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Emulation of epidemics via Bluetooth-based virtual safe virus spread: experimental setup, software, and data

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Abstract

We describe an experimental setup and a currently running experiment for evaluating how physical interactions over time and between individuals affect the spread of epidemics. Our experiment involves the voluntary use of the Safe Blues Android app by participants at The University of Auckland (UoA) City Campus in New Zealand. The app spreads multiple virtual safe virus strands via Bluetooth depending on the social and physical proximity of the subjects. The evolution of the virtual epidemics is recorded as they spread through the population. The data is presented as a real-time (and historical) dashboard. A simulation model is applied to calibrate strand parameters. Participants’ locations are not recorded, but participants are rewarded based on the duration of participation within a geofenced area, and aggregate participation numbers serve as part of the data. Once the experiment is complete, the data will be made available as an open-source anonymized dataset. This paper outlines the experimental setup, software, subject-recruitment practices, ethical considerations, and dataset description. The paper also highlights current experimental results in view of the lockdown that started in New Zealand at 23:59 on August 17, 2021. The experiment was initially planned in the New Zealand environment, expected to be free of COVID and lockdowns after 2020. However, a COVID Delta strain lockdown shuffled the cards and the experiment is currently extended into 2022. The copyright holder for this preprint is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license.
Emulation of epidemics via Bluetooth-based virtual safe virus
spread: experimental setup, software, and data
Azam Asanjarani
1Y*
, Aminath Shausan
2Y
, Keng Chew
3
, Thomas Graham
2
, Shane G.
Henderson4, Hermanus M. Jansen5, Kirsty R. Short3, Peter G. Taylor6, Aapeli
Vuorinen7, Yuvraj Yadav8, Ilze Ziedins1, Yoni Nazarathy2
1Faculty of Science, The University of Auckland, Auckland, State, New Zealand
2School of Mathematics and Physics, The University of Queensland, Brisbane,
Queensland, Australia
3School of Chemistry and Molecular Biosciences, The University of Queensland,
Brisbane, Queensland, Australia
4School of Operations Research and Information Engineering, Cornell University,
Ithaca, NY, USA
5Department of Applied Mathematics, Delft University of Technology, Mekelweg 4,
2628CD Delft, The Netherlands
6Mathematics and Statistics, The University of Melbourne, Melbourne , Victoria,
Australia
7Department of Industrial Engineering and Operations Research, Columbia University,
New York, NY, USA
8Mechanical Engineering Department, Indian Institute of Technology Delhi, New Delhi,
Delhi, India
YThese authors contributed equally to this work.
These authors also contributed equally to this work.
* azam.asanjarani@auckland.ac.nz
Abstract
We describe an experimental setup and a currently running experiment for evaluating
how physical interactions over time and between individuals affect the spread of
epidemics. Our experiment involves the voluntary use of the Safe Blues Android app by
participants at The University of Auckland (UoA) City Campus in New Zealand. The
app spreads multiple virtual safe virus strands via Bluetooth depending on the social
and physical proximity of the subjects. The evolution of the virtual epidemics is
recorded as they spread through the population. The data is presented as a real-time
(and historical) dashboard. A simulation model is applied to calibrate strand
parameters. Participants’ locations are not recorded, but participants are rewarded
based on the duration of participation within a geofenced area, and aggregate
participation numbers serve as part of the data. Once the experiment is complete, the
data will be made available as an open-source anonymized dataset.
This paper outlines the experimental setup, software, subject-recruitment practices,
ethical considerations, and dataset description. The paper also highlights current
experimental results in view of the lockdown that started in New Zealand at 23:59 on
August 17, 2021. The experiment was initially planned in the New Zealand environment,
expected to be free of COVID and lockdowns after 2020. However, a COVID Delta
strain lockdown shuffled the cards and the experiment is currently extended into 2022.
March 29, 2022 1/22
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is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 1, 2022. ; https://doi.org/10.1101/2022.03.31.22273262doi: medRxiv preprint
NOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice.
Author summary
In this paper, we describe the Safe Blues Android app experimental setup and a
currently running experiment at the University of Auckland City Campus. This
experiment is designed to evaluate how physical interactions over time and between
individuals affect the spread of epidemics.
The Safe Blues app spreads multiple virtual safe virus strands via Bluetooth based
on the subjects’ unobserved social and physical proximity. The app does not record the
participants’ locations, but participants are rewarded based on the duration of
participation within a geofenced area, and aggregate participation numbers serve as part
of the data. When the experiment is finished, the data will be released as an
open-source anonymized dataset.
