Using Simulations for Exploring Interventions in Social Networks

Modeling Physical Activity Behaviour in Dutch School Classes

Eric Fernandes de Mello Ara

ujo

, Bojan Simoski

, Thabo van Woudenberg

, Kirsten Bevelander

Crystal Smit

, Laura Buijs

, Michel Klein

and Moniek Buijzen

Behavioural Informatics Group, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands

Behavioural Science Institute, Radboud University, Communication Science, Nijmegen, The Netherlands

Keywords:

Agent-based Modeling, Physical Activity, Social Contagion, Social Networks, Behavioural Informatics,

Children.

Abstract:

The reduction of childhood obesity through the promotion of a healthy lifestyle is one of the most important

public health challenges at the moment. It is known that the unhealthy habits of children can cause unavoidable

side effects in their early stage of life, including both physical and mental consequences. This work considers

that the physical activity level of children is a behaviour that can be spread throughout the social relations of

children in their daily life at school. Therefore, the aim of this work is to deﬁne what the best strategy is to ﬁnd

’targets’ (i.e., inﬂuential children that can initiate behavioural change) for physical activity (PA) interventions

that would affect the average PA of a population of Dutch school classes. We tuned a model based on the

inﬂuence of the children’s peers in their social network, based on the data set from the MyMovez project

– Phase I. Five intervention strategies were implemented, and their efﬁcacy was compared. Once the targets

were chosen, an increase of 17% was applied to their initial PA. Then, the diffusion model was run to verify the

improvement on the PA of the whole network after one year. We discuss implications of the simulation results

on which strategies may be used to make informed choices about the setup of social network interventions

and future model improvements. Our results show that targeting more vulnerable children (i.e. in a worse

environment) and applying a network optimization algorithm are the best solutions for this data set indicating

that future interventions should aim for these two strategies.

1 INTRODUCTION

One of the most important public health challenges

is the prevention and reduction of childhood obe-

sity. It has worldwide priority because the prevalence

of childhood overweight and obesity is still rising.

Childhood obesity has persisting effects on adult adi-

posity and can lead to diseases such as diabetes and

cardiovascular diseases (WHO et al., 2017). Evidence

is accumulating which shows that the social environ-

ment is an important factor underlying the develop-

ment of inappropriate weight gain due to its powerful

impact on energy-balance related behaviours (Chris-

takis and Fowler, 2007). Youth are especially suscep-

tible to environmental inﬂuences and are surrounded

by inﬂuential individuals (i.e., role models such as fa-

mily and peers) who support and/or undermine their

health behaviours. For example, studies have shown

that individual peers as well as peer groups shape a

youth’s consumption behaviour and physical activity

(Salvy et al., 2012; De La Haye et al., 2011; De la

Haye et al., 2010). Numerous studies have shown that

the health of individuals is connected to each other

and that social networks inﬂuence peoples well-being

(Smith and Christakis, 2008; Hammond, 2010).

Social network interventions aim to use inﬂuen-

tial individuals to correct unhealthy behaviours within

social networks by letting them promote speciﬁc he-

alth behaviours (Valente and Pumpuang, 2007). It

is suggested that when inﬂuential individuals stimu-

late and spread the targeted behaviour successfully,

the behaviour will turn into a group norm suppor-

ting long-term behaviour change. The term network

interventions “describes the process of using social

network data to accelerate behaviour change or im-

prove organizational performance” (Valente, 2012).

Social network interventions have been successful in

reducing behaviours such as smoking and unsafe sex

414

Araújo, E., Simoski, B., Woudenberg, T., Bevelander, K., Smit, C., Buijs, L., Klein, M. and Buijzen, M.

Using Simulations for Exploring Interventions in Social Networks - Modeling Physical Activity Behaviour in Dutch School Classes.

DOI: 10.5220/0006857704140425

In Proceedings of 8th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2018), pages 414-425

ISBN: 978-989-758-323-0

(Campbell et al., 2008; Valente et al., 2003; Kelly

et al., 1991). To date, there is great necessity to target

the physical activity of youth because they are even

less active than previous generations and the majo-

rity of adolescents do not meet daily guidelines of

being active for at least 60 minutes (Hallal et al.,

2012). Hence, social network interventions are now

not only dedicated to reducing childhood obesity by

targeting water and sugar-sweetened drinks but also

increasing physical activity (Hunter et al., 2017; Smit

et al., 2016; Hallal et al., 2012; Van Woudenberg

et al., 2018).

An important step in the design of such interven-

tions is the selection of inﬂuential individuals. This

is usually called “inﬂuence maximization” (Kempe

et al., 2003; Chen et al., 2009), which is the task of se-

lecting a small subset of nodes (seed nodes) in a social

network that could maximize the spread of inﬂuence.

Many algorithms have been suggested and developed,

e.g. (Chen et al., 2010; Nguyen and Zheng, 2013; Liu

et al., 2014). However, most of these papers focus on

the efﬁciency of the algorithm for selecting the inﬂu-

ential nodes. The aim of this paper is to explore how a

diffusion model can be used to compare the effect on

the spread of behaviour of: (1) different ways to build

the network from questionnaires, (2) different strate-

gies for selecting inﬂuential nodes, and (3) different

percentages of the people that are targeted. In order to

do this, we created an agent-based model that is sup-

ported by real data collected from Dutch primary and

secondary school children (Bevelander et al., 2018).

