An Agent-Based Model of Epidemic Spread using
Human Mobility and Social Network Information
Enrique Fr
´
ıas-Mart
´
ınez
‡
, Graham Williamson
1#
, Vanessa Fr
´
ıas-Mart
´
ınez
‡
,
‡
Telef
´
onica Research, Madrid – Spain
#
School of Computer Science , University College Dublin – Ireland
{efm,graham,vanessa}@tid.es
Abstract— The recent adoption of ubiquitous computing tech-
nologies has enabled capturing large amounts of human behav-
ioral data. The digital footprints computed from these datasets
provide information for the study of social and human dynamics,
including social networks and mobility patterns, key elements
for the effective modeling of virus spreading. Traditional epi-
demiologic models do not consider individual information and
hence have limited ability to capture the inherent complexity
of the disease spreading process. To overcome this limitation,
agent-based models have recently been proposed as an effective
approach to model virus spreading. However, most agent-based
approaches to date have not included real-life data to characterize
the agents’ behavior. In this paper we propose an agent-based
system that uses social interactions and individual mobility
patterns extracted from call detail records to accurately model
virus spreading. The proposed approach is applied to study the
2009 H1N1 outbreak in Mexico and to evaluate the impact
that government mandates had on the spreading of the virus.
Our simulations indicate that the restricted mobility due the
government mandates reduced by 10% the peak number of
individuals infected by the virus and postponed the peak of the
pandemic by two days.
I. INTRODUCTION
Planning for a pandemic (e.g., H1N1, influenza, etc.) is a
public health priority of any government. Traditional epidemi-
ological approaches base their solutions on using differential
equations that divide the population into subgroups based
on socio-economic and demographic characteristics. Although
these models fail to capture the complexity and individuality
of human behavior, they have been extremely successful in
guiding and designing public health policies. The recent adop-
tion of agent-based modeling (ABM) approaches to simulate
pandemics has allowed to capture individual human behavior
and its inherent fuzziness by representing every person as
a software agent. The ABM model characterizes each agent
with a variety of variables that are considered relevant to
model virus spreading such as mobility patterns, social net-
work characteristics, socio-economic status, health status, etc.
Hence, ABM approaches need realistic data to create agents
that effectively capture human behavior. Typically this data is
obtained from the census or by means of surveys [1].
The adoption of ubiquitous computing technologies by very
large portions of the population (e.g. GPS devices, ubiquitous
cellular networks or geolocated services) has enabled captur-
ing large scale human behavioral data. These datasets contain
1
Work done while author was an intern at Telef
´
onica Research, Madrid.
information that is critical to accurately model the spread of a
virus, such as human mobility patterns or the social network
characteristics of each individual [2][1].
In this paper, we propose an ABM system designed to
simulate virus spreading using agents that are characterized
by their individual mobility patterns and social networks as
extracted from cell phone records. We carry out simulations
with data collected during the 2009 Mexican H1N1 outbreak
and measure the impact that government calls had on the
mobility of individuals and the subsequent effect on the spread
of the H1N1 virus. To the best of our knowledge, this is the
first time that this kind of real-life information is used in an
ABM system.
The remainder of this paper is organized as follows: Section
II discusses the related work regarding traditional disease
models and ABM simulation environments; Section III de-
scribes the infrastructure of a cell phone network and how cell
phone records are captured; our proposed ABM architecture
is presented in Section IV. Section V presents a case study
that evaluates the impact that government mandates regarding
mobility restrictions had on the spreading of the 2009 H1N1
virus outbreak in Mexico. Finally, we describe our conclusions
and outline our future work in Section VI.
