Understanding the Impact of Network Structure on
Propagation Dynamics based on Mobile Big Data
Yuanfang Chen†§, Lei Shu§, Noel Crespi†, Gyu Myoung Lee‡, Mohsen Guizani∗
†Institut Mines-Télécom, Télécom SudParis, France
§Guangdong University of Petrochemical Technology, China
‡Liverpool John Moores University, Liverpool, UK
∗Qatar University, Qatar
Email: yuanfang.chen.2009@ieee.org, lei.shu@ieee.org, noel.crespi@mines-telecom.fr, G.M.Lee@ljmu.ac.uk, mguizani@ieee.org
Abstract—Understanding the propagation dynamics of in-
formation/an epidemic on complex networks is very important
for discovering and controlling a terrorist attack, and even for
predicting a disease outbreak. As an effective method, with
analyzing the structure of a propagation network, a large number
of previous studies have analyzed the propagation dynamics.
Most of these studies are based on a special network structure
to make such analysis. However, a propagation network has
dynamically changed structure during the propagation. How
to track, recognize and model such dynamic change is a big
challenge. Along with the popularity of smart devices and the
rapid development of the Internet of Things (IoT), massive
mobile data is automatically collected. In this article, as a typical
use case, we investigate the impact of network structure on
epidemic propagation dynamics by analyzing the massive mobile
data collected from smart devices carried by the volunteers of
Ebola outbreak areas. From this investigation, we obtain two
observations. Based on these observations and the analytical
ability of Apache Spark on streaming data and graphs, we
propose a simple model to track and recognize the dynamic
structure of a network. Moreover, we introduce and discuss open
issues and future work for developing this proposed recognition
model.
Keywords—Network structure, propagation dynamics, mobile
big data, Internet of Things.
I. INTRODUCTION
Information/epidemic propagation dynamics [1], [2], [3],
[4] has been extensively studied by network-enabled science,
e.g., graph theory, network theory, and probability theory.
When information/epidemic propagation is modelled over net-
works, it is usual to assume that the propagation has the
same probability over each link. Even if different links have
respective propagation probabilities, such modelling is not
enough to reflect the real propagation pattern in the physical
world. As the important feature of networks, network structure
needs to be considered [5], because the patterns of propagation
are different in different network structures. Most of studies
use a special network structure to make such modelling,
and even analysis, for example, the propagation network of
an epidemic is best described as having exponential degree
distribution. However, a propagation network has dynamically
changed structure along with the propagation of information/an
epidemic.
On the basis of the above description, firstly, we need to
figure out: whether the structure of complex networks impacts
the propagation dynamics of information/an epidemic [6].
It is an open issue. Despite a lack of direct experimental
evidence to support such “structure-propagation” hypothesis, a
number of theoretical studies have shown that the topological
structure of complex networks (mostly scale-free and small-
world topologies) leads to markedly different propagation
dynamics compared with the predicted by standard propagation
models. For example, in the literature [7], Michael Small et
al. examine the global spatio-temporal distribution of avian
influenza cases in both wild and domestic birds, and they find
that the cases and the links between these cases during an
outbreak form a scale-free network. It means that such an avian
influenza outbreak will continue to propagate even with a very
small propagation rate. In contrast, by standard mathematical
models of disease propagation [8], the propagation of this
avian influenza has been controlled and even has stopped. This
may cause to miss the best time of vaccination, and thus may
increase the probability of another outbreak.
Then, based on the above explanation, understanding the
impact of network structure on propagation dynamics is very
important, and recognizing the dynamic structure of a network
is a gap in the previous studies of propagation dynamics.
This article reviews the advance of propagation dynamics,
and then as a typical use case, we investigate the impact of
network structure on epidemic propagation dynamics, by ana-
lyzing the massive mobile data collected from the GPS-enabled
wireless devices carried by volunteers (Fig. 1 illustrates an
example). On this basis, we propose a model to recognize the
dynamic structure of a network. Finally, open issues and future
work are provided and discussed for developing this model.
In summary, the scientific contributions of this article are
listed as follows:
• The impact of network structure on epidemic propa-
gation dynamics is investigated, by analyzing the mas-
sive mobile data collected from the wireless devices
carried by volunteers.