The diffusion model is based on the one used by (Be-

heshti et al., 2017) and (Giabbanelli et al., 2012). We

tuned the model parameters on actual data on physical

activity collected among Dutch school children.

In this paper, we ﬁrst discuss the literature on

using agent-based models for predicting the effect of

contagion in social networks. Then, in Section 3, we

describe the data and model that we used and the ways

in which we can generate network graphs from the

questionnaires. In Section 4, we report on the simu-

lations that we have performed to tune the model and

to compare the different strategies and networks. Fi-

nally, we discuss the consequences of our ﬁndings in

Section 5.

2 BACKGROUND

This section starts by presenting an overview of pre-

vious research studies that implemented agent-based

models to predict intervention effects in social net-

works. Most of them consider the social or peer in-

ﬂuence on the agent’s particular health-related beha-

viour. The basis of our model is an agent-based mo-

del (ABM) of network diffusion of obesity behaviour,

that looks at both environmental and social inﬂuences

on physical activity and energy intake in a network.

We continue by looking in detail at the work of (Be-

heshti et al., 2017) and (Giabbanelli et al., 2012), as

our model builds on the model introduced in these pa-

pers.

There are numerous factors to be considered when

selecting an appropriate network intervention, such as

the type of network data, environmental context (e.g.

geographic distance), network structure (highly cen-

tralized network versus decentralized network), pre-

valence of behaviour or agent’s personal characteris-

tics. In the following paragraphs, we review previ-

ous research on network-based interventions for re-

ducing obesity and/or increasing physical activity in

networks. Most of them compare different targeting

methods for testing their effectiveness in diffusion of

health behaviour.

The effects of targeting the most connected indi-

viduals as opposed to random individuals was inves-

tigated by El-Sayed and colleagues (El-Sayed et al.,

2013), with the goal of reducing population obesity

in a social network. They looked at two different in-

terventions, the ﬁrst one preventing obesity, and the

latter treating obesity, both by targeting 10% of the

population. They concluded that targeting the most

connected individuals may not be effective in redu-

cing obesity in the network.

The selection of intervention strategy should de-

pend on the purpose (the goal) of the particular in-

tervention, as suggested by (Zhang et al., 2015a).

They have studied network interventions for incre-

asing children’s physical activity on a real-life so-

cial network, composed of 81 children living in low

socioeconomic status neighborhoods, out of which

41% was labeled as overweighted or obese. They

used three different network intervention strategies

and concluded that targeting opinion leaders is better

for increasing the physical activity levels in the net-

work as a whole, while targeting intervention in the

most sedentary children is best to increase their own

physical activity levels.

(Zhang et al., 2015b) have studied the effect of

both the social networks dynamics, and peer inﬂu-

ence on overweight in adolescents in a real-life so-

cial network. They proposed an ABM for simulating

the environment, and conducted several experiments

on modifying the network’s dynamics or changing

strength of peer inﬂuence, to get a more reﬁned mo-

del. They showed that peer inﬂuence can signiﬁcantly

affect those who are overweight. Bigger peer inﬂu-

ence lowers the prevalence of being overweight, espe-

Using Simulations for Exploring Interventions in Social Networks - Modeling Physical Activity Behaviour in Dutch School Classes

415

cially in low-obesity networks. On the other hand, in

high-obesity networks, inducing stronger peer inﬂu-

ence can have an unwanted reversed effect of further

increasing the population’s weight.

A “bottom-up” agent-based approach was intro-

duced by (Trogdon and Allaire, 2014), modeling

the food consumption and friend selection at indi-

vidual levels, for weight loss interventions. They

have shown that the underlying social network can

inﬂuence the effect of population-level interventions.

Looking at the network structure, they have conclu-

ded that aggregate effects of population-level inter-

ventions are bigger in clustered networks, compared

to scale-free networks. In addition, targeting parti-

cular agents of the network can be important for so-

cial network interventions. Selecting the most popu-

lar obese agents for the weight loss intervention, re-

sulted in greater weight loss in the population than

selecting a random assortment of obese targets.

Looking at the related work, we can conclude that

literature gives contradictory outputs, possibly as a re-

sult of the complexity of social networks and the nu-

merous factors that can inﬂuence network interven-

tions as explained above. Choosing leaders as tar-

gets for intervention is shown as effective in (Zhang

et al., 2015b), (Trogdon and Allaire, 2014), as oppo-

sed to (El-Sayed et al., 2013). Evaluating new met-

hods of targeting obesity interventions is needed in or-

der to create both cost-effective and time-effective so-

cial networks interventions. Following this idea, (Be-

heshti et al., 2017) have developed an ABM, an adap-

tation of the model proposed by (Giabbanelli et al.,

2012), that simulates the results of ﬁve targeting ap-

proaches, and integrates three key factors that inﬂu-

ence the diffusion of intervention effects in a social

network. These factors are: personal characteristics

of agents, social network ties (social inﬂuence) and

environmental inﬂuence. The authors propose two

network interventions, the ﬁrst one with the aim of

reducing energy intake and the latter for increasing

physical activity, both targeting 10% of the popula-

tion. The individual traits of the agents, like BMI,

sex, energy intake, environment, etc. were attributed

based on the NLSY79 data set. The same data set was

used to validate the model, and compare the simulated

weight changes trends of the model, with the histori-

cal weight trends of the NLSY79 dataset. Comparing

the effectiveness of the proposed targeting strategies,

they concluded that targeting based on network infor-

mation, outperforms more traditional targeting appro-

aches like selecting high-risk agents or vulnerable ca-

tegories (e.g., obese or low-income agents, respecti-

vely). Their most efﬁcient targeting method is based

on inﬂuence maximization and is explained in details

in Section 3. (Beheshti et al., 2017) simulations are

based on an artiﬁcial network built following a power

law degree distribution and homophily properties. In

this work, a real social network is used, which is deri-

ved from data collected through surveys, as explained

in Section 3.