II. RELATED WORK
A. Traditional Epidemic Disease Models
Traditional epidemic disease models are based on the SIR
model and its variations (SI, SIR, SIS, SEIR, etc.) [3]. These
approaches, called compartmental models, split the population
into compartments that represent the different stages of a
disease. The most general approach is the SIR model that
typifies the disease progression as follows: (1) S, represents
the susceptible (S) portion of the population i.e. those yet to
be infected; (2) I, represents those that are currently infective
or infectious (I); and (3) R, represents individuals that have
recovered (R) from the disease and no longer take an active
part in the disease spread. Other models like the SEIR, add an
intermediate stage (E) which represents a latent state in which
individuals have been exposed to the disease but are not yet
infective, i.e. the individuals in this stage have the virus but
can not infect others. All these models represent the virus
transmission by a set of nonlinear ordinary differential equa-
tions (ODEs) that associate a transition rate to the mobility of
agents between compartments. These transition rates are used
by the models to define a reproductive rate R
0
that represents
the number of people in a susceptible population that could
be infected by an infective agent. In general, if R
0
> 1 the
disease spreads epidemically and when R
0
≤ 1 the disease
dies out.
One of the main restrictions of the original compartmental
models is that they assume that all members within one
compartment are identical to each other. Recent literature has
evolved the SIR/SEIR models to overcome such homogeneity
by creating metapopulation models. Metapopulation models
extend the traditional epidemiological approaches to differen-
tiate types of population within each epidemic state (S,E,I,R).
For example, Balcan et al. differentiate subgroups within
the population based on vaccinations received, symptomatic
versus asymptomatic individuals, citizens that travel versus
those who do not, natural immunity to diseases, etc. [4].
Similarly, Brockmann et al. define different metapopulations
based on their mobility patterns inferred from the movements
of US bank notes[5].
B. Agent-based Epidemic Models
Compartmental models cannot capture the complexity of
human behavior, particularly regarding mobility patterns and
social networks. Although metapopulation models attempt to
overcome such limitations they still suffer from behavioral
generalizations within the metapopulations. In this context,
agent-based epidemic models (ABMs) are designed to capture
the behavior of each unique individual (agent). As a result,
agent-based epidemiological simulations are more powerful
than metapopulation models to represent the spreading of
viruses given their granularity and capability to model behav-
ior and interactions individually [6].
Although this research line is quite novel, the literature
already reports some relevant results. Apolloni et al. propose
Simdemics, an integrated modeling environment that aids
public health officials in pandemic planning [7]. Simdemics
is an agent-based simulator that defines four models to evolve
the epidemic spread: (1) a statistical model of the population
(based on age, gender or geographical density), (2) a social
interaction model, (3) a disease model, that accounts for the
impact that demographic or socio-economic factors might
have on epidemic spreading, and (4) intervention models e.g.,
public policy changes, agent behavioral changes, etc. In their
conclusions, the authors advocate for the necessity to have
accurate human behavioral models that reveal mobility and
interaction patterns.
Barrett et al. present an agent-based simulator called
EpiSimdemics [8]. The authors build a synthetic population
from the United States Census characterizing each individual
(agent) with 163 different variables. Individuals are mapped to
geographically located housing units, and their daily activities
are modeled from a wide arrange of datasets like education
statistics to model school attendance or transport surveys to
model mobility patterns. The disease model consists of two
parts: the between-hosts disease transmission and the within-
host disease progression. The within-hosts progression is mod-
eled as a finite state machine with probabilistic transitions
(PTTS) that determines the evolution through the various
disease states. The between-hosts transmission is modeled as
follows:
p
i
= 1 − exp(τ
X
r∈R
N
r
ln(1 − rs
i
ρ)) (1)
where p
i
is the probability that an infection is triggered in a
susceptible agent i; τ is the duration of exposure; R is the set
of infective agents and N
r
the number of such agents with
infectivity r; s
i
is the susceptibility of individual i and ρ the
basic transmissibility of the disease. This equation represents
an intuitive process: the probability of inter-agent transmission
increases with the amount of time spent in the presence of an
infective individual and the number of infectious agents (and
their infectivity) present at a given location. This approach is
specially relevant when the transmission is mainly by direct
contact, which is the case of H1N1.
ABM simulations, specially if done for large populations,
require large amounts of memory and time. Recent literature
has also explored how to effectively compute ABM models.