The experimental setup, software, subject recruitment practices, ethical 1
considerations, and dataset description are all described in this paper. In addition, we 2
present our current experimental results in view of the lockdown that started in New 3
Zealand at 23:59 on August 17, 2021. The information we provide here may be useful to
4
other teams planning similar experiments in the future. 5
Introduction 6
The COVID-19 pandemic is the most significant global event of the 21st century to date.
7
In response to the pandemic, multiple solutions have been and are still being developed
8
and deployed, including vaccines and contact tracing technologies. As part of this effort,
9
various initiatives that integrate digital health and “AI systems” (artificial intelligence 10
for pandemics) are being thought out. A key initiative includes measuring the spread of
11
pathogens as well as the level of physical human contact. The Safe Blues project is one
12
such idea, where virtual safe virus-like tokens are spread between cellular phones in an
13
attempt to mimic biological virus spread for purposes of measurement and analysis, 14
while respecting the privacy and safety of the population. 15
Much COVID-19 data is being gathered by contact-tracing apps to aid in identifying
16
infected people or their contacts. However, there can be a time lag of 1 to 2 weeks 17
between being infected and being diagnosed as positive with the result that data 18
obtained in this way is always lagging and biased. Also, asymptomatic cases who may 19
have already spread the virus to others are frequently missed by such methods. Data 20
delays and bias make it difficult for public health officials and others who want to use 21
the data to implement timely mitigation measures. Our approach, on the other hand, is
22
specifically designed to make inferences about the global characteristics of an epidemic
23
in real-time, allowing governments to implement relevant mitigation measures in a 24
timely fashion. 25
Safe Blues, introduced in [1, 2], works by spreading virtual ‘virus-like’ tokens, which
26
we call strands. The strands can be of Susceptible-Exposed-Infectious-Removed (SEIR),
27
Susceptible-Infectious-Removed (SIR), Susceptible-Exposed-Infectious (SEI), or 28
Susceptible-Infectious (SI) type. Each strand is artificially seeded into the system at 29
chosen times and can then spread between phones of users. At any given time, a phone
30
can be infected with many strands, and the phone reports its strand infections to the 31
server periodically. Individuals’ identities and social contacts are not recorded in this 32
reporting, ensuring anonymity. A key aim of the Safe Blues idea is to give policymakers
33
another tool that they can use in their effort to visualize the real-time spread of an 34
epidemic. In contrast to those systems that model population contact and implement 35
agent-based simulations, Safe Blues is an emulation of a group of epidemics based upon
36
a contact process that takes place in the population itself. 37
We devised a campus-wide experiment at The University of Auckland City Campus.
38
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Table 1. The timeline of the experiment at The University of Auckland.
Phase
Dates Study
period Comments
1 May 1 - Jun. 10, 2021 S1, 2021 Used for debugging
2 Jul. 18 - Sep. 16, 2021 S2, 2021 Lockdown on Aug. 17, 2021
3 Sep. 17 - Nov. 4, 2021 S2, 2021 Cancelled due to lockdown
4 Jun. 10 - Sep. 8, 2022 S2, 2022 Currently planned
5 Sep. 9 - Nov. 3, 2022 S2, 2022 Currently planned
This is the first attempt to implement such a system. An outcome of this experiment is
39
an open-source (virtual) epidemic spread dataset which can be used for further 40
modeling, training, and analysis. Our initial plan was to conclude the experiment 41
during November 2021, with the release of data afterwards. However, due to an 42
extensive lockdown in Auckland, the experiment will now run through the second half of
43
2022. In this paper, our primary focus is on the experiment’s methods and the 44
experience gained. Also, we illustrate general outcomes and results to date. The details
45
we present may be valuable to other teams planning similar experiments in the future. 46
Table 1 describes the phases of the experiment, their timelines, and the period at the 47
University of Auckland during which these phases run. 48
As an illustration of the experiment and some of the collected results, consider Fig 1
49
where we depict the timeline July 28 September 9, 2021. Phones of participants were
50
“infected” with strands on July 29 and the figure presents the trajectories of the ensuing
51
epidemics along with the number of participants who attended the campus during that
52
period. There are multiple Safe Blues strand trajectories, the (artificial) infection on 53
July 29 included multiple repeats of the same type of strand and multiple types of 54
strands. In fact, not displayed in this figure, about 600 strands were seeded into the 55
participating population. The black trajectory depicts the daily count of campus 56
participants. The weekly attendance pattern, with lower attendance at weekends, can 57
be seen clearly. The green and red trajectories represent the hourly counts of 58
participants whose phones were in the states of exposed (infected but not infectious) and
59
infected, respectively. As is apparent from the plot, Safe Blues infections continued until
60
the week of August 17 at which point the campus was closed due to a (real) government
61
lockdown. At that point, the number of participants who attended the campus 62
immediately dropped to fewer than 5 per day. As a result, the number of new infections
63
(exposed participants) immediately decreased and within several weeks the number of 64
infected participants also decreased to zero. 65
The Safe Blues experiment was not intended to interact with actual COVID 66
numbers or lockdowns. In fact, we chose New Zealand as a destination because it was 67
essentially COVID free for the second half of 2020 and the first half of 2021 and we 68
