Predicting Infectiousness for Proactive Contact Tracing
Authors: Yoshua Bengio
Prateek Gupta
Tegan Maharaj
Nasim Rahaman
Martin Weiss
Tristan Deleu
Eilif Benjamin Muller
Meng Qu
victor schmidt
Pierre-Luc St-Charles
hannah alsdurf
Olexa Bilaniuk
david buckeridge
gaetan caron
pierre luc carrier
Joumana Ghosn
satya ortiz gagne
Christopher Pal
Irina Rish
Bernhard Schölkopf
abhinav sharma
Jian Tang
andrew williams
Venue: ICLR 2021 Spotlight (2021)
Keywords: covid-19
contact tracing
distributed inference
set transformer
deepset
epidemiology
applications
domain randomization
retraining
simulation

Abstract: The COVID-19 pandemic has spread rapidly worldwide, overwhelming manual contact tracing in many countries and resulting in widespread lockdowns for emergency containment. Large-scale digital contact tracing (DCT) has emerged as a potential solution to resume economic and social activity while minimizing spread of the virus. Various DCT methods have been proposed, each making trade-offs be-tween privacy, mobility restrictions, and public health. The most common approach, binary contact tracing (BCT), models infection as a binary event, informed only by an individual’s test results, with corresponding binary recommendations that either all or none of the individual’s contacts quarantine. BCT ignores the inherent uncertainty in contacts and the infection process, which could be used to tailor messaging to high-risk individuals, and prompt proactive testing or earlier warnings. It also does not make use of observations such as symptoms or pre-existing medical conditions, which could be used to make more accurate infectiousness predictions. In this paper, we use a recently-proposed COVID-19 epidemiological simulator to develop and test methods that can be deployed to a smartphone to locally and proactively predict an individual’s infectiousness (risk of infecting others) based on their contact history and other information, while respecting strong privacy constraints. Predictions are used to provide personalized recommendations to the individual via an app, as well as to send anonymized messages to the individual’s contacts, who use this information to better predict their own infectiousness, an approach we call proactive contact tracing (PCT). Similarly to other works, we find that compared to no tracing, all DCT methods tested are able to reduce spread of the disease and thus save lives, even at low adoption rates, strongly supporting a role for DCT methods in managing the pandemic. Further, we find a deep-learning based PCT method which improves over BCT for equivalent average mobility, suggesting PCT could help in safe re-opening and second-wave prevention.

Published as a conference paper at ICLR 2021
PREDICTING INFECTIOUSNESS FOR PROACTIVE CONTACT TRACING
Yoshua Bengio af
Prateek Gupta Sabl
Tegan Maharaj Nasim Rahaman "cc Martin Weiss "ag
Tristan Deleu io
Eilif Muller
Meng Qu
Victor Schmidt Pierre-Luc St-Charles
Hannah Alsdurfid
Olexa b
David Buckeridge Gáetan Marceau Caron
Pierre-Luc Carrier
Joumana Ghosn
Satya Ortiz-Gagne" Chris Pat Irina Rish lef
Bernhard Schölkopfic
Abhinav Sharma Jian Tang Andrew Williams
ABSTRACT
The COVID-19 pandemic has spread rapidly worldwide, overwhelming manual contact tracing in many countries and resulting in widespread lockdowns for emer- gency containment. Large-scale digital contact tracing (DCT) has emerged as potential solution to resume economic and social activity while minimizing spread of the virus. Various DCT methods have been proposed, each making trade-off's be- tween privacy, mobility restrictions, and public health. The most common approach, binary contact tracing (BCT), models infection as a binary event, informed only by an individual's 's test results, with corresponding binary recommendations that either all or none of the individual's contacts quarantine. BCT ignores the inherent uncertainty in contacts and the infection process, which could be used to tailor messaging to high-risk individuals, and prompt proactive testing or earlier warnings. It also does not make use of observations such as symptoms or pre-existing medical conditions, which could be used to make more accurate infectiousness predictions. In this paper, we use recently-prove proposse COVID-19 epidemiological simulator to develop and test methods that can be deployed to a smartphone to locally and proactively predict an individual's 's infectiousness (risk of infecting others) based on their contact history and other information, while respecting strong privacy constraints. Predictions are used to provide personalized recommendations to the individual via an app, as well as to send anonymized messages to the individual's 's contacts, who use this information better predict their own infectiousness, an approach we call proactive contact tracing (PCT). Similarly to other works, we find that compared to no tracing, all DCT methods tested are able to reduce spread of the disease and thus save lives, even at low adoption rates, strongly supporting a role for DCT methods in managing the pandemic. Further, we find a deep-learning based PCT method which improves over BCT for equivalent average mobility, suggesting PCT could help in safe re-opening and second- -ave prevention.