3 METHODS

This section presents the methods used for this rese-

arch. First we describe the data collected and how the

characteristics of the population of children were used

for the design of the ABM. Next we explain the model

in detail, as well as the process of tuning the parame-

ters to better ﬁt the model to the empirical data. Then,

we explain the strategies tested for selecting the tar-

gets for the interventions.

3.1 The Data

The data have been collected in the MyMovez pro-

ject – Phase I (Bevelander et al., 2018). This is

a large-scale cross-sequential cohort study among

school children (N=953; 8-12 and 12-15 years-old)

from 21 primary and secondary schools in the Net-

herlands. The MyMovez project – Phase I consists

of ﬁve data collection waves over 3 years, starting

in 2016: February/March 2016 (Wave 1), April/May

2016 (Wave 2), June/July 2016 (Wave 3), Febru-

ary/March 2017 (Wave 4) and February/March 2018

(Wave 5). In this paper, we used data from the 4 ﬁrst

waves, as the data collected for wave 5 is still being

processed. The collected data contains information

about the children’s social network, media consump-

tion, psychological determinants of behaviour, physi-

cal environment, eating behaviour, socialization cha-

racteristics and physical activities. The children were

surveyed in many aspects through the MyMovez appli-

cation on a research smartphone provided by the pro-

ject in order to collect their impressions about their

classmates and their own routine and habits. Parti-

cipants’ weight and height are measured individually

by a trained researcher following standard procedu-

res (without shoes but fully clothed) in Wave 2 and

4. The BMI is calculated as

weight(kg)

height(m)

. Data on physi-

cal activity is collected using a wearable device (bra-

celet) that tracks the steps of the participants for 5

days in a row (week and weekend days). For more

detailed information, see the MyMovez project (Beve-

lander et al., 2018). For the current study, we selected

school classes with more than 80% of participation in

the experiment, resulting in 26 classes out of 196. 455

participants were removed from the data set for not

SIMULTECH 2018 - 8th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

416

taking part in the selected classes. The total number

of children after the cleaning of the data (removal of

participants with missing data) is 451. The data was

processed using Python 3 and the NetworkX library

combined with Pandas data frames.

3.2 Model Implementation

The network-oriented model used for this work is ba-

sed on diffusion dynamics of behaviour throughout a

social network. That means we assume that behavi-

our change regarding obesity aspects (physical acti-

vities and energy intake) are spread throughout one’s

relationships. The model is based on the work of (Gi-

abbanelli et al., 2012) and some of the adaptations of

(Beheshti et al., 2017) were also taken into account,

as explained below. Two main factors are considered

as determinants for the agents’ behaviour change: the

inﬂuence via the social network and the environmen-

tal inﬂuence.

Social network inﬂuence is the inﬂuence from

peers, i.e. those people who are connected to the

agents. The environmental inﬂuence is based on the

social-economical conditions of each child. Many

factors are important to assess the lifestyle of child-

ren and quantify it. In this paper, we focus on the

spread of physical activity (PA) as a measure of he-

althy behaviour. Therefore the interventions applied

will increase the PA of the selected participants.

The PA changes for the simulations are calcula-

ted in 3 steps, according to the method presented by

(Giabbanelli et al., 2012):

1. the inﬂuence on the individual by their friends;

2. the combination of the friends inﬂuence with the

inﬂuence from the environment; and

3. a threshold used to decide if an individual’s PA

will be changed or not.

(Beheshti et al., 2017) and (Giabbanelli et al.,

2012) treated the connections as binary variables,

where a connection has a weight of 1 in case a relati-

onship exists and 0 otherwise. For this work we mea-

sured the strength of the connections as ﬂoat numbers

between 0 and 1, as is going to be explained in Section

3.3. For this reason, we adjusted the formulas for step

(1) regarding the weights of the edges as being part of

the calculation of the peers’ inﬂuences. For step (1),

equation 1 show the friends inﬂuences based on the

weight of the connections and the difference between

the states of PA.

in f

(t) =

∑

(PA

(t − 1) − PA

(t − 1)) × w

( j,i)

∑

( j,i)

(1)

A positive in f

for node i means that the over-

all inﬂuence from i’s friends is positive towards the

PA of agent i. In these circumstances, a good envi-

ronment will further increase PA, while a bad envi-

ronment would do the opposite. For the simulation,

the environment is beneﬁcial when 0 < env < 1 and

harmful when 1 < env < 2. The environment calcula-

tion is explained in detail in Section 3.4.1. Equations

2 and 3 show how step (2) is calculated, combining

the inﬂuence of the peers with the inﬂuence of the en-

vironment.

in f

(t),env

= env × in f

(t)