Parker et al. present the Global-Scale Agent Model, GSAM,
which focuses on achieving high performance while com-
puting realistic agents [9]. The GSAM system can generate
over a billion distinct agents with models that include daily
interactions. Additionally, the authors show how to use GSAM
system to model epidemic evolutions at a planetary scale.
In general, although agent-based epidemic models improve
traditional epidemiological approaches, all the solutions imple-
mented so far face the same limitation: the information used
to model human mobility and social networks is extracted
from census data and surveys. Although these data might
approximate real behavior, it does not account for changes
in behavior due to the epidemic itself. The model proposed in
this paper aims to achieve a more realistic representation of
human behavior which includes the behavioral changes that
might take place during the epidemic.
III. PRELIMINARIES
In order to capture realistic human mobility patterns and
social dynamics, we use the ubiquitous infrastructure provided
by a cell phone network. Cell phone networks are built using
a set of cell towers, called Base Transceiver Stations (BTS),
that connect the cell phones to the network. Each BTS has a
latitude and a longitude – its geolocation – and gives cellular
coverage to an area called a sector. We assume that the sector
of each BTS is a 2-dimensional non-overlapping polygon,
and we use a Voronoi tessellation to define its coverage area.
Figure 1(left) shows a set of BTSs with the original coverage
area of each cell, and Figure 1(right) presents its approximated
coverage computed using Voronoi.
Call Detail Record (CDR) databases are generated when a
mobile phone connected to the network makes or receives a
phone call or uses a service (e.g., SMS, MMS, etc.). In the
process, and for invoice purposes, the information regarding
the time and the BTS tower where the user was located when
Fig. 1. (Left) Example of a set of BTSs and their coverage and (Right)
Approximated coverage obtained applying Voronoi tesselation.
the call was initiated is logged, which gives an indication of
the geographical position of a user at a given moment in
time. Note that no information about the exact position of
a user in a cell is known. From all the data contained in a
CDR, our study only uses the encrypted originating number,
the encrypted destination number, the time and date of the
call, the duration of the call, and the BTS towers used by the
originating and destination cell phone numbers.
We use CDR data to compute the individual mobility and
social models that are part of the proposed ABM architecture
to model virus spreading. Specifically, we build: (1) a mobility
user model that estimates the position of each agent at each
moment in time and (2) a social user model that identifies
each agent’s social network (in the sense of close relations).
Due to the nature of the CDR data available, each agent’s
mobility model is computed at the BTS level i.e., the ABM
system will be able to determine, at each moment in time, the
BTS coverage area where an agent is located. The position of
the agent within the coverage area of the BTS is unknown.
As a result of that limitation, the ABM system will provide
more accurate mobility models in areas with high densities
of towers (urban areas) where coverage areas per BTS are
smaller in size. Each individual’s social network is modeled
as the set of close relations obtained from the CDRs. Specifics
about its computation are explained in Section IV. Note that
this model is critical to determine when the transmission of
the virus takes place. We assume that two agents that are part
of the same social network are more likely to be physically
close than two agents that do not know each other. Hence,
whenever two agents are in the same coverage area (BTS),
the probability of infection between the two will be higher if
they are part of the same social network.
This approach of capturing and modeling agent behavior
from CDRs sets our work apart from others because: (1)
we model agents from real individual data and not from
census or surveys as previously explained; and (2) we capture
behavioral adaptations to the spread of the disease i.e., changes
in mobility patterns or in the social network of the agents as
the disease spreads over time. In fact, census or survey data
give a one snapshot view of a society’s behavioral patterns.
However, cell phone data is collected in real time and provides
an accurate daily representation of the agents’ behaviors and
their changes due to external events. Finally, note that although
the ABM system we present is designed for cell phone records,
a similar approach could be used with logs from any other
location-based service, such as e.g. geolocalized Twitter.
IV. ABM OF VIRUS SPREADING USING CDRS
We propose an ABM architecture with two main com-
ponents: (1) a set of agents that are modeled using the
information contained in call detail records; and (2) a discrete
event simulator (DES) that simulates the virus propagation
over time based on the agents’ models.