INTRODUCTION
Until pharmaceutical interventions such as a vaceine become available, control of the COVID-19 pandemic relies on nonpharnaceutical interventions such as lockdown and social distancing. While these have often been successful in limiting spread of the disease in the short term, these restrictive measures have important negative social, mental health, and economic impacts. Digital contact tracing (DCT), technique to track the spread of the virus among individuals in population using smartphones, is an attractive potential solution to help reduce growth in the number of cases and thereby allow more economic and social activities to resume while keeping the number of cases low.
Most currently deployed DCT solutions use binary contact tracing (BCT), which sends a quarantine recommendation all recent contacts of person after positive test result. While BCT is simple
'lll bolded terms are defined in the Glossary; Appendix 1.
*,i.t Equal contributions, alphabetically sorted; "Mila, Québec; University of Oxford: Mlxx-Paanck Institute for Intelligent Systems Tubingen: "niiversity of Ottawa; McGill University; Uniierssiéé de Montreal; ecole Polytechnique de Montreal; "The Alan Turing Institute; 'HEC Montréal

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and fast to deploy, and most importantly can help curb spread of the disease (Abueg al., 2020). epidemiological simulations by Hinch et al. (2020) suggest that using only one bit of information about the infection status can lead to quarantining many healthy individuals while failing to quarantine infectious individuals. Relying only on positive test results as a trigger is also inefficient for a numher of reasons: (i) Tests have high false negative rates (Li et al.] 2020); (ii) Tests administered late, only after symptoms appear, leaving the asympiomatic population, estimated 20%-30% of cases (Gandhi et al. 2020), likely untested; (ii) It is estimated that infectiousness is highest before symptoms appear, well before someone would get a test (Heneghan et al. 2020p. thus allowing them to infect others before being traced, (iv) Results typically take at least 1-2 days, and (v) In many places, tests are in limited supply.
Recognizing the issues with test-based tracing. Gupta et al. (020)) propose a rule-based system leveraging other input clues potentially available on smartphone (e.g. symptoms, pre-existing medical conditions), an approach they call feature-based contact tracing (FCT). Probabilistic (non- binary) approaches, using variants of belief propagation in graphical models, e.g. (Baker et al. 2020 Satorras & Welling| 2020: Briers et al. 2020), could also make use of features other than test results to improve over BCT, although these approaches rely on knowing the social graph, either centrally or via distributed exchanges between nodes. The latter solution may require many bits exchanged between nodes (for precise probability distributions), which is challenging both in terms of privacy and bandwidth. Building on these works, we propose a novel FCT methodology we call proactive contact tracing (PCT), in which we use the type of features proposed by Gupta et al. (2020) as inputs to predictor trained to output proactive (before current-day) estimates of expected infectiousness (i.e. risk of having infected others in the past and of infecting them in the future). The challenges of privacy and bandwidth motivated our particular form of distributed inference where we pretrain the predictor offline and do not assume that the messages exchanged are probability distributions, but instead just informative inputs to the node-level predictor of infectiousness.
We use a recently proposed COVID-19 agent-based simulation testbed (Gupta et al. 2020) called COVI-AgentSim to compare PCT to other contact tracing methods under a wide variety of conditions. We develop deep learning predictors for PCT in concert with a professional app-development company, ensuring inference models are appropriate for legacy smartphones. By leveraging the rich individual-level data produced by COVI-AgentSim to train predictors offline, we are able to perform individual-level infectiousness predictions locally to the smartphone, with sensitive personal data never required to leave the device. We find deep learning based methods to be consistently able to reduce the spread of the disease more effectively, at lower cost mobility, and at lower adoption rates than other predictors. These results suggest that deep learning enabled PCT could be deployed in a smartphone app to help produce a better trade-off between the spread of the virus and the economic cost of mobility constraints than other DCT methods, while enforcing strong privacy constraints.
