Joint work with Lars Lorch, William Trouleau, Efstratios Tsirtsis, Heiner Kremer, Aron Szanto and Bernhard Schölkopf
Manuel Gomez Rodriguez
A Spatiotemporal Epidemic Model �to Quantify the Effects of �Testing, Contact Tracing and Containment
Contact tracing technology for Covid-19
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Location-based technologies�(e.g., GPS, Wifi triangulation, LTE, QR)
Proximity-based technologies�(e.g., bluetooth)
Use smartphones to track �who you have met in the �recent past
If a person is tested �positive, notify contacts
The promise of contact tracing technologies
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Predict the spread of COVID-19 at an unprecedented spatiotemporal resolution
When and where new individual infections may happen
The promise of contact tracing technologies
4
Design more effective containment & mitigation strategies
Predict the spread of COVID-19 at an unprecedented spatiotemporal resolution
When and where new individual infections may happen
This would allow authorities to lift the most restrictive measures
The promise of contact tracing technologies
5
Design more effective containment & mitigation strategies
Predict the spread of COVID-19 at an unprecedented spatiotemporal resolution
When and where new individual infections may happen
This would allow authorities to lift the most restrictive measures
Data-driven insights into disease parameters
Relative importance of different modalities of disease transmission
The promise of contact tracing technologies
6
Design more effective containment & mitigation strategies
Predict the spread of COVID-19 at an unprecedented spatiotemporal resolution
When and where new individual infections may happen
This would allow authorities to lift the most restrictive measures
Data-driven insights into disease parameters
Relative importance of different modalities of disease transmission
For this to happen, we need �data-driven models designed to make use of individual contact tracing data
Most models: country or state level predictions
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https://arxiv.org/pdf/2004.01105.pdf
Li et al., Science 2020
Most models make country or state level predictions & they �do not characterize the state of each individual over time
What about agent-based epidemiological models?
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Agent-based models proceed in �sequential discrete epochs
Epoch 1
Epoch 2
Epoch 3
What about agent-based epidemiological models?
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Agent-based models proceed in �sequential discrete epochs
How long is each epoch?
How do we faithfully go beyond memoryless distributions?
How do we aggregate events within a epoch?
Epoch 1
Epoch 2
Epoch 3
However, epidemiological state, �mobility, testing, tracing & containment measures spans �wide range of temporal scales:
What about agent-based epidemiological models?
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Agent-based models proceed in �sequential discrete epochs
How long is each epoch?
How do we faithfully go beyond memoryless distributions?
How do we aggregate events within a epoch?
Epoch 1
Epoch 2
Epoch 3
However, epidemiological state, �mobility, testing, tracing & containment measures spans �wide range of temporal scales:
In addition, they cannot characterize individual mobility & contacts patterns within specific towns or cities
Our spatiotemporal epidemic model
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Our model uses marked temporal point processes (TPP) to jointly represent…
Epidemiological state�[contact-based variation of SEIR]
Mobility pattern�[Check-in’s or encounters]
Testing�[A variety of testing policies]
Social distancing & business restrictions
[per demographic groups & business type, dynamic]
Each �individual
Health authority & government
Tracing�[A variety of testing policies]
Want to know more? http://learning.mpi-sws.org/tpp-icml18/
How does the TPP representation work?
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Temporally sorted �queue of events
Social distancing �business restrictions
[thinning]
[superposition principle]
…
Epidemiological & �mobility events
Testing & contact tracing events
Individual mobility patterns
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Bob
Time
Time
Time
Time
Individual mobility pattern
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Bob
Time
Time
Time
Time
Intensity (or rate) at which Bob goes to a supermarket
Duration distribution for supermarket visits
Epidemiological state of each individual
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Time
Susceptible
Exposed
Asymptomatic
Resistant
Presymptomatic
Symptomatic
Hospitalized
Deceased
[1] Lauer et al., Annals of Internal medicine, 2020
[1]
[2] He et al., Nature Medicine, 2020
[2]
[1]
[2, 3, 4]
[2, 3, 4]
[3] Woelfel et al., medRxiv, 2020
[4] WHO, 2020
[5] Wang et al., JAMA, 2020
[6] Linton et al., JCM, 2020
[5]
[6]
[6]
Time to event distributions:
Exposure intensity
[2, 3, 4]
Exposure intensity depends on mobility patterns
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Christine
Time
Time
Time
Time
Exposure intensity depends on mobility patterns
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Christine
Time
Time
Time
Time
Exposure intensity depends on mobility patterns
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overlap
Christine
Time
Time
Time
Time
Environmental �transmission
Exposure intensity depends on mobility patterns
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overlap
Christine
Time
Time
Time
Time
Environmental �transmission
Exposure intensity depends on mobility patterns
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overlap
Christine
overlap
Environmental �transmission
Time
Time
Time
Time
Exposure intensity depends on mobility patterns
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overlap
Christine
Environmental �transmission
overlap
Time
Time
Time
Time
Environmental �transmission
Social distancing & business restrictions
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Before social distancing & business restrictions:
3 times a week
…
…
…
…
twice a week
once a week
…
…
Time
Time
Time
Social distancing & business restrictions
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During social distancing & business restrictions:
3 times a week
…
twice a week
once a week
…
…
once a week
university is closed
once every two weeks
Closed
…
Time
Time
Time
Social distancing & business restrictions
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Time
Time
Time
During social distancing & business restrictions:
3 times a week
…
twice a week
once a week
…
…
once a week
university is closed
once every two weeks
Closed
…
Given historical mobility/contact patterns, we can use thinning to simulate different social �distancing measures & business restrictions
