Estimating high-resolution daily encounter networks withactivity-travel diaries
I. Saadia,∗ , E. Cômea , L. Luongb , S. Lassarrea and M. Zargayounaa
a Univ. Gustave Eiffel, F-77454 Marne-la-Vallée, France{ismail.saadi,etienne.come,sylvain.lassarre,mahdi.zargayouna}@univ-eiffel.frb AP-HP Hôpital Cochin, F-75014 Paris, Franceliem.luong@aphp.fr∗ Corresponding author
Extended abstract submitted for presentation at the 11th Triennial Symposium onTransportation Analysis conference (TRISTAN XI)
June 19-25, 2022, Mauritius Island

April 12, 2022Keywords: Activity-based model (ABM), daily contact networks, COVID-19

1INTRODUCTION

SARS-CoV-2 has become one of the most devastating pandemics in human history and is still,
two years after the pandemic onset, contributing to the breakdown of societies around theworld. As a result, several countries are experiencing deep economic, social and political crises.
Furthermore, multiple non pharmaceutical interventions (NPIs), i.e. social distancing, travel
restrictions, partial/full lockdowns, have been put in place to mitigate human contacts. Theseinterventions have important social, economic, public health, legal implications and they should
be strongly justified. In general, decision making of such measures is based on epidemiologicalforecasts. Thus, understanding human contact patterns and their underlying social interactions
is crucial to estimate reliable infectious disease transmission models. This is especially the casein large densely-crowded urban and transportation systems where complex social interactions arewidespread. In this paper, we present a new estimation method of human contact patterns basedon an activity-based model of travel demand. The latter are used in transportation research
to model persons’ travel behavior. Nonetheless, they are not explored enough in epidemiology.
Therefore, we demonstrate the effectiveness of our modeling strategy by setting up an activitybased model based on publicly available data, such that the approach is easily reproducible.
Afterwards, we derive large scale multi-layer contact networks. Finally, we estimate the related
age-stratified contact matrices.

2MODELING FRAMEWORKThe modeling framework consists of three parts. The first part is dedicated to the behavioral
synthetic population of Île-de-France based on multiple open data sources. In the second part, weset up an efficient and fast algorithm to estimate the large scale multi-setting contact network
based on the targeted behavioral synthetic population. Finally, at the end of this process,we compute the age-specific contact matrices that estimate contact frequencies of individuals
clustered by age groups in two particular settings, i.e. household and overall layers.
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I. Saadi, E. Côme, L. Luong Nguyen and M. Zargayouna

2.12

Behavioral synthetic population

A behavioral synthetic population is a detailed representation of the true population basedon multiple data sources. It includes several millions of individuals grouped into households.
Socio-demographic attributes are inferred and daily activity-travel schedules are associated tothe individuals of that population. The integrated modeling framework simulates the synthetic
population of Île-de-France, a densely populated area of 12,011 km2 consisting of eight departments, including Paris the capital of France. As of January 2021, the population size ofÎle-de-France is around 12,213,447 inhabitants, resulting in a population density of 1,017 inhabitants/km2. The proposed behavioral synthetic population is based on multiple datasets which
are publicly available, thus allowing full transparency and reproducibility of the present study.
We use the generation process proposed by Hörl & Balac (2021). Data gathering and pipelinerunning are described at https://github.com/eqasim-org/ile-de-france.

2.2

Multi-layer contact network estimation

Infectious disease transmission dynamics are heavily reliant on the social interactions of theindividuals constituting the population. Modeling the human mixing patterns is indeed crucial
to understanding how epidemics spread in-between individuals. In this regard, the most appropriate approach consists of representing the contact patterns as a graph G = (V, E) where V ,the set of vertices, are the individuals and E, the set of edges, are the contacts.
The total number of contacts is computed based on the spatiotemporal co-presence. In
other words, if a group of individuals share the same location at the same time, then we assume
that they might have met. The individuals’ spatiotemporal co-presence can be derived fromthe activity-travel diaries. In doing so, we obtain detailed information on the spatiotemporal
meeting patterns, resulting in underlying exact upper-bound contact duration distributions. An
activity travel diary contains the reference number of the person, the activity purpose, start/end
times and location ID. For instance, we use activity-travel diaries (ATD) consisting of 20,716,218
records. We group the activity-travel diaries by unique location to apply the spatial constraintof the co-presence. Then we compute a systematic pairwise comparison of individuals sharing
the same location to check for joint time windows.
In particular, we distinguish between the potential contact network Gp = (Vp , Ep ) and theeffective contact network Ge = (Ve , Ee ), and the relationship is described by |Vp | = |Ve | andπ|Ep | = |Ee |. Indeed, we consider a Bernoulli model by assuming a single parameter π. It
means that if a contact is detected, it is accepted with a probability π. We compute the contact
duration and we assign its purpose, e.g. household (H), work (W), education (E), leisure (L),shop (S), other (O) and/or hybrid (X-X). Given that the daily average number of contacts µc
is around 8 (5-14) (Béraud et al., 2015), and taking into account the statistical properties ofthe potential contact network (before making the decision on preserving or not the contacts
after detecting the spatiotemproal co-presence), we can estimate the optimal value of π. Indeed,2(|E H |+|E O |π)ppwe can state that µc =where µc is the observed overall average daily numberNpop
Hof contacts (from the survey), |Ep | is the total number of contacts in the household layerfrom the potential graph Gp , |EpO | the total number of contacts in all the other layers fromtheir corresponding potential graphs and Npop (= |V |) the number of vertices/individuals of thegraph. Thus, π =2.3µc Npop−|EpH |
2|EpO |. Note that |Ee | = |EeO | + |EeH | = |EpO |π + |EpH |.