• By the investigation, we obtain two observations
which are the motivation to design the recognition
model of dynamic structure.
Fig. 1: Contact Tracing module of Ebola Care [9]. It can track
each individual who contacts with a sick Ebola patient. The
collected data by this application is shared with the World
Health Organization (WHO). WHO is using information from
hundreds of aid organizations to make big strategic decisions.
• A streaming data and graph based model is designed
to recognize the dynamic structure of a network. A
propagation network can be formulated as a dynamic
graph with processing massive streaming data. The
streaming data processing is an important research
issue in Big Data analytics as well.
This article is structured as follows. The advance of prop-
agation dynamics is introduced in Section II. As a typical
use case, in Section III, we investigate the impact of network
structure on epidemic propagation dynamics based on the prop-
agation network of the Ebola outbreak in 2014. On the basis
of this investigation, Section IV proposes a recognition model
of network structure. This model is designed to recognize the
dynamic structure of a propagation network. For developing
this model to practical applications, in Section V, we present
the open issues and future work. This article is concluded in
Section VI.
II. ADVANCE OF PROPAGATION DYNAMICS
It is important to understand the propagation processes
arising over the networks with different structures. For ex-
ample, in knowledge mining, how a behaviour on a specially
structured network to impact the nodes of the network, is
worth understanding. Such understanding is helpful to model
the behaviour as well.
In recent years, there is an increased effort to study
propagation dynamics based on a variety of complex networks.
Recent achievements can be divided into two categories based
on different types of networks:
• Propagation dynamics on social networks [10]. On
such networks, information is the main research target.
Exponential and power-law models that reflect net-
work structure have been widely used to model the
dynamics of information propagation.
• Propagation dynamics on contact networks [11]. A
contact network describes the real relationships among
individuals/ecosystems in the physical world. Based
on the real relationships from the physical world, the
propagation dynamics on contact networks is different
from the propagation dynamics on social networks.
With the development of IoT (Internet of Things) and
the help of various sensors and wireless devices, some
researchers have paid their attention to this propaga-
tion dynamics, and have obtained some achievements
in: (i) the propagation of infectious diseases, and
(ii) the propagation of contaminants. Analyzing and
studying the dynamics of propagation among individ-
uals/ecosystems can help us understand and control
the dynamic behaviours on these real networks.
As an important aspect of propagation dynamics, theo-
retical studies on the “structure-propagation” hypothesis are
classified into two classes: information-related and epidemic-
related propagation dynamics on respective complex networks.
Information-related propagation dynamics. As impor-
tant recent achievements in information-related propagation
dynamics [1], Jure Leskovec et al. have obtained three interest-
ing observations, along with tracking information propagation
among media sites and blogs: (i) The information pathways
for general recurrent topics are more stable across time than
for on-going news events. It means that the former has a more
stable network structure; (ii) clusters of news media sites and
blogs often emerge and vanish in a matter of days for on-
going news events. From this observation, we can acquire
that hub nodes (clusters) exist in an information propagation
network. As a key element to reflect a network structure,
clusters are dynamically varying over time, and different
information propagation networks have different clusters; (iii)
major events, for example, large-scale civil unrest such as
Libyan civil wars and the Syrian uprising, increase the number
of information pathways among blogs, and also increase the
network centrality of blogs and social media sites.
Epidemic-related propagation dynamics. As a recent
achievement in epidemic-related propagation dynamics [12],
Louis Kim et al. propose a parameter estimation method by
learning network characteristics and disease dynamics. This
method is applied to the data collected during the 2009 H1N1
epidemic. On this basis, they find the outbreak network is
best fitted into a scale-free network. This finding implies that
random vaccination alone will not efficiently stop the propaga-
tion of influenza, and instead vaccination should be based on
understanding the propagation dynamics of the epidemic with
exploiting the special structure of an outbreak network.
However, network structure is time-varying along with in-
formation/epidemic propagation on the network. It is necessary
to recognize the dynamic structure of such a network.
III. IMPACT OF NETWORK STRUCTURE
As a typical use case, the impact of network structure on
epidemic propagation dynamics is investigated based on the
propagation network of the Ebola outbreak in 2014.