Testing
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Individuals are added to a testing queue according to a testing policy (e.g., add all symptomatic individuals)
Time
Time
Queue additions are �event-driven
n individual from the queue �are tested
time period T
Each individual receives test outcome after 𝝙 units of time
testing capacity
reporting delay
Contact tracing for testing and/or isolation
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Identify contacts the last N days before testing positive
Bob
Contact tracing for testing and/or isolation
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Pick the M contacts with the highest empirical probability �of infection due to Bob
Identify contacts the last N days before testing positive
Bob
Contact tracing for testing and/or isolation
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Pick the M contacts with the highest empirical probability �of infection due to Bob
Those contacts who overlap the longest with Bob in locations k with high
Identify contacts the last N days before testing positive
Bob
t - N
t
Christine
Bob
overlap
overlap
Environmental �transmission
Environmental �transmission
Contact tracing for testing and/or isolation
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Pick the M contacts with the highest empirical probability �of infection due to Bob
Those contacts who overlap the longest with Bob in locations k with high
Test them and/or isolate them for T days
Identify contacts the last N days before testing positive
Bob
t - N
t
Christine
Bob
overlap
overlap
Environmental �transmission
Environmental �transmission
Proximity-based vs. spatial-based technology
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overlap
Environmental �transmission
Time
To identify overlaps, we only �need to record
To identify environmental transmissions, �we need to record
Christine
Bob
Proximity �Spatial︎
Proximity* �Spatial
✓
✕
✓
✓
*Proximity with beacons
✓
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How did we test our model?
Case study using data from
Switzerland
&
Germany
Publicly available data sources: mobility model
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High resolution �population density maps
[tile size: 600m x 600m]
Open street maps (OSM) data
[bars/restaurants, schools/unis, offices, bus stops, supermarkets]
+
assumptions
Individuals’ mobility patterns
[sites check-in’s]
Census data
[age groups, household size]
+
Publicly available data sources: epidemiology
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New daily positive cases and fatalities per age group for each…
Landkreis �( )
Canton�( )
Publicly available data sources: testing
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Maximum testing capacity per day for both Germany and Switzerland, as reported by authorities
Rescaled according to �the population of the
town, city, landkreis or canton
Model calibration using Bayesian Optimization
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+
Individuals’ �mobility patterns
[sites check-in’s]
Bayesian �optimization�[BoTorch]
Testing settings
[testing capacity, delay,�testing policy]
Model simulator
True and simulated daily positive cases �per age group
Transmission rates per site type
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What kind of questions can our model answer in Tübingen (Germany)?
What would have happened without “lockdown”?
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*Population/sites are downsampled by 10x, results in the (updated) preprint will be without downsampling
Model simulation with �social distancing & business closures from “lockdown”
Model simulation without �social distancing & business closures from “lockdown”
What would have happened without “lockdown”?
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Model simulation with �social distancing & business closures from “lockdown”
Model simulation without �social distancing & business closures from “lockdown”
*Population/sites are downsampled by 10x, results in the (updated) preprint will be without downsampling
When should we lift the ”lockdown”?
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It resurges and there is �a second wave
*Population/sites are downsampled by 10x, results in the (updated) preprint will be without downsampling
What about alternating curfews for K random subgroups?
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Monday morning
Monday afternoon
Tuesday morning
Group 1
Group 2
Rationale: alternating curfews may break chain of infections
What about alternating curfews for K random subgroups?
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Enough to keep the �epidemic under control
*Population/sites are downsampled by 10x, results in the (updated) preprint will be without downsampling
Contact tracing for highly granular social distancing
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Flattens the curve & decrease �the peak significantly
N = 3 days, M = 25 contacts, T = 7 days
*Population/sites are downsampled by 10x, results in the (updated) preprint will be without downsampling
Contact tracing requires high compliance
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It gradually �worsens performance
N = 3 days, M = 25 contacts, T = 7 days
*Population/sites are downsampled by 10x, results in the (updated) preprint will be without downsampling
Contact tracing for narrowcasting
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Probability that a person who visited this location in a given time period is exposed
The ranking of sites in terms of exposure probability does not change in expectation when adjusting for adoption levels across sites
It does not suffer from the “x2 adoption problem”
It requires location-based contact tracing or proximity-based with (bluetooth) beacons
*Population/sites are downsampled by 10x, results in the (updated) preprint will be without downsampling
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Open source implementation: https://github.com/covid19-model
It includes a collection of auxiliary functions and notebooks that can be used to mimic our experimental setup from publicly available data at any desired location
Open source implementation
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Open source implementation: https://github.com/covid19-model
It includes a collection of auxiliary functions and notebooks that can be used to mimic our experimental setup from publicly available data at any desired location
Open source implementation
Already used by a growing set of researchers, e.g.,
Teams from Stanford, Uni Bonn, Uni Vienna, Facebook, Google...
We are happy to help anybody get started [Slack channel]
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Arxiv preprint [to be updated later this week]:
https://arxiv.org/abs/2004.07641
Details on the model and results