=Paper=
{{Paper
|id=Vol-3182/paper7
|storemode=property
|title=Using Agent-Based Simulation to Investigate Behavioural Interventions in a Pandemic using Mobility Data
|pdfUrl=https://ceur-ws.org/Vol-3182/paper7.pdf
|volume=Vol-3182
|authors=Jan de Mooij,Davide Dell’Anna,Parantapa Bhattacharya,Mehdi Dastani,Brian Logan,Samarth Swarup
|dblpUrl=https://dblp.org/rec/conf/jurix/MooijDBD0S21
}}
==Using Agent-Based Simulation to Investigate Behavioural Interventions in a Pandemic using Mobility Data==
https://ceur-ws.org/Vol-3182/paper7.pdf
Using Agent-Based Simulation to Investigate
Behavioral Interventions in a Pandemic
Simulating Behavioral Interventions in a Pandemic
Jan de Mooij1 , Davide Dell’Anna2 , Parantapa Bhattacharya3 , Mehdi Dastani1 ,
Brian Logan1,4 and Samarth Swarup3
1 Intelligent Systems, Information and Computing Sciences, Utrecht University
2 Control and Operations, Delft University of Technology
3 Biocomplexity Institute and Initiative, University of Virginia
4 University of Aberdeen
Abstract
Simulation is a useful tool for evaluating behavioral interventions when the adoption rate among a
population is uncertain. Individual agent models are often prohibitively expensive, but, unlike stochastic
models, allow studying compliance heterogeneity. In this paper we demonstrate the feasibility of evaluating
behavioral intervention policies using large-scale data-driven agent-based simulations. We explain how
the simulation is calibrated with respect to real-world data, and demonstrate the utility of our approach
by studying the effectiveness of interventions used in Virginia in early 2020 through counterfactual
simulations.
Keywords
Agent-based Computational Epidemiology, Agent-based Modeling, Policy Evaluation, Normative Reason-
ing, Complex Social Simulation, Belief-Desire-Intention, Synthetic Population, Multi-agent Simulation
Introduction
In the absence of pharmaceutical interventions, behavioral interventions are often the first line of
defense early in an epidemic. However, the effect of behavioral interventions can be unpredictable,
especially when the adoption rate of the population is unknown. While stochastic models are often
used to evaluate the costs and benefits of such interventions [1, 2] due to their low computational
complexity, agent-based models allow the effects of compliance heterogeneity to be studied [3].
In this work, we demonstrate the feasibility of using large-scale data-driven agent-based
simulation for evaluating the effectiveness of behavioral interventions. In addition, we address
the concern of generalization of a population to the ‘standard human’ [4] by instantiating the
simulated agents from a detailed and representative synthetic population [5]. Each agent in the
population is associated with an activity schedule that is representative of their socio-demographic
AMPM’21: First Workshop in Agent-based Modeling & Policy-Making, December 8, 2021, Vilnius, Lithuania
A.J.deMooij@uu.nl (J. de Mooij); d.dellanna@tudelft.nl (D. Dell’Anna); parantapa@virginia.edu
(P. Bhattacharya); m.m.dastani@uu.nl (M. Dastani); b.s.logan@uu.nl (B. Logan); swarup@virginia.edu (S. Swarup)
0000-0003-4129-6074 (J. de Mooij); 0000-0002-1162-8341 (D. Dell’Anna); 0000-0002-3626-9939
(P. Bhattacharya); 0000-0003-0648-7107 (B. Logan); 0000-0003-3615-1663 (S. Swarup)
© 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073
CEUR Workshop Proceedings (CEUR-WS.org)
background, and which is used to drive their default behavior. By calibrating mobility patterns
and disease progression, the framework may be applied to other regions where interventions or
compliance rates may differ, provided the required data is available.
1. A Data-Driven Agent-Based Simulation
Between March and June 2020, nine subsets of the interventions shown in Table 1 were imple-
mented in the form of Executive Orders (EOs) issued by the Governor of Virginia to mitigate
the spread of COVID-19. The interventions are parameterized by the individuals affected and
circumstances under which they apply. The timeline of these interventions is shown in Figure 1.
Table 1
A brief explanation of the behavioral interventions enforced in our simulation and their parameters.