A. Agent Generation
We define the behavior of each agent with three models:
(1) a mobility model extracted from CDR data; (2) a social
network model computed from CDR data; and (3) a disease
model that characterizes the progression of the disease through
its various states in each agent.
1) Mobility Model: The mobility model provides the po-
sition (at the BTS level) where the agent is at each moment
in time. This model is used by the event simulation process
to predict the location of each agent at each simulation step.
The temporal granularity of the mobility model determines the
granularity of the simulation steps e.g., if the mobility model
computes hourly distributions of locations, the simulation step
will be one hour.
We propose a mobility model that divides each day into a
set S of i non-overlapping equal-length time slots. Formally,
the mobility model of agent n, M
n
, is defined as:
M
n
= {M
wday
n
, M
wend
n
} =
{{M
wday,0
n
, .., M
wday,i
n
}, {M
wend,0
n
, .., M
wend,i
n
}} ∀i ∈ S
M
wday,i
n
= {p
wday,i,0
n
, . . . , p
wday,i,j
n
} ∀j ∈ B
M
wend,i
n
= {p
wend,i,0
n
, . . . , p
wend,i,j
n
} ∀j ∈ B
(2)
where B is the number of BTS towers that give coverage
to a geographic area; and p
wday,i,j
n
and p
wend,i,j
n
denote the
probability that agent n may be found at BTS j in timeslot
i during a weekday or weekend, respectively. Given a CDR
dataset, the mobility model is built by associating with each
time slot i the set of BTSs where each person has been
observed during weekdays or weekends during the period of
time under study. Note that each individual might be assigned
to more than one BTS in a specific time slot i. In this case,
the event simulator assigns the position of the tower with the
highest probability, i.e., the BTS that the individual has used
the most over the training period. Since people tend to show
monotonic behaviors, an average person typically has very few
BTS towers in his/her mobility model. In the cases where a
time slot contains no data, which typically happens for time
slots at night, we assume that the person did not move from
the latest predicted location in time.
As shown by Song et al. in [10], mobility models computed
from CDRs can accurately predict the real locations of users
with 93% accuracy. However, two pre-requisites need to be
fulfilled in order to achieve this level of accuracy: (1) individ-
uals need to visit more than two locations (BTSs) during the
training set; and (2) they need an average call frequency of
≥ 0.5 calls per hour. Additionally, research by Candia et al.
[11] indicates that there exist relevant behavioral differences
between weekend and weekday behaviors and advocate for
mobility models that can capture such differences. We will
explain details about the computation of our mobility models
that satisfy these requirements in Section V.
2) Social Network Model: The social network of an individ-
ual plays a key role in virus spreading because it identifies the
set of individuals with whom a person has a close relationship.
This is specially relevant for viruses that are transmitted by
direct physical contact, like H1N1. We compute the social
network of an agent as the set of individuals with whom there
was at least one reciprocal contact during the time period under
study. By contact, we mean any type of communication: call,
SMS or MMS, and does not need to be the same type to
imply bidirectionality. Note that an agent can be a member of
more than one social network. Additionally, given that humans
show clear different behavioral patterns between weekday and
weekend, we compute two social networks per agent. Formally
speaking, the social network S
n
of agent n is computed as:
S
n
= {S
wday
n
, S
wend
n
} =
S
wday
n
= {list of reciprocal contacts in wdays}
S
wend
n
= {list of reciprocal contacts in wends}
where S
wday
n
is the social network during the weekdays and
S
wends
n
the social network during the weekends. Given the
social networks of an agent, we assume that the probability
of being physically close to another agent will be higher
if that other agent is part of its social network. To model
physical proximity within a BTS coverage area we define
two probabilities: (1) p
1
is the probability that two agents
that are in the same BTS at the same time of the simulation
and are part of the same social network are physically close
enough for the virus to be possibly transmitted; and (2) p
2
the
probability that two agents that are in the same BTS and are
not in the same social network at the same moment in time
are physically close for the virus to be possibly transmitted.