believed that a university campus could serve as a good first testbed for Safe Blues. In
69
making this decision, we were aware that the university campus did not directly mimic
70
the population dynamics in all of New Zealand. For instance, during the Auckland 71
lockdown in Phase 2, the campus was completely shut down, while in contrast, people in
72
greater New Zealand still interacted, for example, to go shopping. We did not foresee 73
this lockdown in planning the experiment. Nevertheless, the closure of the campus due
74
to the actual physical lockdown served to illustrate the key point of Safe Blues: safe 75
virtual virus strands that are measured in real-time can give an indication of how actual
76
viruses are spreading, and with enough data and proper machine learning techniques, 77
prediction can take place as well. The Safe Blues system could thus be applied to 78
predict the spread of viral diseases within a subgroup of the population. 79
This paper outlines the experimental setup, software, subject recruitment practices,
80
ethical considerations, and dataset description of the experiment. It also presents our 81
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Fig 1. The effect of campus closure, due to actual lockdown in New Zealand on August 17, on
the virtual Safe Blues epidemic. Red and green trajectories show the daily counts of
participants whose phones were infected (red) and exposed (green) respectively. The black
trajectory shows the daily count of participants who attended the campus.
current experimental results. Our goal in doing so is to showcase the methodologies and
82
experience gained from the experiment. The source code for the project is freely and 83
openly available at [3]. Further, at the conclusion of the experiment, data will be made
84
available via [4]. 85
Background 86
We now present an overview of current practices and specific non-clinical experimental 87
studies that share similar concepts with Safe Blues. Most COVID-19 data are gathered
88
by public health authorities from testing, hospitalizations, and deaths. Various 89
non-government organizations, such as the World Health Organization (WHO) [5], the 90
Center for Systems Science and Engineering at Johns Hopkins University [6], and 91
nCOV2019 [7], collect this data on a global scale and provide daily trend updates. 92
However, such data are prone to lags, biases and inconsistencies, and may not reveal the
93
true characteristics of the disease in real-time. Hence, alternative surveillance methods
94
are needed. 95
Participatory syndromic-surveillance is one such approach that collects self-reported
96
data on COVID-19 symptoms, test results, and other risk factors for COVID-19 via 97
mobile applications or web-based surveys. Examples of such web surveys include 98
InfluenzaNet [8], FluTracking [9], Outbreaks Near Me [10], CoronaSurveys [11], and the
99
Global COVID Trends and Impact Survey [12]. Among the most recent mobile apps are
100
the COVID Symptom Study [13] and Beat COVID-19 Now [14]. 101
To identify potential COVID-19 hot spots, artificial intelligence is being used in 102
conjunction with information obtained from informal sources, such as Google News, 103
eyewitness reports, social media, and validated official alerts. HealthMap [15,16], 104
BlueDot [17], and Metabiota [18] are such tools. Early detection of outbreak regions 105
through wastewater examination is also used in some countries [19]. Remote patient 106
monitoring devices, such as continuous wearable sensors (e.g. smartwatches, Fitbit, 107
Oura Ring, WHOOP strap) and smart thermometers, are also being tested as potential
108
tools for tracking COVID-19 [2025]. These tools measure some of the physiological 109
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indicators of an individual’s health, such as temperature, heart rate, blood oxygen level,
110
pulse rate, sleep performance, and step counts, on a daily basis. The device can identify
111
deviations from an individual’s baseline level which may indicate the possibility of an 112
illness developing. 113
Contact tracing is a popular method for identifying infected but asymptomatic 114
individuals. Under this approach, people who have a history of exposure to a positive 115
case are identified and tested as soon as possible. Various mobile applications and 116
web-based surveys are used for contact tracing [11, 12, 26–33]. Many Bluetooth-based 117
apps, however, were abandoned after their initial release in 2020 [34,35]. Many 118
jurisdictions have QR code scanning systems in place to track and manage COVID-19. 119
However, data from such apps are typically useless when prevalence increases. For 120
example the Check In Qld app [36] in the Australian state of Queensland was 121
successfully applied to trace contacts of positive cases during 2020 to mid-December 122
2021 when the Queensland state border was closed and case numbers were single or 123
double digit at most. However, once the border opened and daily new cases grew to 124
three or four digits, the Check In Qld app was generally abandoned. 125
Moving on to experimental studies, we mention two major non-clinical citizen 126
science experiments conducted prior to the pandemic for disease surveillance purposes. 127
The first is the FluPhone experiment which took place in the United Kingdom between
128
2009 and 2011 [37]. In this experiment, participants reported their influenza like illness
129
symptoms using the FluPhone app, which also recorded the proximity of participants’ 130
devices via Bluetooth and their location via GPS. The number of people encountered by
131
each participant was then estimated and published on the study website [38]. The 132
FluPhone app, like the Safe Blues app, modeled the spread of virtual SEIR type 133
diseases, allowing participants to see real-time profiles of disease propagation in their 134
contact network [39]. However, unlike the Safe Blues app, which is designed to simulate
135
hundreds or thousands of strands, the FluPhone software was designed specifically to 136