, i f in f

< 0 (2)

in f

(t),env

in f

(t)

env

, i f in f

≥ 0 (3)

The last part of the inﬂuence spread is to compare

the amount of inﬂuence with the given threshold. (Be-

heshti et al., 2017) deﬁned the values for low and high

thresholds for EI and PA as 0.002 and 0.2. When tes-

ting these values, many problems with convergence

and steepness were raised in our simulations. For that

reason, we went back to the original model, by (Giab-

banelli et al., 2012) and kept only one threshold, ap-

plying a simulated annealing algorithm to ﬁne tune it,

as explained in Section 3.5. The threshold is used to

deﬁne the minimum amount of impact that is going to

cause the behaviour change to take effect. Equations

4 and 5 show the ﬁnal value for PA in the next time

step t, where f actor = 1+I

, in case in f

(t),env

> 0,

and f actor = 1 − I

otherwise.

(t) = PA

(t − 1), i f |in f

(t),env

| < T

(4)

(t) = PA

(t − 1) × f actor, i f |in f

(t),env

| ≥ T

(5)

3.3 Building the Network

The simulations in (Beheshti et al., 2017) are based on

an artiﬁcial network, which is built following a power

law degree distribution and homophily properties. In

this work, a real social network is used, which is deri-

ved from data collected through surveys. Twelve que-

stions about the relationships and impressions of other

classmates were asked. In our experiment, we com-

pared three different subsets of questions to build the

network:

1. (Friendship). One question regarding friendship:

“who are your friends?”;

2. (General). 6 general questions, including the

question about friendship regarding respect, ad-

vice, leadership and who they would like to re-

semble; and

3. (All). The questions from 1 and 2 (above) plus

questions regarding physical activities and food

intake behaviours, 12 in total. The extra questi-

ons are related to peers that inﬂuence you to eat

healthier, exercise and practice sports.

Using Simulations for Exploring Interventions in Social Networks - Modeling Physical Activity Behaviour in Dutch School Classes

417

Table 1: Density of the networks generated by the different

subsets of questions.

Class Friendship General All

1 0.45 0.67 0.75

2 0.29 0.65 0.71

3 0.34 0.66 0.80

4 0.69 0.85 0.86

5 0.48 0.65 0.72

6 0.58 0.80 0.84

7 0.30 0.46 0.51

8 0.64 0.88 0.95

9 0.60 0.78 0.87

10 0.70 0.79 0.80

11 0.53 0.83 0.87

12 0.53 0.67 0.76

13 0.63 0.81 0.89

14 0.42 0.68 0.73

15 0.50 0.76 0.84

16 0.57 0.78 0.81

17 0.72 0.89 0.89

18 0.46 0.69 0.76

19 0.64 0.91 0.96

20 0.32 0.62 0.73

21 0.40 0.64 0.77

22 0.39 0.59 0.68

23 0.62 0.89 0.91

24 0.50 0.77 0.85

25 0.43 0.67 0.70

26 0.25 0.58 0.72

The edges of our network are bidirectional, and

they account for the amount of inﬂuence that the ori-

gin of the edge has on the destination. Every question

generates a nomination from node i to j. This nomi-

nation is interpreted as the inﬂuence that node j has

on i. The more nominations a node i gives to j, the

stronger the inﬂuence of node j is over i, and therefore

the value for the edge w

j,i

is higher. Each question re-

ceives a different weight of 0 or 1. For each subset

of questions, a different conﬁguration of the weights

for the questions q

is given. The total weight for the

edge from node j to node i is given by equation 6.

j,i

∑

n=1

nomination

i, j

)

∑

n=1

(6)

The use of different subsets of questions is a way

of mapping different networks based on levels of in-

ﬂuence that can affect a social network. We assume

that the question about friendship explains well who

the people that children prefer to spend their time to-

gether with are, but it can be biased towards other

children in the class who they want to be like, but are

not as close as they want to be. For instance, popu-

lar children in the classroom might inﬂuence others,

even if they don’t spend much time together, or are

considered friends. Table 1 shows the density of the

networks for each of the classes selected. As can be

seen, the networks generated by the single friendship

question alone are the least dense, while the networks

generated by using all questions present more con-

nections that raise other levels of inﬂuence between

the children.

Table 2: Hamming Distance between the three graphs ge-

nerated by the subsets of questions.

Classes All x General General x Frienship All x Friendship

1 0.08 0.22 0.30

2 0.06 0.36 0.41

3 0.14 0.32 0.46

4 0.02 0.15 0.17

5 0.06 0.17 0.24

6 0.04 0.22 0.26

7 0.05 0.15 0.20

8 0.07 0.24 0.31

9 0.09 0.18 0.27

10 0.00 0.10 0.10

11 0.03 0.30 0.33

12 0.09 0.14 0.23

13 0.08 0.18 0.26

14 0.05 0.26 0.30

15 0.07 0.26 0.34

16 0.04 0.21 0.25

17 0.00 0.17 0.17

18 0.07 0.23 0.30

19 0.05 0.27 0.32

20 0.11 0.29 0.40

21 0.14 0.24 0.37

22 0.09 0.20 0.29

23 0.02 0.27 0.29

24 0.08 0.27 0.35

25 0.03 0.24 0.27

26 0.14 0.33 0.47

To verify if there are signiﬁcant differences bet-

ween the three generated networks, a Hamming dis-

tance was applied to the edges in the graphs. Table

2 shows the Hamming distance for each of the clas-

ses and the three possible comparisons between the

generated graphs. As is shown, the distance is close

to zero to almost all the classes when comparing the

graph for all questions (3) and the graph of general

questions (2), while the friendship graph (1) presents

a bigger distance compared to the other two. That me-

ans that the network generated by all questions and

the network generated by the general questions pre-

sent almost the same edges in their graphs, while the

graph generated with the friendship question alone

has many different edges from the other networks.