Id Interpretation Parameters
n1 Mask wearing is allowed and encouraged -
type ∈ {NEB}: the type of business,
n2 Businesses of type type are closed
NEB = Non Essential Business
Employees working in retail must
n3 -
wear a mask during work activities
n4 Telework is encouraged -
n5 Physical distance of 1.5m should be maintained -
n6 Capacity of business should be reduced to perc perc: percentage of business capacity
type ∈ {K12, HE, K12 or HE}: the type of school,
n7 Schools of type type are closed K12 = primary and secondary education
HE = Higher Education (HE)
type ∈ {public, private, all}: the target settings,
The maximum allowed size of
n8 either public, private or both (all);
groups of type type is size
size ∈ N: maximum size of groups
appl ∈ {sick or age ≥ 65, all}:
the group of agents to which the norm applies,
n9 Stay at home if belong to category appl
either people sick or older than 65
(sick or age ≥ 65), or everyone (all)
n10 Only take away allowed for restaurants -
n11 A mask must be worn in public indoor settings -
In previous work, we developed a large-scale data-driven normative agent-based simulation to
study the effects of compliance with these interventions [6, 7] 1 . The simulation was developed
using an extension of the agent programming language 2APL [8, 9] called Sim-2APL 2 , and
consisted of 86 thousand agents drawn from a detailed synthetic population [5]. Each agent
adopts goals to perform actions from a representative activity schedule. When no norms are active,
1 The version of the framework described in this paper is archived at https://github.com/
A-Practical-Agent-Programming-Language/Normative-COVID-19-Simulation/releases/tag/v1.0.0.
2 Archived at https://github.com/A-Practical-Agent-Programming-Language/Sim-2APL/releases/tag/v1.0.0
Mar, 12131517 23 30 May, 8 26Jun, 2 Jul, 1
EO1 : n1 , n4
EO2 : n7 (K12)
EO3 : n8 (100, public)
EO4 : n6 (10), n2 (DMV), n8 (10, public), n9 (sick or age ≥ 65)
EO5 : n2 (NEB), n9 (all), n10 (rest)
EO6 : n5 , n7 (K12 or HE), n8 (10, all)
EO7 : n3 , n6 (50%)
EO8 : n11
EO9 : n7 (K12), n8 (50, all)
Figure 1: Timeline of the 9 major Executive Orders (EOs) implemented in Virginia, USA, between
March and June, 2020. The column on the left indicates the norms belonging to the 9 EOs. For each
norm in an EO (e.g., n1 in EO1 ) a black line indicates the period during which the norm was enforced
(e.g., the first two black lines indicate that both n1 and n2 from EO1 were enforced from March 12 to
July 1).
these are exactly the activities they perform. However, throughout the simulation, we activate or
deactivate norms according to the timeline from Figure 1. When a scheduled activity is prohibited
by an intervention modeled as a norm, the agents use previous observations and intrinsic values
to determine whether to comply with the norm by altering or canceling the activity, or to violate
the norm by performing the activity as scheduled. Two important factors used in this reasoning
are the agent’s trust in institutions, and the behavior of other agents. In particular, agents tend
towards the compliance behavior of other agents they have encountered in the past. However, the
magnitude of this tendency is determined by the trust the agent holds in institutions, which is
sampled from a Beta distribution at the start of the simulation. The normative deliberation process
followed by the Sim-2APL agents each simulated day is shown in Figure 2. Agent deliberation
essentially follows the Belief-Desire-Intention (BDI) approach: each agent pursues a set of goals
(in the current work, these are the activities from their activity schedules), and responds to a set
of triggers, such as messages, or events from the environment. At each stage in the reasoning
process, each agent also has access to a context that encodes its beliefs and other persistent data.
Plan Schemes map triggers to plans. Each plan encodes a particular form of agent behavior as
a sequence of zero or more actions. When the reasoning process of all agents is complete, the
actions generated by the plans selected by each agent are processed by the environment to move
the global simulation state to the next time step.
A contagion simulator called PanSim simulates the progression of COVID-19 based on agents’
collocation [7]. PanSim also allows the distribution and synchronization of a simulation across
multiple compute nodes, which allows scaling up beyond the initial 86 thousand agents.
2. Calibration
To ground the model in real-world data, both the behavior model and the disease model were
calibrated. For the behavior model, the parameters that were calibrated were the mean of the Beta
distribution from which the agents’ trust is sampled, a discount factor termed fatigue and the start
time at which fatigue comes into effect. Fatigue reduces the trust of all agents linearly starting
from the start time, and models the gradual increase in mobility after the first intervention which
is not associated with the deactivation of norms. For the disease model, the parameters that were
remove goal
each norm is applied to each trigger modifies
remove plan yes yes
deliberation plan goal
start triggers / plan- contexts adopted finished achieved
goals schemes plans
execute
each
For each conditions adopted
for each find plan plan application plan
trigger & norm for trigger rule put plan
on plan plan
regi- base
no applies yes yes
mented
produces
no
external
actions
trigger & collected by
>= θ
transform no belief conditions yes Sim-2APL
attitude
trigger match? after deliberation
<θ
Figure 2: The normative deliberation process of a Sim-2APL agent
calibrated were the probability of symptomatic and asymptomatic infected agents infecting their
susceptible contacts.
The behavior interventions had—by design—significant impact on mobility patterns. This was
used to calibrate the behavior model using the mobility index: the percentage change in Cuebiq
mobility data for each county compared to pre-pandemic levels. The mobility index of each of the
four simulated counties in our calibrated simulation is plotted against those reported by Cuebiq in
Figure 3a.
The disease model was calibrated using the cumulative number of reported cases. To account
for under-testing at the start of the pandemic, we multiplied the number of reported cases by 30.