mimic the spread of SARS, flu, and the common cold. FluPhone was a unique 137
experiment at that time, but in contrast to Safe Blues, it was designed with less of a 138
focus on capturing physical social interactions in a privacy preserving manner, and more
139
of a focus on mimicking real disease. The second study is “Contagion! The BBC Four 140
Pandemic experiment”, which also took place in the UK, but this time in 2018-2019. 141
The BBC Pandemic mobile phone app was used in the experiment to record 142
participants’ locations and self-reported contacts. A subset of this dataset was used to 143
simulate various non-pharmaceutical intervention (NPI) strategies, such as case 144
isolation, tracing, contact quarantining, and social distancing, to investigate their 145
effectiveness in limiting the spread of COVID-19 [40]. 146
Since the middle of 2020, many countries have been investigating the risk factors 147
involved in opening their society through mass-gathering experiments. Two well-known
148
examples are the RESTART-19 [41] experiment, which took place in Germany in August
149
2020, and a study which took place in Spain in December 2020 [42]. Both assessed the 150
risk of COVID transmission during an indoor live concert, using a variety of seating, 151
standing, and hygiene measures, as well as maintaining optimal air ventilation inside the
152
venue. In both studies, contact tracing devices were used to measure contacts made 153
during the event, and PCR tests were performed a few days later. The RESTART-19 154
study showed that when moderate physical distancing was applied in conjunction with
155
mask-wearing and the conditions for good ventilation were met, indoor mass-gathering
156
events could be held safely. Also, the trial in Spain demonstrated that with 157
comprehensive safety measures, such as face masks and adequate ventilation, indoor 158
mass events could be held without the need for physical distancing. 159
Some experiments have included a series of mass-gathering events with a variety of 160
indoor and outdoor settings, seated and standing audience styles, structured and 161
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unstructured audience styles, and participant numbers. Two such examples are the 162
Fieldlab Events [43] which took place in the Netherlands in February and March 2021, 163
and the Events Research Program [44], which took place in the United Kingdom from 164
April to July 2021. In both experiments, comprehensive public health measures, such as
165
face mask use, hand sanitizing, social distancing, and adequate ventilation at indoor 166
events were observed. Following the events, contact tracing and PCR testing were 167
carried out. According to the Fieldlab Events, outdoor events with 50-75% of the 168
normal visitor capacity could be held provided that strict non-pharmaceutical 169
intervention measures are followed. A robust result from the Events Research Program
170
is yet to be published 171
Other relevant experiments include a health workers protest [45] in South Korea in 172
August 2020 and a martial arts competition [46] in the UAE in July 2020. During both
173
events, participants were required to wear face masks, practice hand hygiene, and 174
maintain physical distance. COVID-19 symptoms were self-reported by protesters in 175
South Korea after the rally. All PCR tests performed on a subset of rally participants 176
returned negative results. PCR tests were conducted twice weekly during the UAE 177
event, and none of the contestants had positive results, indicating that mass-gathering 178
events with restrictive measures could be held safely. 179
Materials and methods 180
We now describe the experimental setup, ethics, software, participant management, and
181
data collection aspects of the experiment as well as supporting tools such as a 182
simulation model. 183
Experimental setup and the Safe Blues system 184
As stated in the introduction, the overarching purpose of the campus experiment is to 185
test the performance of the Safe Blues system. In doing so, we are interested in 186
assessing the ability to use virtual safe virus-like tokens to predict the spread of 187
pathogens. However, an experiment involving actual biological pathogens, or relying on
188
the actual spread of disease is infeasible and hence our experiment uses measurements 189
from the digital domain. The key question is then to test if the spread of some Safe 190
Blues strands can be detected and predicted by measuring the spread of other strands. 191
In its most basic form, our purpose is to treat a single strand as a red strand which is
192
assumed not to be measurable in real time. Further, we treat all other Safe Blues 193
strands as real-time measurable virtual viruses, namely blue strands. The statistical goal
194
is then to benchmark predictions of the future evolution of the red strand based on 195
either, 196
(I) only past measurements of the red strand (a proxy for estimation in the absence 197
of blue strands), or 198
(II) the combination of past measurements of the red strand, past measurements of 199
blue strands, and current measurements of blue strands. 200
For example, Fig 2, which also appeared in [1], presents a simulation run where blue 201
strands are measured in real time, but the red strand is only measurable with a 202
two-week delay. Here the Safe Blues machine learning framework was used to predict 203
the current unobserved state of the red strand. Similarly, it can be used for near future
204
predictions. However, this figure is taken from Monte Carlo simulations of physical 205
contact processes, and not from actual experimental measurements. The Safe Blues 206
experiment attempts to improve upon this by using the actual physical mobility of 207
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Fig 2. Estimation via simulated epidemics. At day 115, we only have red strand information
up to day 100. Nevertheless, current blue strand measurements allow us to estimate the current
state of the epidemic during days 101-115.