By using the wireless communication devices carried by
the volunteers of epidemic areas, new cases (with correspond-
ing locations and the relationships between these cases) are
reported to a control center. Then, these reported cases with
corresponding locations construct a propagation network (an
example is illustrated in Fig. 2). During an epidemic, the
network is time-varying along with the propagation of an
infectious disease. The propagation network can be modelled
as a dynamic graph G
t
. The weight w
{i,j}
is the transmission
probability (p
{i,j}
) of a disease from vertex i to vertex j (on
the corresponding edge e
{i,j}
).
468 10 12 14
−15 −10 −5 0 5
X
Y
468 10 12 14
−15 −10 −5 0 5
Fig. 2: An example of a propagation network during an epi-
demic. This example displays 50 cases and their relationships
(contact). X and Y are only used to denote the relative locations
of cases (no units). These cases come from three typical coun-
tries and seven regions of the Ebola outbreak in 2014. Three
countries are: Guinea, Nigeria and Liberia. Seven regions are:
Gueckedou, Macenta, Kissidougou, Conakry, Monrovia, Lagos
and Port Harcourt. The black nodes of this network are cases
(suspected and confirmed), and if there is an edge between two
nodes, it means that there is contact between the corresponding
individuals of the two cases.
Outbreak Data. The outbreak data of the Ebola in West
Africa from March 2014 is used as real surveillance data
to analyze the impact of network structure on propagation
dynamics.
As the latest disease outbreak, until February 15, 2015,
Ebola has killed 9380 people, and the total cases have reached
23253. Researchers generally believe that from a two-year-
old boy of Guinea to his mother, sister and grandmother (a
propagation network), Ebola rapidly spreads in West Africa
from March 2014.
The reported Ebola cases with time series and location
information are collected by the World Health Organization
(WHO), as well as the ministries of health of epidemic coun-
tries. In this study, we select part of the data from three typical
outbreak countries, Guinea, Nigeria and Liberia. Guinea is the
source of this outbreak, and has relatively high quantity of
confirmed cases (2727, as of February 15, 2015), and Nigeria
is far away from the source of the outbreak, and has relatively
low quantity of confirmed cases (19, as of February 15, 2015),
and Liberia is close to the source of the outbreak, and has
high quantity of confirmed cases (3149, as of February 15,
2015). In addition, the seven regions of these three countries
are: Gueckedou of Guinea, Macenta of Guinea, Kissidougou
of Guinea, Conakry of Guinea, Monrovia of Liberia, Lagos
of Nigeria, and Port Harcourt of Nigeria. Moreover, these
variables are included in the outbreak data:
1) Case ID. A unique number indicates a case.
2) Source ID. Source identification indicates the source
of an infection for a case.
3) Date. It is the date that a case is reported.
4) Location. It indicates the coordinates (longitude and
latitude) of a reported case.
Investigation and Results.
Investigation. In this article, we analyze the degree distri-
bution
1
of the propagation network that is constructed by the
collected Ebola outbreak data. Such analyses are completed
by:
(i) Conducting the Maximum-Likelihood Fitting (MLF) to fit
the calculated degree distribution of the propagation network
into exponential, normal, poisson and power-law distributions.
Definition 1 (Maximum-Likelihood Fitting). The Maximum-
Likelihood Fitting (MLF) for a set of data points θ =
{θ
1
, ......, θ
m
} is the method that maximizes lik(θ), where
lik(θ) is the probability of observing the given data as a
function of θ.
For example, the data points θ = {θ
1
, ......, θ
m
} are the
degrees of nodes, and lik(θ) ⇒ lik(exp(θ)) is the probability
that the data points conform to the exponential distribution.
(ii) Calculating and comparing the estimated standard
deviations and the estimated variance-covariance matrices of
these fittings.
Figure 3a illustrates the degree distribution of the prop-
agation network constructed by Ebola outbreak data. And
then the maximum-likelihood fitting is conducted to fit the
calculated degree distribution into exponential, normal, poisson
and power-law distributions. Finally, the estimated standard
deviations and the estimated variance-covariance matrices of
these fittings are measured to quantify: “how many differ-
ences between two different distributions”. The results of
these fittings are illustrated in Fig. 3b.