Numerical experiment

We build a representative population sample which represents 100% of the true populationsize. The sampling procedure consists of the generation of a behavioral synthetic population ofaround 12M persons grouped into 4M households. The basic statistical properties of the contact
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I. Saadi, E. Côme, L. Luong Nguyen and M. Zargayouna

3network are presented in Table 1.
Parameter|Ee ||V |(= Npop )π

Value
47,029,073
11,758,464
0.013

Table 1 – Properties of the effective contact network
Most contacts are non-hybrid (Figure 1a). Furthermore, the modeling framework highlights
two key aspects: the distributions of the location sizes (number of people sharing the samelocation) (Figure 1b) and the daily number of contacts per person (Figure 1c) look like power law
distributions with cutoffs. The upper bound contact duration distribution is presented in Figure
1d. The waves are strongly influenced by the temporal patterns in workplaces and educationrelated locations, e.g. 8 hours/day of working time and/or morning/afternoon presence atworkplaces. This is a mixture of layer-related contact duration distributions.

E-W
WL/L-W
E-L/LEWS/S-W
E-S/SE
L-S/SL
WO/O-W
E-O/O
-E
OL/L
-O
OS/S
-O

O

WE/

O-

S-S

L-L

E-E

WW

Density

Without household contacts
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0

Contact type(a)

0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.00

Distribution of the number of contacts (Île-de-France)

log-log scale

log-log scale

10 2

DensityDensity

Distribution of location sizes (Île-de-France)

10 402000

101

103

4000

6000

10 20.2

10 4
10 60.1
0.0

8000

Location size

0.3

100
0200

101
400

102
600

Daily number of contacts / person

(b)

(c)

Distribution of the u-b contact durations
0.12

Density

0.10
0.08
0.06
0.04
0.02
0.00

0.0

2.5

5.0

7.5 10.0 12.5 15.0

Upper bound (u-b) contact durations (in hours)(d)Figure 1 – Key results
In households (Figure 2b), the main diagonal corresponds to the contacts of people of similar age groups, i.e. children and parents. The secondary diagonals mainly correspond to theparent-children contacts. In work (W)/education (E)/leisure (L)/shop (S)/other (O) layers,
we mainly find contacts in-between individuals of age 25-, 25 and 65, with some spread below
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I. Saadi, E. Côme, L. Luong Nguyen and M. Zargayouna
overall layer

120

104

102
40
101

200

2040

60

Age(a)

80

100

120100Age of contact

Age of contact

60

104
80
103

60

102

40

101

200

Frequency of contacts

103

105

100

Frequency of contacts

800

household layer

120

100

40

204060

Age

80

100

120

100(b)

Figure 2 – Age-specific contact matrices
and above these boundaries. Therefore, the corresponding patterns clearly emerge in the joint(non-household layers) age-specific contact matrix (Figure 2a).

3CONCLUSIONSThe pipeline framework (Eqasim) (Hörl & Balac, 2021) was initially designed for simulating
mobility of multi-agent systems. In this context, it adopts different modeling assumptions
regarding the spatiotemporal activity sequencing. The socio-demographic description of thesythetic population is based on open data (INSEE) which are relatively reliable and highly
detailed with the possibility of matching individuals with their corresponding households. Suchdata are rarely available in other countries. Nonetheless, the travel behavior description of
the agents is based on the National Household Travel Survey of 2008 (ENTD) as no viable
alternative is available, which may be a limitation. In fact, travel habits might have evolved.
Although the initial purpose of Eqasim is about transport and mobility, we demonstrate in thispaper that it can be an interesting option for modeling infectious disease transmission. From acontact pattern standpoint, we show that a conventional activity-based model of travel demand
clearly captures the underlying human mixing patterns characterizing the different layers. We
also demonstrated that it is possible to reproduce the visitation and contact patterns (superspreaders, super-spreading events) previously described in the literature.
Further research is needed (a) to estimate the intra/inter-layer related parameters taking into
account key statistical properties from the existing literature. At this stage, we only considereda parameter π. Incorporating variability into and/or in-between the layers is required to improve
the statistical representativeness of the effective contact network Ge . (b) To incorporate dynamicfeatures into the model. For example, a dynamic contact network can be used to take into
account the effects of NPIs. (c) To validate the contact network with respect to key observed
statistical indicators. (d) To run infectious disease transmission models on the estimated contact
networks to assess the effects of various mobility-related NPIs on the confirmed cases/deaths.

ReferencesBéraud, Guillaume, Kazmercziak, Sabine, Beutels, Philippe, Levy-Bruhl, Daniel, Lenne, Xavier, Mielcarek, Nathalie, Yazdanpanah, Yazdan, Boëlle, Pierre-Yves, Hens, Niel, & Dervaux, Benoit. 2015. The
French connection: the first large population-based contact survey in France relevant for the spread ofinfectious diseases. PloS one, 10(7), e0133203.
Hörl, Sebastian, & Balac, Milos. 2021. Synthetic population and travel demand for Paris and Île-de-France
based on open and publicly available data. Transportation Research Part C: Emerging Technologies,
130, 103291.

TRISTAN XI Symposium

Original abstract submittal