1.1 SUMMARY OF TECHNICAL CONTRIBUTIONS
1. We examine the consequential problem of COVID-19 infectiousness prediction and propose a new method for contact tracing, called proactive contact tracing (see Sec.
2. In order to perform distributed inference with deep learning models, we develop an architectural scaffold whose core is any set-based neural network. We embed two recently proposed networks, namely Deep Sets (Zaheer et al. (017)) and Set Transformers (Lee et al. 2018) and evaluate the resulting models via the COVI-AgentSim testbed (Gupta et al. 2020) (see Sec. 3.1).
3. To knowledge the combination of techniques in this pipeline is entirely novel, and of potential interest in other settings where privacy, safety, and domain shift are of concern. Our training pipeline consists of training ML infectiousness predictor on the comain-randomizee output of an agent-based epidemiological model, in several loops of retraining to mitigate issues with (i) -ta-stationartty and (ii) distributional shift due to predictions made by one phone influencing the input for the predictions of other phones. (see Sec. 3.2
4. To our knowledge this is the first work to apply and benchmark a deep learning approach for probabilistic contact tracing and infectiousness risk assessment. We find such models are able to leverage weak signals and patterns in noisy, heterogeneous data to better estimate infectiousness compared binary contact tracing and rule-based methods (see Sec. 4
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2 PROACTIVE CONTACT TRACING
Proactive contact tracing (PCT) is an approach to digital contact tracing which leverages the rich suite of features potentially available on smartphone (including information about symptoms, preexisting conditions, age and lifestyle habits if willingly reported) to compute proactive estimates of individual's 's expected infectiousness. These estimates used (a) provide an individualized recommendation and (b) propagate a graded risk message to other people who have been in contact with that individual (see Fig. D.. This stands in contrast with existing approaches for contact tracing, which are either binary (recommending all-or-nothing quarantine to contacts), or require centralized storage of the contact graph or other transfers of information which incompatible with privacy constraints in many societies. Further, the estimator rums locally on the individual's device, such that any sensitive information voluntecred does need leave the device.
In Section we formally define the general problem PCT solves. In Section 2.2 we describe how privacy considerations inform and shape the design of the proposed framework and implementation. Finally, in Section 3.1 we introduce deep-learning based estimators of expected infectiousness, which we show Section to outperform DCT baselines by a large margin.
Hol-from
Inference Module
Legend
Contacts
Healthy
agent
Symptons
Text Remults
Predictor (an device, traisd
Diegnosod
Pre-eaisting Conditions
RiA Hiserry
Risk messoge
opont
O
londl)
Figure 1: Proactive contact tracing overview. Diagram showing Left: the propagation of anonymized, graded (non-binary) risk messages between users and Inset: overview of the inference module deployed to each user's phone. The inference module for agent takes in observables O, and uses a pretrained predictor f to estimate that agent's ' risk (expected infectiousness) for each of the last 14 days. Anonymized selected elements of this risk vector are sent messages appropriate contacts, allowing them to proactively update their own estimate of expected infectiousness.