While this scale factor is arbitrary, it can be changed without affecting the methodology of our
work. The simulated case counts are plotted against the reported case count in Figure 3b.
For both calibration processes, Nelder-Mead [10] was used to minimize the Root Mean Square
Error (RMSE) between the real-world data and the simulated data across 5 simulations for each
proposed configuration of parameters.3 Each simulation spans the time period 1 March to 29
June, and in each simulation, the activation and deactivation of norms follows the timeline from
Figure 1. For the behavior model, the RMSE was calculated as the error between the real-world
and simulated mobility index for each county individually. The final obtained RMSE was 17.65.
For the disease model, where numbers are significantly lower, the cumulative value across all
simulated counties was used. The final obtained RMSE was 2052 on a population of 86150
agents.
As can be seen in Figure 3b, the disease model was not able to accurately reproduce either
our estimate of the total number of infections or the time at which infections start to increase
significantly. Other approaches to estimating the real number of cases, such as the number of
3 Initial simulations indicated that the standard deviation is sufficiently small for a reasonable level of confidence;
the purpose of using more than one simulation is to avoid a statistical outlier as a global minimum
Figure 3: The mobility index observed in the simulation plotted against that recorded by Cuebiq in
each simulated county (3a), and percentage of recovered agents in the simulation plotted against the
percentage of reported cases (×30) in the same counties (3b).
hospitalizations or deaths, may give better results. However, while the number of hospitalizations
or deaths is generally assumed to be more accurate, like the number of positive tests, they are
only a proxy for actual disease spread, and the effect of disease spread on these metrics needs to
be known or calibrated as well.
3. Experiment
In this section, we briefly show how our simulation framework can be used to help policy makers
evaluate interventions through counterfactual simulations. For the interventions implemented in
Virginia, we ran 10 experiments E0 . . . , E9 . In E0 , we disabled all interventions, in E1 we included
only the interventions from EO0 (n1 and n4 ); in E2 we included the interventions from the first
two EOs, in E3 the first three EOs, and so on up to E9 in which we simulate all interventions
reflecting the actual policy implemented in Virginia. Note that, in each experiment, all activated
EOs still follow the timeline from Figure 1. For each experiment we ran 10 simulations to
account for stochastic variation. Figure 4 shows the average progression of the disease in each
of the 10 experiments plotted against the reported (and scaled) number of cases. Compared to
no interventions at all (E0 ), the policy implemented in Virginia (E9 ) can be considered effective
in the sense that it reduced the number of infections in the first four months from ∼ 50% of the
population to only ∼ 7%. Moreover, the results show that each additional set of interventions both
reduced the number of infections and delayed the exponential spread compared to the previous
set of interventions. The largest gain appears to be made by going from E3 (in yellow) to E4
(max group size of 10, stay home when sick, reduce business capacity to 10), and from E4 to
E5 (Closure of all non-essential businesses, everyone asked to stay home as much as possible,
restaurants closed except for take-away).
Figure 4: Cumulative simulated (blue lines) and reported (×30, orange lines) in E0 − E9
4. Conclusion
We showed the feasibility of using data-driven multi-agent simulation to evaluate the effectiveness
of behavioral intervention policies. We explained how both the behavior and disease model
components can be calibrated with real-world data, and demonstrated the utility of such a
model through a simple experiment in which we quantify the effect of the 9 different sets of
behavioral interventions that were implemented in Virginia in the early months of the COVID-19
pandemic through counterfactual simulations. Given the availability of suitable data, such as a
synthetic population, the model can be calibrated and applied to different regions with different
interventions or varying rates of compliance.
Our model is not able to correctly approximate the spread of disease, both temporally and in
magnitude. In future work, we plan to both incorporate age-stratified infectivity and calibrate
against better estimations of true infections, which may help improve the calibration and modeling
of the spread of disease. This may also prove useful for studying the effects of interventions in
regions with different age distributions.
We also plan to investigate the use of the Stringency Index [11], a measure to express the
stringency of a set of measures as a single dimension to allow easy comparison of intervention
policies between regions. Because this metric was designed for comparing regions, it does not
capture the finer details of any specific region, as categories to which measures are assigned are
relatively broad. For this reason, we have not used the stringency index to determine the impact of
mitigation measures in this work. Instead, we are investigating how the stringency index can be
used to define the cost of a policy, as part of a methodology to efficiently find effective mitigation
policies that balance the effect on transmission with societal impact.
Acknowledgments
We thank Cuebiq; mobility data is provided by Cuebiq, a location intelligence and measurement
platform. Through its Data for Good program, Cuebiq provides access to aggregated mobility
data for academic research and humanitarian initiatives. This first-party data is collected from
anonymized users who have opted-in to provide access to their location data anonymously,
through a GDPR and CCPA compliant framework. To further preserve privacy, portions of the
data are aggregated to the US Census block group level.
PB and SS were supported in part by NSF Expeditions in Computing Grant CCF-1918656.
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