It is expected for p
1
to be larger than p
2
given the social
connection. These two probabilities are a novel contribution
of our work since previous ABM approaches did not have
access to real behavioral data. It is important to clarify that p
1
and p
2
define the probability of two agents being physically
close when they are in the same BTS at the same moment in
time. The probability for the infection to occur between those
agents will be defined by the disease model (explained below).
3) Disease Model: The disease model captures the pro-
gression of the disease in each agent. This model, together
with the mobility and social models, is used by the discrete
event simulator to reproduce the evolution of the disease at a
global scale. We follow a similar approach to that of Barret
et al. [8] and define a disease model that is composed of two
parts: the between hosts transmission model and the within
host progression model.
In Figure 2 we observe that the between hosts transmission
model happens at a probability p
i
, given by Eq. 1, and
represents the probability that an agent goes from Susceptible
to Exposed. In our model, we assume that all agents have
the same initial susceptibility and infectivity i.e., r
i
= 1 and
s
i
= 1∀i.
The within host model represents the evolution from Ex-
posed to Infective in a given period of time , and from
Infected to Removed in period of time β.
Once an agent reaches the Removed state, it is considered
to be protected from the virus and thus is removed from the
simulation. The specific values of and β in Eq. 1 depend on
the disease being modeled and are determined experimentally
from epidemiological studies. Details about their computation
are given in Section V.
Fig. 2. Disease Model composed of Between hosts and Within hosts models.
B. Discrete Event Simulator
The Discrete Event Simulator (DES) simulates the evolution
of the epidemic spreading for a set of agents over a specific pe-
riod of time. To bootstrap the epidemic spreading, we assume
that an initial agent is Infected and starts the transmission.
The DES has a global clock and evaluates, at each simulation
step, the state of all the agents in terms of mobility, social
network and disease model. The size of the simulation step is
determined by the temporal granularity of the mobility model
(see next section for computation details). Specifically, the
DES does the following consecutive tasks: (1) It identifies the
geographical area (BTS) where each agent is located using the
mobility model; (2) it identifies the geographical areas where
there is, at least, one Infective agent; (3) for each Infective
agent, it takes all the Susceptible agents of his social network
that are located in the same geographical area (BTS coverage)
and applies probability p
1
that they will be physically close
for the virus to be transmitted; (4) for each Infective agent and
the rest of Susceptible agents included in its geographical area
(not part of its social network), it applies the probability p
2
that
they will be physically close for the virus to be transmitted; (5)
for the set of agents physically close obtained from steps (3)
and (4), it applies the between hosts transmission probability
to go from Susceptible to Exposed; (6) for the agents that
are already in the Exposed or Infective state of the disease
model, it applies the corresponding progression; and at last
(7) it removes from the simulation all agents that have reached
the Removed state.
These steps are repeated for each simulation step during the
overall simulation time.
V. EXPERIMENTS: THE CASE OF H1N1 IN MEXICO
In case of a pandemic, the World Health Organization
(WHO) recommends authoritative bodies to consider the sus-
pension of activities in educational, government and business
units as a measure to reduce the transmission of the disease.
The actions implemented by the Mexican government to
control the H1N1 flu outbreak of April 2009 constitute an
illustrative example. The actions consisted of alerts and/or
mandates aimed at reducing mobility, and where issued in
three stages: (a) a medical alert issued on Thursday, April 16th,
which was triggered by the diagnosis of the first H1N1 flu
cases; followed by (b) the closing of schools and universities,
enacted from Monday April 27th through Thursday, April
30th; and (c) the suspension of all non essential activities,
implemented from Friday, May 1st to Tuesday, May 5th.