3.4 Agents Characteristics

The agent-based model for the behaviour spread ex-

plained in Section 3.2 requires some information

about the agents. More speciﬁcally, it is necessary

to know the PA-level of each agent, as well as the

inﬂuence of the environment on each of them, cal-

culated using socio-economic status (SES). The BMI

is also important to know for the interventions that

target high risk children. Here we explain how these

characteristics of the children were extracted from the

empirical data set.

3.4.1 Environment

One of the most inﬂuential factors for a healthy li-

festyle is a person’s living environment. Family we-

alth can be a good predictor for a child’s healthy li-

ving environment, with better opportunities for he-

althy eating and physical activity facilities. The Fa-

mily Afﬂuence Scale (FAS) is a simple metric created

SIMULTECH 2018 - 8th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

418

to avoid the difﬁculties that youth have in reporting

family income or other measures for wealth (Boyce

et al., 2006). (Boyce et al., 2006) argue that the FAS

measures are related to food intake habits and to phy-

sical activity, meaning that this questionnaire can also

be a good predictor for factors related to health as-

pects of a youth’s lives.

In MyMovez project the participants were asked

the following questions:

1. Does your family own a car, van or truck? (No

[0]; Yes, one[1]; Yes, two or more[2]);

2. Do you have your own bedroom for yourself? (No

[0]; Yes [1]);

3. During the past 12 months, how many times did

you travel away on holiday with your family?

(Not at all [0]; Once [1]; Twice [2]; More than

two [3]); and

4. How many computers does your family own?

(None [0]; One [1]; Two [2]; More than two [3]).

The model used for the simulation consider that

more obesogenic environments have a scale factor be-

tween 1 and 2, while healthier environments present a

scale from 0 to 1 (Beheshti et al., 2017). An environ-

ment factor of 1 means neutral. We normalized the

values so all four questions have the same weight in

the overall calculation.

3.4.2 BMI

The Body Mass Index (BMI) is the metric used to de-

ﬁne children with higher risk. That means that the

higher the BMI the higher the risk of a child to be-

come an obese adult. We compared the BMI of the

children from the same class and sorted them to de-

ﬁne the best targets for high risk interventions.

In (Giabbanelli et al., 2012) the overall change in

BMI is used as the outcome measure of the effect of

interventions. Their assumption is that the population

is made of adults, and their height is ﬁxed. But for

children the same assumptions do not stand, as child-

ren have a much more dynamic and complex process

of growing (Sch

onbeck et al., 2011), which is follo-

wed by their BMI. For that reason, in our experiments

we do not use the BMI as the outcome measure, but

the PA level instead. The BMI is only used for the

selection of the targets to apply the interventions.

3.4.3 PA

The participants in the experiment were asked to wear

a Fitibit Flex bracelet for 5 days. The device measu-

red their steps in continuous time with minute to mi-

nute precision. The PA used for the simulations was

based on the number of steps. In (Giabbanelli et al.,

2012) the PA of the simulated agents were drawn as

a normal distribution with a mean value of 1.53, the

level of sedentary individual according to (Food and

of the United Nations, 2004). To normalize the va-

lues for PA in our data set we took the mean PA (in

steps) and converted it to 1.53, in order to keep the

same scale presented in the previous work.

The initial PA for the simulations is calculated as

the average of the 3 ﬁrst waves, and the ﬁnal PA is

given by wave 4. Waves 1, 2 and 3 are closer in time

to each other, and also closer to the initial date of the

experiment, while wave 4 is 1 year further.

3.5 Parameter Tuning

Two parameter tuning algorithms are used to ﬁne tune

the thresholds and the speed factors of the model.

First we applied a grid search in the bi-

dimensional space with the threshold (T

) and the

factor (I

) of change. These variables are explained

in Section 3.2 in detail. The grid search guided us to a

subspace where the best results were obtained. Then

we applied simulated annealing to ﬁne tune our opti-

mization search. The simulated annealing algorithm

is an optimization combinatorial method for problem

solving. It is inspired by condensed matter physics,

where annealing denotes a process in which a solid in

a heat bath is heated up to a maximum temperature so

all particles are liquid, and then cooled down slowly

so the solid particles are reorganized (Van Laarhoven

and Aarts, 1987).

We started our simulations with a temperature of

1.0, and the cooling factor was 0.9, until the tempe-

rature was less than 0.01. For each temperature we

explored 20 neighbors. The parameters found by the

simulated annealing are used for the spread of beha-

viour model.

3.6 Strategies for Selecting Targets for

Intervention

The aim of this work is to explore the effect of diffe-

rent strategies to ﬁnd targets for PA interventions. Se-

veral selection strategies were implemented, and the

effect of applying an (imaginary) intervention to the

selected agents on the overall PA is simulated.