individuals. The experiment aims to test whether (II) can yield much better predictions
208
than (I). 209
An additional salient feature of Safe Blues is the interaction with social distancing 210
measures. For this, we would ideally like to ask participants to group together or stay 211
apart similarly to the way that government social distancing measures work. However, 212
this is clearly not feasible with real-life participants and hence the experiment creates 213
virtual social distancing to mimic social-distancing measures. The details of how this is
214
done are described below in the subsection Virtual social distancing. 215
As a first attempt for such an experiment, we chose the University of Auckland City
216
Campus due to the fact that the campus was open to students and staff during 2021 217
(up until the unexpected lockdown of Aug 17, 2021). The experiment consists of 5 218
phases. Table 1 provides the timeline of the experiment including the time period of the
219
year, the study period and a brief description of each phase. The target population of 220
the experiment is the student body, but participation is open to any regular attendee or
221
visitor of the UoA City Campus who is at least 16 years of age and uses an Android 222
mobile phone. All participation is voluntary, and at any time, participants could opt-out
223
of the experiment and uninstall the Safe Blues app. By default, participants are invited
224
to join prize draws which we carefully designed to maximize participation (see details in
225
subsection Participant management and ethical considerations below). However, 226
participants are allowed to take part in the experiment without joining the prize draws.
227
The Safe Blues system is made out of four components: (1) the Safe Blues app, (2) 228
the campus simulation dashboard, (3) the campus experiment leader dashboard, and (4)
229
the Safe Blues data dashboard. All four components are available online at [47], [4], [48],
230
and [49] respectively. Fig 3 displays a snapshot of these four components. 231
Strand and device management 232
Participants run the Safe Blues app [47] (see also Fig 3 (top left) for an illustration of 233
the app) as they go about their normal day to day activities on campus while enabling
234
Bluetooth and location services. Location services are only needed for prize based 235
rewards as described below. A participant’s app then communicates with the apps of 236
other participants via Bluetooth to pass on digital ‘virus-like’ tokens, namely Safe Blues
237
‘strands’. This simulates an epidemic spreading through the community. There are 238
many types of strands of such virtual safe epidemics, and the live emulation of all of the
239
epidemics happens in parallel driven by the actual physical contact processes of 240
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Fig 3. The Safe Blues system: the Safe Blues app (top left), the simulation dashboard (top
right), the campus experiment (campus hours leader board on bottom left), and the data
dashboard (bottom right).