The Mexican H1N1 outbreak has been investigated in a
number of recent papers using analytical SIR models [12],
agent-based approaches [13], [14] or metamodels [15]. From
a public health perspective, there are studies that focus on clin-
ical features, incubation times and transmission channels [16];
or on measuring the impact of interventions such as anti-viral
drugs [4], [17] or vaccination campaigns [15]. However, re-
search into the impact that the Mexican government mandates
had on the spread of the H1N1 virus and on the mobility
of the population is limited [12]. This is mainly due to the
lack of large scale data about social and mobility behavioral
patterns. We overcome these limitations by computing social
and mobility models using Call Detail Records collected from
a Mexican urban area during the H1N1 flu outbreak. We use
these models in the ABM system previously presented and
measure the impact that the actions taken by the Mexican
government had on human mobility and subsequently on the
spread of the virus. Note that we assume that changes in hu-
man behavior are exclusively caused by government mandates.
Although it is probably the main cause, there might be other
reasons – such as fear induced by the media– that could also
have influenced behavioral changes and that are not considered
in our simulations. Next, we describe the experimental setting,
the generation of the agents and our results.
Period Date Range Description
preflu 1/1 – 16/4 Period before any H1N1 case has been
discovered. Agents will move largely
unaffected and showing their usual mo-
bility patterns.
alert 17/4 – 26/4 April 16th - Diagnosis of H1N1 cases
and medical alert triggered the follow-
ing day. People may be reacting to the
news and modify their usual mobility
patterns.
closed 27/4 – 31/4 Schools and Universities closed. Nor-
mal behavior disrupted as people
change their usual mobility patterns.
shutdown 1/5 – 5/5 Closure of all non-essential activities.
reopened 6/5 – 31/5 Restrictions lifted.
TABLE I
TIME PERIODS OF STUDY.
A. Experimental Setting
In order to examine the impact of government restrictions
we evaluate changes in the mobility and disease models in
five chronological periods. Table I presents the timeline under
study. It covers from January 1
st
, 2009 to May 31
st
, 2009.
Each period is related to specific events that took place
during the outbreak i.e., preflu, alert, closed, shutdown and
reopening. We generate agents (with corresponding mobility
and social models) for each of these time periods. In order
to measure behavioral changes, we define two scenarios: a
baseline scenario and an intervention scenario.
The baseline scenario is built using the mobility and social
models obtained during the pre-flu period, when individuals
show normal – not affected by medical alerts – mobility
behavior. The intervention scenario considers the models that
are built with data from the alert, closed, shutdown and
reopened periods. In this case, depending on the moment of
the simulation, the DES will jump from one set of models
to the next. The evaluation is done by comparing the results
obtained by both scenarios. Due to the inherent randomness
of the spreading process we run each scenario 10 times and
average the results.
B. Generation of Agents
To generate realistic agent mobility and social network
models, we collected CDRs from January 1
st
to May 31
st
of 2009 of one of the most affected Mexican cities. The
entire dataset contains around 1 billion CDRs and around 2.4
million unique cell phone numbers. Each cell phone number is
associated with one agent and we compute the mobility, social
and disease models for both the baseline and the intervention
scenarios.
The mobility models are computed using Eq. 2 with a
granularity of one hour. As described in Section IV, we need
to fulfill a set of requirements to guarantee that the mobility
models computed from CDRs are realistic representations of a
human’s motion. Following the research carried out by Song et
al. [10], we filter the individuals such that only those that (1)
are assigned to at least two BTSs throughout the time periods;
(2) have a minimum average calling rate of 0.25 calls/hour;
and (3) have at least 20% of the hourly time slots filled,
are considered. Finally, since we want to measure behavioral
changes during the outbreak, we only take into account agents
that are active during the five time periods under study.
These requirements narrow down the final number of agents
to 25, 000.
We also build the social network models for the baseline and
the intervention scenarios. As part of these models, we needed
to define values for the contact probabilities p
1
and p
2
. In order
to compute their values, we make use of the work by Cruz-
Pacheco et al. [12], where the authors examined the effect of
the government intervention measures on the epidemic spread
using SIR. We use their simulation to determine the optimal
values of p
1
and p
2
as follows: we implement an exhaustive
search in the range [0 − 1] over all combinations of p
1
and
p
2
, using .1 increments. For each pair of values tested, we