The effect of the imaginary intervention to an in-

dividual is modeled as an increase of 17% of their

initial PA. This value is taken from (Beheshti et al.,

2017) and is chosen based on other research that ap-

ply different sorts of strategies to increase the amount

of PA of people. The initial states of the remaining

Using Simulations for Exploring Interventions in Social Networks - Modeling Physical Activity Behaviour in Dutch School Classes

419

nodes is based on the empirical data. Then, the dif-

fusion model is run to verify the improvement on the

PA of the whole network after one year.

The strategies to select the targets are:

1. Higher risk children (BMI);

2. More vulnerable children (Environment);

3. Most central children in the network (degree cen-

trality);

4. Optimized selection based on the impact of the

children in the whole network;

5. Random selection of the targets.

Strategies (1) and (2) are based on the children’s

characteristics. Strategy (1) uses the BMI as indica-

tor for the risk (the higher the BMI, the higher the

risk). For the BMI we used the data about the child-

ren’s height and weight in the ﬁrst wave, as shown in

Section 3.4.2. Strategy (2) targets vulnerable child-

ren. Vulnerability is measured based on the child’s

environment. The worse the environment (i.e. lower

socio-economic status), the higher the vulnerability.

For environment we used the FAS measures, as ex-

plained in Section 3.4.1. Strategies (3) and (4) are

based on network characteristics. Strategy (3) is ba-

sed on degree centrality of the nodes given by the Py-

thon toolbox NetworkX 2.1. The degree centrality for

a node v is the fraction of nodes it is connected to.

These values are normalized by dividing them by the

maximum degree possible in the graph.

Strategy (4) selects the k nodes that propagate (or

inﬂuence) the other nodes in the network the most.

This is a simple algorithm in which the diffusion mo-

del algorithm is run for each of the nodes in the net-

work after applying the intervention to each of these

nodes separately. After running for all the nodes, the

selected agent is the one that causes the biggest incre-

ase of PA in the whole network. Then after the ﬁrst

node is selected, the same is done to the other nodes

that were not selected, together with the ﬁrst node in

the subset of targets. This strategy is based on the “in-

ﬂuence maximization” algorithms used for viral mar-

keting and advertising (Chen et al., 2010; Morone and

Makse, 2015). The difference here is that instead of

searching for nodes being “activated” as an objective

function, we quantify the impact spread throughout

the network as our optimization goal. (Beheshti et al.,

2017) used the same strategy, but the goals were rela-

ted to the decrease of the number of obese people in

the network as the goal. For our optimization algo-

rithm we are interested in the overall increase in PA

for all the participants.

Lastly, strategy (5) selects the targets by random.

This strategy is useful to verify if the other strategies

Table 3: Ratio between boys and girls per class and amount

of targets for each fraction selection.

Class Total of kids Boys Girls 10% 15% 20%

1 18 9 9 2 3 4

2 20 13 7 2 3 4

3 20 14 6 2 3 4

4 12 6 6 1 2 2

5 19 6 13 2 3 4

6 20 10 10 2 3 4

7 25 12 13 2 4 5

8 28 15 13 3 4 6

9 14 7 7 1 2 3

10 16 8 8 2 2 3

11 20 10 10 2 3 4

12 18 7 11 2 3 4

13 17 12 5 2 3 3

14 14 10 4 1 2 3

15 11 9 2 1 2 2

16 17 7 10 2 3 3

17 11 7 4 1 2 2

18 14 9 5 1 2 3

19 9 6 3 1 1 2

20 21 10 11 2 3 4

21 11 8 3 1 2 2

22 20 8 12 2 3 4

23 18 8 10 2 3 4

24 19 9 10 2 3 4

25 20 7 13 2 3 4

26 19 6 13 2 3 4

Total 451 233 218 45 70 91

provide better results than just selecting targets wit-

hout any criteria.

As a third variable (in addition to the different

methods to build the network and the different se-

lection strategies), we compared the effect of the

amount of different percentages of people to which

the (imaginary) intervention was applied. We com-

pared three different fractions: 10%, 15% and 20%

of the nodes in a class. Table 3 shows the ratios bet-

ween boys and girls per class, as well as the amount

of targets to select in each fraction selection.

4 RESULTS

The experiments aim to explore the effect of diffe-

rent networks, different target selection strategies and

different fractions of targets on the overall PA of the

social network. We ﬁrst present the results of the mo-

del tuning on the empirical data, and then we present

the results of the different simulation scenarios.

4.1 Tuning of Threshold and Change

Factor

Section 3.2 explained the model and the two parame-

ters that should be tuned in order to ﬁt the empirical

data to the simulations: threshold T

and the factor

of change I

. T

is the amount of inﬂuence a child

needs to receive from their peers combined with the

environment to be affected and change their behavi-

our. The factor of change I

is the amount of inﬂu-

ence that is going to be propagated to the receiving

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420

Figure 1: Grid search for the general questions.

node within the network. We used a grid search follo-

wed by a simulated annealing algorithm to minimize

the difference between the empirical data and the si-

mulated data and ﬁnd the best values for T

and I

The tuning was performed in two steps: ﬁrst, a grid

search algorithm was applied to identify the search

space, and then a simulated annealing algorithm was

used to ﬁnd the optimal values.

4.1.1 Grid Search

The grid search was performed with interval steps of

0.05. The values for T

and I

were tuned for each

of the networks generated with: (1) all questions, (2)

general questions and (3) friendship questions. As

can be seen in Figure 1, the space where I

< 0.35

showed the smaller errors. The grid search for the ot-

her graphs follow almost the same pattern as the one

presented in Figure 1.