participants. 241
The app is not malicious and does not interact with any other app that users may be
242
running on their phone. Open-source code is available on GitHub via the Safe Blues 243
website [50]. Nevertheless, the app, like any other mobile app, consumes the battery of
244
the phone. It is the participants’ responsibility to manage their phone battery usage, 245
and our experience has shown that some participants turn off the app while away from
246
the campus. The app is only available for Android due to the fact that iOS phones 247
cannot run such an app in the background. This clearly limits the participating 248
population. We discuss the technical details of the app software in S2 Appendix. 249
With the exception of participant reward information, described in 250
subsection Participant management and ethical considerations below, information 251
recorded by the Safe Blues system is limited to the aggregated counts of each strand. 252
Every 15 minutes a phone uploads the status of its infections in terms of ‘exposed’, 253
‘infected’, and ‘recovered’ for each strand. The total number of ‘susceptibles’ is then 254
inferred based on the total number of phones participating at any given time. This 255
uploading occurs via a temporary anonymous 256 bit ID which changes every 24 hours
256
on the phone. Thus the Safe Blues server does not keep track of the individual infections
257
of phones and it cannot uniquely identify a phone beyond a 24 hour period. The 258
temporary ID is still useful for correct counting of infections on the server side, since 259
messages are sometimes lost or not sent if the phone is without connectivity (see S4 260
Appendix where we describe the algorithm for interpolation and imputation of counts to
261
handle this). The individual phone strand information is never cross-referenced with 262
private participant information, further preserving the anonymity of participants. 263
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The injection of new infections into the participating phone population is carried out
264
via an API (Application Program Interface) available to the phones. In each phase of 265
the experiment we inject multiple strands with each batch containing a collection of 266
individual strands. For example, in phase 1, where we focused on testing and tweaking
267
the system, there were 7 batches in total labeled 1.01 to 1.07. Similarly, in phase 3 268
there were 22 batches in total, labeled
3.01
to
3.22
. We discuss the number of strands
269
in each batch, their parameters, and their purposes in the experiment in S5 Appendix. 270
When a batch of strands is ‘injected’, all participating phones become aware of the 271
strands of the batch and each strand has a pre-specified seeding probability which is 272
typically set to 0.05, 0.1, or 0.2. Then at a specified start time, each phone is 273
independently infected by the new strand in accordance with the seeding probability. 274
This ‘seeding’ of new strands thus emulates the arrival of new outbreaks of the epidemic
275
into the population. 276
We applied four types of epidemic models for the phone population: SEIR, SIR, SEI,
277
and SI. In both SEIR and SEI models, when a susceptible phone receives a strand, it 278
first becomes exposed and remains in this state for a random time period known as the
279
incubation period. During the incubation period, the phone is unable to infect other 280
phones. After the incubation period, the phone becomes infected and remains in this 281
state for a random time period known as the infection period. During this time, the 282
phone has the ability to infect nearby phones by exchanging a Bluetooth token. The 283
distribution of the incubation and infection periods is explained further below. The 284
infection period in the SEIR type epidemic is finite, and the phone stops infecting other
285
phones at the end of this period. Consequently, its state is labeled as recovered. The 286
infection period in the SEI epidemic is infinite, and the phone cannot recover. There is
287
no incubation period in the SIR and SI epidemics, and a susceptible phone becomes 288
infected immediately after receiving the strand. The SIR epidemic has a finite infection
289
period and the phone recovers at the end of it. The infection period of the SI epidemic
290
is infinite, and the phone remains in the infected state throughout the epidemic. 291
During phases 1-3, and including the intervening period between phase 3 and 292
phase 4, we injected 4155 strands in total into the system. Of these, 28% are of the SI 293
or SEI type (not involving removal/recovery) and the remaining 72% are of the SIR or
294
SEIR type (allowing recovery). Fig 4 depicts the cumulative counts of strands released
295
over time during phases 1-3. 296
Beyond the classification of SI, SEI, SIR, and SEIR, each strand, uniquely identified
297
by a strand id, which has specific parameters that influence its spread. A full 298
specification of the protocol for these parameters is in Appendix A1 of [2]. However, the
299
protocol there does not deal with specific distributional information and the infection 300
probability mechanism. Hence we now outline these details. 301
We use gamma distributions for both the incubation and infection times and 302
parameterize them by a mean
µ
and a shape parameter
k
. That is, for each
x
(0
,
),
303
the probability density function is 304
f(x;µ, κ) = 1
Γ(κ)µ
κκxκ1eκx
µ,(1)
where Γ(·) is the gamma function. In this case, the ratio between the variance and the 305
square of the mean is 1/k. In many cases we used k= 3; in other cases to create 306
(nearly) deterministic times we set k= 10,000. 307
The other important strand information deals with the probability of infections of 308
nearby phones. At every time where two participating phones are near each other, 309
Bluetooth messages are exchanged during a session and throughout this session, 310
distance measurements are carried out. In principle using individual Bluetooth messages
311
may appear to be preferable to creating sessions. However the nature of the Bluetooth
312
March 29, 2022 9/22
. CC-BY-NC-ND 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 1, 2022. ; https://doi.org/10.1101/2022.03.31.22273262doi: medRxiv preprint
Fig 4. The cumulative number of strands over time broken up into SI, SEI, SIR, and
SIER types and phases of the experiment.