2.1 PROBLEM SETUP
We wish to estimate infectiousness uf of an agent on day d', given access to locally observable information Of now day d 2 d' and over the past d days (d' 2 d d'max) Some of the information available on day d is static, including reported age, sex, pre-existing conditions, and lifestyle habits (e.g. smoking), denoted gi, the health profile. Other information is measured each day: the health status hg of reported symptoms and known results. Finally, O also includes information about encounters in the last dmaaz days, grouped in eς for day d. Thus:
0 (gt, h c he-1 dd-1 hdd-dmxx ddddmax)
The information ef about the encounters from day d' is subject to privacy constraints detailed in Section 2.2] but provides indications about the estimated infectiousness of the persons encountered at d', given the last available information by these contacts as of day d, hence these contacts try estimate their past infectiousness posteriori. Our goal is thus to model the history of the agent's 's infectiousness (in the last dmaar days), which is what enables the recommendations of PCT to be proactive and makes possible for an infected asymptomatic person receive a warning from their contact even before they develop symptoms, because their contact obtained sufficient evidence that they were contagious on the day of their encounter. Formally, we wish to model Po(y?1 where y = (v,' "uuly//-- d- ..... y dddmax) is the vector of present and past infectiousness of agent i and 0 specifies the parameters of the predictive model. In our experiments only estimate conditional expectations with a predictor fo. with J (i ...., ddddmar) (o an estimate of the conditional expected per-day present and past infectiousness E 1
The predicted expected values are used two ways. First, they are used to generate messages transmitted day d to contacts involved in encounters day d' E (d dmaz; d). These messages
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contain the estimates i of the expected infectiousness of i at day d', quantized to 4 bits for privacy reasons discussed in section 2.2 Second, the prediction for today of is also used to form a discrete recommendation level ç: E {0, 1, ..... n regarding the behavior of agent at day d via recommendation mapping v. i.e. Çi = ( At ç = 0 agent i is not subjected to any restrictions, S = 1 is baseline restrictions of a post-lockdown scenario (as in summer 2020 in many countries), 5 = 72 is full quarantine (also the behaviour recommended for contacts of positively diagnosed agents under BCT), and intermediate levels interpolate between levels I and n.
Here we make two important observations about contact tracing: (1) There is a trade-off between decelerating spread of disease, measured by the reproduction number R. as number of cases and minimizing the degree of restriction on agents, c.g., measured by the average number of contacts between agents. Managing this tradeoff is social choice which involves not just epidemiology but also economics, politics, and the particular weight different people and nations may put on individual freedoms, economic productivity and public health. The purpose of PCT is to improve the corresponding Pareto frontier. A solution which performs well on this problem will encode a policy that contains the infection while applying minimal restrictions on healthy individuals, but it may be that different methods are more appropriate depending on where society stands on that tradeoff. (2) A significant challenge comes from the feedback loop between agents: observables O of agent i depend on the predicted infectiousness histories and the pattern of contacts generated by the behavior So of other agents j. This is compounded by privacy restrictions that prevent us from knowing which agent sent which message; we discuss our proposed solution in the following section.
2.2 PRIVACY-PRESERVINY PCT
One of the primary concerns with the transmission and centralization of contact information is that someone with malicious intent could identify and track people. Even small amounts of personal data could allow someone to infer the identities of individuals by cross-referencing with other sources, a process called re-identification (El Emam et al., 201T). Minimizing the number of bits being transmitted and avoiding information that makes it easy to triangulate people is a protection against big brother attacks, where a central authority with access to the data can abuse its power, as well as against little brother attacks, where malicious individuals (e.g. someone you encounter) could use your information against you. Little brother attacks include vigilante attacks: harassment, violence, hate crimes, or stigmatization against individuals which could occur if infection status was revealed to others. Sadly, there have been a number of such attacks related to COVID-19 (Russell] 2020). To address this, PCT operates with (1) no central storage of the contact graph; (2)
de-identification (Sweeney) (2002) and encryption of all data leaving the phones; (3) informed and optional consent to share information (only for the purpose of improving the predictor); and (4)
distributed inference which can achieve accurate predictions without the need for a central authority. Current solutions (Woodhams) 2020) share many of these goals, but are restricted to only binary CT.
Our solution achieves these goals while providing individual- level graded recommendations.
Each app records contacts which are defined by Health Canada (2020) as being an encounter which lasts at least 15 minutes with a proximity under 2 meters. Once every 6 hours, each application processes contacts, predicts infectiousness for days d to dmazs and may update its current recom- mended behavior. If the newly predicted infectiousness history differs from the previous prediction on some day (e.g. typically because the agent enters new symptoms, receives a negative or positive test result, receives significantly updated infectiousness estimate), then the app creates and sends small update messages to all relevant contacts. These heavily quantized messages reduce the network bandwidth required for message passing as well as provide additional privacy the individual. We follow the communication and security protocol for these messages introduced by Alsdurf et al. (2000). We note that naive method would tend over-estimate infectiousness in these conditions, because repeated encounters with the same person (a very common situation, for example people living in the same household) should carry a lower predicted infectiousness than the same number of encounters with different people. To mitigate this over-estimation while not identifying anyone, messages are clustered based on time of receipt and risk level as in Gupta et al. (2020).