4.1.2 Simulated Annealing

After the space was deﬁned, the simulated annealing

was run. As a result of the grid search, the value of I

was restricted to a maximum of 0.4. To calculate the

error (i.e. the difference between the empirical data

and the simulation) we compared the simulation out-

comes with the data in waves 1 and 4. Waves 2 and

3 were ignored because they are too close to Wave

1. For the simulated annealing, the initial temperature

was 1.0, with an alpha (cooling factor) of 0.9, and a

number of neighbors explored was 20. Increasing the

number of neighbors or slowing down the speed of

the cooling process didn’t signiﬁcantly improve the

results obtained. The initial parameters for the simu-

lated annealing were threshold = 0.2 and I

= 0.05.

Figure 2 shows the space of search on the simulated

annealing algorithm for the graph created from the ge-

neral questions.

Figure 2: Simulated annealing space of search explored for

the general questions.

Table 4: Best threshold and factor of change for the three

networks generated with (1) all questions, (2) general ques-

tions and (3) friendship question.

All (1) General (2) Friendship (3)

Threshold 0.0942 0.0588 0.0426

0.0055 0.0057 0.0041

The best results for threshold and I

for each of

the three networks are presented in table 4.

4.2 Exploring Different Strategies

After ﬁne tuning the model parameters, the diffusion

model was run combined with the strategies to select

targets for intervention in the network. For each class,

three different percentages of the children were cho-

sen as targets. To select the targets, we compared the

use of 5 different strategies: (1) Random selection;

(2) High-risk selection; (3) Vulnerability selection;

(4) Degree centrality selection; and (5) Optimization

selection.

Figure 3 shows the comparisons between the

random selection of 10, 15 and 20% of the agents for

the three networks generated with all questions, gene-

ral questions and friendship question.

We used the random selection (1) of the children

to receive interventions on their PA as a baseline. We

run the random selection for 100 samples and used

the mean to evaluate the average impact of this met-

hod. Increasing the number of tests didn’t cause any

difference to the results.

The selection of the high-risk agents (2) is based

on the BMI of the children in the classes. The child-

ren with a higher BMI have a higher risk of obesity

later on. As shown in Figure 3, the “high risk” is the

worse intervention causing the smallest inﬂuence on

increasing PA. Table 5 shows the differences between

the initial (and ﬁnal) mean PA of the whole network

with no interventions and the initial (and ﬁnal) mean

Using Simulations for Exploring Interventions in Social Networks - Modeling Physical Activity Behaviour in Dutch School Classes

421

Figure 3: Simulation of average PA for all the strategies for the different percentages of targets in the three rows. The left

column shows the results for the network generated with all questions. The center column is for the network generated with

the general questions set. The right column shows the results for the network generated using the friendship question alone.

PA for the networks with the interventions applied.

The overall difference is how much the difference of

the mean PAs increased (or decreased) from the be-

ginning to the end of the simulation (start-to-end dif-

ference). The overall difference for the high risk is

the only negative one, meaning that after one year of

simulation the mean PA of this intervention is closer

to the simulations without interventions.

The vulnerability (3) was used to select the child-

ren with the least socio-economic situation as targets

for the interventions. For most of the scenarios, this

strategy was one of the two best interventions, perfor-

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422

Table 5: Differences between initial and end mean PA for

the network generated with all questions and 20% of the

nodes selected for intervention.

Diff (day 0) Diff (day 364) Overall diff

High Risk 0.0491 0.0469 -0.0022

Vulnerability 0.0515 0.0871 0.0356

Random 0.0516 0.05599 0.0044

Centrality 0.0548 0.0623 0.0075

Optimized 0.0508 0.0985 0.0476

ming almost as well as the optimized solution especi-

ally for the network created with the single friendship

question. Strategy (3) shows an overall difference of

0.0356, the second highest (see Table 5).

Strategies based on network degree centrality (4)

were also tested and compared with the others. This

intervention presents better results than the random

selection (1), but are not as good as the strategies (3)

and (5). Some positive improvement in the distance

to the expected changes in the network without inter-

ventions is also perceived (Table 5).

The highest overall PA increase are in the inter-

ventions based on the optimization algorithm. This

strategy is beaten by strategy (3) in one of the nine

scenarios, though it shows the best results for all the

other remaining scenarios. Table 6 presents the va-

lues for the differences between the strategies applied

and the simulation with no interventions. The column

Beginning (day 0) is the initial point and the diffe-

rence between the mean PA for each strategy and no

intervention. The same is valid for the column End

(day 364), that represents the distance (or difference)

on the last day of simulation. The column Difference

is calculated as the value for the day 364 minus the

day 0 for each of the percentages. The Difference (%)

column represents how much increase (or decrease)

of PA is caused by increasing the amount of interven-

tion targets from 10 to 15% of the agents, and from 15

to 20% of the agents. The results from table 6 are im-

portant in order to make the right decision of selecting

the appropriate nodes for real-life intervention. The-

refore, increasing the fraction for the “high risk” stra-

tegy is not beneﬁcial, as there is a degradation of the

difference between mean PA for this strategy and for

the simulation without any interventions.