protocol and the underlying software implies that sessions are the preferable technique;
313
see S2 Appendix. 314
At the end of the session (capped at 30 minutes), the median distance from all 315
messages is computed and denoted by d. The duration of the session is denoted by t.316
We expect that with closer distances and longer duration, infection is more likely. We 317
chose the probability of infection parameterized by the strand’s strength, σ, and the 318
maximal infection distance, ρ, to be 319
p(d, t;σ, ρ) = (1eσt(1d/ρ), d < ρ,
0dρ. (2)
In general, we expect strands with higher ρor higher σto be more infectious. 320
In setting the strand parameters σand ρwe initially used a simulation model (see 321
subsection A campus simulation model for details). Subsequently, we adjusted the 322
parameters based on field experience (see section Results and discussion section for 323
details). 324
Participant management and ethical considerations 325
Our goal in participant management is to motivate participants to run the Safe Blues 326
app while on campus. A first decision was whether to couple participation data with 327
strand data (number of virtual infections). We chose not to do so. While such coupled 328
data could be useful, our primary goal is the strand-count time series for which coupling
329
is not needed. 330
A second decision was whether to pay participants a ‘flat rate’ for participation, for
331
example with coffee vouchers proportional to their participation hours or to use prizes. 332
As the total budget was limited, and in accordance with other experimental 333
research [51,52], we opted for prizes. As this is a digital experiment we chose iPad, 334
Android phone, and Fitbit prizes, with 9 prizes per prize draw. See S1 Appendix for 335
details of the prize draw rules. 336
Participants were recruited directly via online flyers, posters and videos. To take 337
part in the experiment, participants first needed to install the Safe Blues Android app 338
March 29, 2022 10/22
. CC-BY-NC-ND 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 1, 2022. ; https://doi.org/10.1101/2022.03.31.22273262doi: medRxiv preprint
on their mobile phones. This gave them a random 10 digit ID which identifies them 339
only for purposes of experiment participation and prizes but is not associated with their
340
strand infections. With this ID, participants can then register their email address which
341
is used for communicating experiment messages and prize winners. 342
As participants enter the city campus, an Android geofencing mechanism spawns an
343
event on the app, and then when they leave the campus (leave the geofence) an 344
additional event is spawned. A message of participation hours is recorded on a server. 345
The participation hours contribute to the chance of winning a prize. In general, the 346
more hours a participant runs the app on campus, the higher the chance of winning a 347
prize (see S1 Appendix). The app does not track the location of participants with the 348
exception of indicating whether or not the participant is within the campus geofence 349
area. Fig 5 (left) displays a snapshot map of the UoA City Campus with the geofenced
350
area marked on it.
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Campus
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Campus
Recreation
Centre
Recreation
Centre
General
Library
General
Library
Old Choral
Hall
Old Choral
Hall
BiologyBiology
Student
Comm
Student
Comm
Kate Edger
Info Comm
Kate Edger
Info Comm
Social
Sciences
Social
Sciences
MusicMusic
Kenneth Myers
Centre
Kenneth Myers
Centre
Newman
Hall
Newman
Hall
Fisher
Building
Fisher
Building
Maclaurin
Chapel
Maclaurin
Chapel
Old Government
House
Old Government
House
University
House
University
House
George Fraser
Gallery
George Fraser
Gallery
ThomasBldgThomasBldg
Cultures,
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& Linguistics
Cultures,
Languages
& Linguistics
MaraeMarae
Fale Pasifika
Complex
Fale Pasifika
Complex
High CourtHigh Court
Pullman HotelPullman Hotel
Copthorne
Anzac Ave
Copthorne
Anzac Ave
UniLodge
Anzac / Beach
UniLodge
Anzac / Beach
Sir Owen G Glenn
Building
Sir Owen G Glenn
Building
Conference
Centre
Conference
Centre
Alfred Nathan
House
Alfred Nathan
House
LodgeLodge
Science
Centre
Science
Centre
Science
Centre
Science
Centre
Starship Childrens
Hospital
Starship Childrens
Hospital
O’Rorke
Hall
O’Rorke
Hall
Auckland
Bioengineering
House
Auckland
Bioengineering
House
Elam
School
Elam
School
University
Hall Towers
University
Hall Towers
University Hall
Apartments
University Hall
Apartments
WaipārūrūHall
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WaipārūrūHall
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Auckland City HospitalAuckland City Hospital
Grafton
Student Flats
Main Building Auckland
War Memorial
Museum
Auckland
Domain
Auckland
Domain
Auckland
Domain
The ClockTowerThe ClockTower
Albert
Park
Albert
Park
PORT OF AU CKLA ND
Mahuhukiterangi
Reserve
Mahuhukiterangi
Reserve
Te Taou
Reserve
Te Taou
Reserve
Fraser ParkFrase
Scarborough
Reserve
Tahaki Reserve
WintergardenWintergarden
Auckland
Town Hall
Aotea Centre
Myers
Park
Carlaw Park
Student Village
Carlaw Park
Student Village
Emily Place
Park
Emily Place
Park
Alten
Reserve
Alten
Reserve
Grafton
Cemetery
East
Grafton
Cemetery
East
Grandstand
Ferry Building
Auckland
Public Library
Auckland
Public Library
Newmarket Park