By the maximum-likelihood fitting, we can fit the calculat-
ed degree distribution into exponential, normal, poisson, and
power-law distributions, and the fitted parameter values for
these distributions are listed as follows:
(i) rate parameter λ = 0.50159915 for the exponential distri-
bution.
(ii) µ = 1.99362380 and σ = 2.77914691 for the normal
distribution.
(iii) λ = 1.9936238 for the poisson distribution.
(iv) x
min
= 2 and α = 2.803973 for the power-law distribu-
tion.
Table I provides the estimated standard deviations and
the estimated variance-covariance matrices for the parameter
values of these fittings.
Comparing the estimated standard deviations and estimated
variance-covariance matrices listed in Tab. I, the minimum
standard deviation is 0.01635166. This minimum standard de-
viation is corresponding to the exponential distribution with the
rate parameter λ = 0.50159915. This result indicates that the
1
Degree distribution is the basic and most important structure knowledge
of a network. It is the probability distribution of degrees over the propagation
network.
0 5 10 15 20 25 30
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Degree(x)
P(x)
0 5 10 15 20 25 30
0.0 0.1 0.2 0.3 0.4 0.5 0.6
(a) Degree distribution of the propagation network con-
structed by Ebola outbreak data. There are 942 nodes
and 938 edges in this network. The black spots are the
probability distribution of nodes’ degrees.
5 10 15 20
0 200 400
Exponential distribution
Degree
Frequency
5 10 15 20
0 200 400
5 10 15 20
0 200 400
Normal distribution
Degree
Frequency
5 10 15 20
0 200 400
5 10 15 20
0 200 400
Poisson distribution
Degree
Frequency
5 10 15 20
0 200 400
5 10 15 20
0 200 400
Power−law distribution
Degree
Frequency
5 10 15 20
0 200 400
(b) The maximum-likelihood fitting of degree distribu-
tions. The degree distribution of the constructed propa-
gation network is fitted into exponential, normal, poisson
and power-law distributions by the maximum-likelihood
fitting. The black spots indicate the calculated probability
distribution of nodes’ degrees, and the red lines are the
corresponding fittings for exponential, normal, poisson
and power-law distributions.
Fig. 3: Degree distribution and the maximum-likelihood fitting for the propagation network of the Ebola outbreak
TABLE I: Estimated standard deviations and estimated
variance-covariance matrices
Distribution
Standard
deviation
Variance-covariance
matrix
Exponential
λ (rate parameter):
0.01635166
λ (rate parameter)
λ (rate parameter)
2.673769e − 04
Normal
µ (mean):
0.09059760,
σ (standard deviation (sd)):
0.06406218
µ σ
µ
0.008207925 0.000000000
σ
0.000000000 0.004103963
Poisson
λ (lambda):
0.0460285
λ (lambda)
λ (lambda)
0.002118623
Power-law
x
min
+ α:
0.03831463
NULL
degree distribution of the propagation network is approximate
to the exponential distribution with λ = 0.50159915.
However, based on the description of the network that is
studied in this article, the propagation network is time-varying
along with the propagation of an infectious disease. As an
example, the analytical results of the subnetwork constructed
by 96 time periods of August 26th, 2014, are illustrated in
Fig. 4 and Tab. II.
By the maximum-likelihood fitting for the subnetwork, the
results of the parameter estimation for different distributions
are listed as follows: (i) the rate parameter λ = 0.74796748
for the exponential distribution, (ii) µ = 1.33695652 and
σ = 1.00841216 for the normal distribution, (iii) λ =
1.33695652 for the poisson distribution, and (iv) x
min
= 1
and α = 3.041947 for the power-law distribution.
Table II provides the estimated standard deviations and the
estimated variance-covariance matrices of the above fittings.
By observing the fittings and the estimated results, the
degree distribution of the subnetwork is approximate to the
power-law distribution with x
min
= 1 and α = 3.041947.
Results. Based on the above detailed analyses on the
structure of the networks, we obtain these observations:
• In Fig. 3a and Fig. 4a, the probabilities (P(x)) of 1
degree are both zero. It means that the suspected or
confirmed cases at least contact with two other cases.
It is an important feature of network structure, but the
maximum-likelihood fitting to the four kinds of degree
distributions fails to capture it.
• Network structure is time-varying during an epidemic.
