˜

U+U0(t)≤N.˜

Urepresents

the number of zealots, agents that, by external reasons, will not change their

state [20, 21, 22]. On the contrary, U0is the corresponding population of un-

aware individuals that can change state, therefore all the temporal evolution

of the unaware population is precisely due to U0.

We consider two mechanisms of state change. The ﬁrst is an SIS-like

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arXiv:2210.15286v1[physics.soc-ph]27Oct2022InterplaybetweenexogenoustriggersandendogenousbehavioralchangesincontagionprocessesonsocialnetworksClaraEminentea,∗,OriolArtimeb,ManlioDeDomenicoa,caDepartmentofPhysicsandAstronomy‘GalileoGalilei’,UniversityofPadua,Padova,Veneto,ItalybCHuBLab,FondazioneBrun...

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Interplay between exogenous triggers and endogenous behavioral changes in contagion processes on social networks

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