Endeavour
Park
Olympic
Corner
Lumsden
Green
Station
Square
Outhwaite
Park
Mountain
Reserve
Khyber Pass
Reserve
Basque
Park
Grafton Cemetery
West
Alberon
Reserve
Bassett
Reserve
MonaMona
OkaretaOkareta
BelgraveBelgrave
BayreuthBayreuth
John Hood
Plaza
John Hood
Plaza
Beach Road CyclewayBeachRoad Cycleway
CyclewayCycleway
GullyGully
GraftonGrafton
Grafton Gully CyclewayGrafton Gully Cycleway
HumanitiesHumanities
55 Symonds55 Symonds
Pembridge
House
Pembridge
House
Waikohanga
House
Waikohanga
House
UniLodge
Whitaker
UniLodge
Whitaker
Grafton Hall
Ko te Ako
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Waipārūrū
Hall
Waipārūrū
Hall
Recreation
Centre
Recreation
Centre
Ray Meyer
Building
Court
Te Tirohanga
o te Tōangaroa
Te Tirohanga
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ArchitectureArchitecture
Auckland
Domain
Auckland
Domain
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262 368
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Alfred StreetAlfred Street
StreetStreet
AltenAlten
RoadRoad
Anzac AvenueAnzac Avenue
Waterloo Quadr antWaterloo Quadra nt
Parliament StreetParliament Street
BowenLaneBowenLane
Bowen AvenueBowen Avenue
Wynyard StWynyard St
Princes StreetPrinces Street
CharlesNalden LaneCharlesNalden Lane
Churchill StreetChurchill Street
StreetStreet
StanleyStanley
NichollsNicholls
StanleyStanley
StreetStreet
Lower DomainLower Domain
DriveDrive
CarlawCarlaw
ParkPark
AvenueAvenue
Grafton RoadGrafton Road
Short StreetShort Street
EdenEden
CrescentCrescent
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Emily PlaceEmily Place
EmilyEmily
BanksideBankside StreetStreet
ShortlandShortland
StreetStreet
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Mount StreetMount Street
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Whitaker PlaceWhitaker Place
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Park Road
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Domain
Grafton RoadGrafton Road
GraftonGrafton
RoadRoad
KariKari
StreetStreet
Fencroft StFencroft St
Carlton Gore Road Carlton Gore Road
Grafton
Road
Beckham Place
Wellesley Str eetWellesley Street EastEast
St Paul StreetSt Paul Street
St Paul StreetStPaul Street
Wakefield StWakefield St
Lyndock StLyndock St
Airdale StreetAirdale Street
City Road
LaneLane
TennisTennis
Grafton BridgeGrafton Bridge
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Road
Chancery StreetChancery Street
Bacon LaneBacon Lane
Freyberg PlFreyberg Pl
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Pakenham Street East
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Harbour
Avenue
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Lane
Market Place
Market Lane
Sturdee Street
Lower
Hobson Street
Customs Street
West
Customs
Street West
Fanshawe Street
Fanshawe
Street
Quay Street
Customs Street East
East
Queen Street
Quay Street
Tyler Street
Tyler Street
Galway Street Galway Street
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St
Commerce
St
Street
Gore StGore St
Street
Fort LaneFort Lane
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StreetStreet
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Wyndham StreetWyndham Street
LaneLane
Mills Lane
Lane
Federal Street
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BrandorLane
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Nelson Street
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Lorne StreetLorne Street
Lorne StreetLorne Street
St Patricks
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Hobson Street
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Wellesley Str eet West
Wellesley Street West
West
Sale St
Cook Street
Nelson Street
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Tinley Street
Plumer Street
Tangihua StTangihua St
Te Taou CrescentTe Taou Crescent
Te Taou CrescentTe Taou Crescent
CrescentCrescent
MahuhuMahuhu
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StreetStreet
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NgahoeNgahoe
Shipwright LnShipwright Ln
TheThe
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Street
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Street
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St
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StreetStreet
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Street
Gibraltar
Crescent
Aorere Street
Parnell Road
Parnell Road
ScarboroughLane
Saint Georges Bay Road
Saint Stephens Avenue
Birdwood
Cres
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Cath
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Ayr Street
Laurie Avenue
Dom
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Parnell Road
Cowie Street
Maunsell Road
Titoki Street
Maunsell Road Extension
Cenotaph RoadCenotaph
Cenotaph Road
MuseumMuseum Circuit
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Football
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Wintergarden RoadWintergarden Road
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DomainDomain
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George
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YoungsLane
Laxton
Terrace
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North
Road
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EdwardWayte
Place
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Ely Avenue
Nikau
Street
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Rur