IV. RECOGNITION MODEL
How to accurately recognize the dynamic structure of a
propagation network is a valuable research issue.
During an epidemic, a disease propagates along a propaga-
tion network, and such propagation makes the structure of the
propagation network be dynamically changed. By recognizing
the dynamic structure of a propagation network, we can
acquire the propagation dynamics of a disease. Moreover, it
is important to quantify and predict the propagation dynamics
during an epidemic. If the quantification and prediction can be
achieved for a disease outbreak, it will be helpful to allocate
12345678
0.0 0.2 0.4 0.6 0.8
Degree(x)
P(x)
12345678
0.0 0.2 0.4 0.6 0.8
(a) Degree distribution for the subnetwork of the prop-
agation network. There are 96 time periods of August
26th, 2014 in this subnetwork. The black spots are the
probability distribution of nodes’ degrees.
1 2 3 4 5 6 7
0 50 100 150
Exponential distribution
Degree
Frequency
1 2 3 4 5 6 7
0 50 100 150
1 2 3 4 5 6 7
0 50 100 150
Normal distribution
Degree
Frequency
1 2 3 4 5 6 7
0 50 100 150
1 2 3 4 5 6 7
0 50 100 150
Poisson distribution
Degree
Frequency
1 2 3 4 5 6 7
0 50 100 150
1 2 3 4 5 6 7
0 50 100 150
Power−law distribution
Degree
Frequency
1 2 3 4 5 6 7
0 50 100 150
(b) The maximum-likelihood fitting of degree distribu-
tions. The degree distribution of the subnetwork is fitted
into exponential, normal, poisson and power-law distribu-
tions by the maximum-likelihood fitting. The black spots
indicate the probability distribution of nodes’ degrees, and
the red lines are the corresponding fittings for exponential,
normal, poisson and power-law distributions.
Fig. 4: Degree distribution and the maximum-likelihood fitting for the subnetwork of the propagation network
TABLE II: Estimated standard deviations and estimated variance-covariance matrices
Distribution Standard deviation Variance-covariance matrix
Exponential
λ (rate parameter): 0.05514089
λ (rate parameter)
λ (rate parameter)
0.003040518
Normal
µ (mean): 0.07434113,
σ (standard deviation (sd)): 0.05256712
µ σ
µ
0.005526604 0.000000000
σ
0.000000000 0.002763302
Poisson
λ (lambda): 0.08524123
λ (lambda)
λ (lambda)
0.007266068
Power-law
x
min
+ α: 0.02865438
NULL
public health resources and respond to public health events,
accurately and duly.
Based on the analytical ability of Apache Spark [13] on
streaming data and graphs, we propose a recognition model of
network structure. The work flow of this model is illustrated
in Fig. 5.
Location & Time
Spark
Streaming
Spark
Engine
Raw Spatio-
Temporal Data
Construct
Graph
Spark
Engine
Real-time algorithm to
acquire structure
properties (e.g., degree
distribution)
Fig. 5: Work flow of our recognition model.
In this model, there are three main parts:
1) The input stream is the cases’ spatio-temporal data
with GPS location information and time stamps. The
GPS location of a case is associated with the physical
location where the case is found and reported.
2) On the basis of the input stream, the cases and their
relationships are used to construct a graph. In this
graph, each vertex corresponds to a case, and the dis-
tance between two vertices can be calculated by the
coordinates of corresponding two cases. Moreover,
the graph is time-varying: the vertex and edge sets
are changed over time, along with the propagation of
a disease.
By the processing of Spark Streaming
2
, and based
on the time stamps of cases, the dynamic change of
the graph can be tracked.
3) Based on the graph tracking and a real-time algo-
rithm, corresponding structure properties (e.g., degree
distribution) can be calculated for this dynamic graph.
2
Spark Streaming provides a language-integrated API to stream processing.
It makes the processing of streaming data be easy as processing batch data.
![Fig. 1: Contact Tracing module of Ebola Care [9]. It can track each individual who contacts with a sick Ebola patient. The collected data by this application is shared with the World Health Organization (WHO). WHO is using information from hundreds of aid organizations to make big strategic decisions.](/figures/fig-1-contact-tracing-module-of-ebola-care-9-it-can-track-3ghfwehn.webp)