Choosing targets based on centrality shows that

selecting 15% of agents is better than selecting 20%.

For random and vulnerability selections the impro-

vements caused when increasing the percentage of

targets shows that 20% is a good choice, while for the

optimized strategy there is a very small percentage in-

crease from 15 to 20% (3.03%), which would require

further investigation to decide if selecting 20% of the

nodes instead of 15% is a good decision.

5 DISCUSSION

The simulation results allow us to discuss potential

strategies that may be used to make informed choices

about ways to improve simulation models as well as

the setup of social network interventions.

The strategy of targeting children with high risk

(i.e., higher BMI) turned out to be the least success-

ful compared to the other strategies in this speciﬁc

data set and model. It should be noted that our sam-

ple had a small variance in BMI. The majority of the

BMIs are healthy. Therefore, future studies should

test whether a more heterogeneous sample would ge-

nerate different ﬁndings. In addition, the model can

be further improved. For example, if BMI would be

used as the dependent variable, it would show how

the overall prevalence of obesity in social networks is

reduced by the intervention. For this, a more com-

plex model is required which accounts for the dyna-

mic change in the BMI categorization in adolescents.

The inclusion of the information regarding the energy

intake of the children would also enrich the model

by providing another independent variable which di-

rectly affects the obesity of the group. The difﬁculties

of including this variable are related to the data col-

lection, as it would be required to have a method for

assessing the children’s food intake habits. Targeting

children who reported to live in a less wealthy home

environment appeared to be one of the best solutions

and very close to—or even better than—the optimi-

zed strategy in some scenarios. This insight can also

be helpful for the selection of targets in the absence

of the network structure, as a personal characteristic

provides good improvement of the overall PA of the

whole group.

The change in the networks based on different

subsets of question did not reﬂect drastically diffe-

rent results for the scenarios. That is a good indicator

that the weights of the connections present some sta-

bility when you compare the different graphs, and it

does not affect the spread of behavior process. This

suggests that previous peer-driven intervention stu-

dies which used subsets of 5 nomination questions to

identify the peer leaders have chosen a sufﬁcient num-

ber of questions (Smit et al., 2016; Campbell et al.,

2008). For future research and data collection, these

results indicate that a small subset of nomination que-

stions can be asked to the participants, without losing

quality on the description of the inﬂuential ties and

overburdening the participants with questions.

With respect to the fraction of people that are tar-

geted, our results show that it differs per strategy

whether it is beneﬁcial to increase the target group.

This is a ﬁnding with important consequences, as the

Using Simulations for Exploring Interventions in Social Networks - Modeling Physical Activity Behaviour in Dutch School Classes

423

Table 6: Differences from the mean PA for each intervention to the simulations without any intervention. The results are

referred to the network generated from all the questions combined.

Beginning (day 0) End (day 364) Difference Difference (%)

10% 15% 20% 10% 15% 20% 10% 15% 20% 10% 15% 20%

High risk 0.0250 0.0374 0.0491 0.0225 0.0371 0.0469 -0.0024 -0.0003 -0.0022 0.00 -88.16 664.07

Vulnerability 0.0267 0.0408 0.0515 0.0560 0.0718 0.0871 0.0294 0.0310 0.0356 0.00 5.69 14.71

Random 0.0256 0.0398 0.0516 0.0286 0.0439 0.0560 0.0030 0.0041 0.0044 0.00 37.31 8.45

Centrality 0.0280 0.0418 0.0548 0.0362 0.0503 0.0623 0.0082 0.0085 0.0075 0.00 3.81 -12.28

Optimized 0.0268 0.0401 0.0508 0.0650 0.0863 0.0985 0.0382 0.0462 0.0476 0.00 20.92 3.03

costs of an intervention usually increases linearly with

the increase of the size of the target group.

6 CONCLUSION

This paper shows how an agent-based model can be

used to explore the effect of different scenarios on the

diffusion of physical activity in children. It is the ﬁrst

study in which simulations are based on real social

networks and the model has been tuned on actual me-

asurements of physical activity in the network. Study

ﬁndings indicate that social network interventions ai-

med at increasing physical activity should take the

socio-economic status of children into account. In ad-

dition, a small subset of peer nomination question is

sufﬁcient to map the children’s social network.

In this study, we have simulated the effect of tar-

geting speciﬁc children and applying an intervention

that increases in 17% their PA. We have compared 5

strategies for the selection, in 3 differently generated

networks and with 3 different percentages of targets

selected. We compared these 45 different scenarios

with the expected results when no intervention is ap-

plied. Although this is a comprehensive strategy, the

model used in the simulations is a straightforward dif-

fusion model. As a future work, we would like to test

other, more realistic, contagion models on the same

data set. For example, an option is to use a differen-

tial equation model that includes personality traits to

account for other factors that play a role in the process

of social contagion. Other potential ways to improve

the results would be to combine an optimized strategy

with the vulnerability trait of the agents to verify if it

can show better results than of two strategies alone.

ACKNOWLEDGEMENTS

The research leading to these results has received fun-

ding from the European Research Council under the

European Union’s Seventh Framework Programme

(FP7/2007-2013) / ERC grant agreement n

[617253].

E.F.M. Ara

ujo’s funding is provide by the Brazi-

lian Science without Borders Program, through the

Coordination for the Improvement of Higher Educa-

tion Personnel, CAPES (reference 13538-13-6).

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