"The recommendations for each level are those proposed by Gupta et al 2020), hand-tuned by behavioural experts lead to reduction in the number of contacts; details in Appendix 5. Full compliance with recommen-
dations is not assumed.
NNoe that the the number of cases is highly non-stationary; it grows exponentially over time, even where R, which is in the exponent, is constant.
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3 METHODOLOGY FOR INFECTIOUSNESS ESTIMATION
3.1 DISTRIBUTED INFERENCE
Distributed inference networks seek to estimate marginals by passing messages between nodes of the graph to make predictions which are consistent with each other (and with the local evidence available at each node). Because messages in our framework are highly constrained by privacy concerns in that we are prevented from passing distributions or continuous values between identifiable nodes, typical distributed inference approaches (e.g. loopy belief propagation (Murphy et al., 1999), variational message passing (Winn & Bishop 2005), or expectation propagation (Minka) 2001)) are not readily applicable. We instead propose approach to distributed inference which uses a trained ML predictor for estimating these marginals (or the corresponding expectations). The predictor f is trained offline on simulated data to predict expected infectiousness from the locally available information O for agent i on day d. The choice of MI. predictor is informed by several factors. First and foremost, expect the input ef (a component of O to be variable-sized, because we do not know a priori how many contacts individual will have on any day. Further, privacy constraints dictate that the contacts within the day cannot be temporally ordered, implying that the quantity ed is set-valued. Second, given that we are training the predictor on large amount of mamaain-aandmmzed data from many epidemiological scenarios (see Section 3.2) we require the architecture to be sufficiently expressive. Finally, we require the predictor to be easily deployable on edge devices like legacy smartphones.
To these ends, we construct a general architectural scaffold in which any neural network that maps between sets may be used. In this work, we experiment with Set Transformers (Lee et al. 2018) and a variant of Deep Sets (Zaheer et al. 2017). The former is a variant of Transformers /Vaswani cet al. 2017). which model pairwise interactions between all set elements via multi-head dot-product attention and can therefore be quite expressive, but scales quadratically with elements. The latter relies on iterative max-poolin poooloooin of features along the elements of the set followed by a broadcasting of the aggregated features, and scales linearly with the number of set elements (see Figure 2
In both cases, we first compute two categories of embeddings: per-day and per-encounter. Per-day, we have embedding MLP modules Φn of health status, 0g for the health profile, and a linear map øad for the day-offset 5d d d'. Per-encounter, the cluster matrix ef can be expressed as the set (6r9 )) je where is in the set Ký of putative anonymous persons encountered by i at d, Ty-s is the risk level sent from j to i and Ny-ii is the number of repeated encounters between and j at d. Accordingly, we define the risk level embedding function ( and d!!") for the number of repeated encounters. oE is parameterized by embedding matrix, while oin) by the vector
= sin ("/10000*) and (m) (n) (n))2i+1 = cos (7/10000+)
(2)
which resembles the positional encoding in Vaswani et al. 2017) and counteracts the spectral bias of downstream MLPs (Rahaman et al. 2019: Mildenhall et al. (222)). We tried alternative encoding schemes like thermometer encodings (Buckman al.) 2018), but they did not perform better in
our experiments. Next, we join the per-day and per-encounter embeddings to obtain Dj and &d respectively. Where & is the concatenation operation, we have:
D (dx @ (gi)) & dsald' - d) Id'd {d. d dmar]}
(3)
E = (19"" s (l)) (nf-x)) & dn (1(")) 8 Φoald' - d) li E K Vd' d E (d....d- dmar
The union of D.d and El forms the input to a set neural network fs, that predicts infectiousness:
) = f0(; where O = DD. U & and 8 E Rddma
(4)
The trunk of both models - deep-set (DS-PCT) and set-transformer (ST-PCT) - is a sequence of 5 set processing blocks (see Figure 2p. A subset of outputs from these blocks (corresponding to
DÍ)) is processed by a final MLP to yield sg. As training objective for agent i, we minimize the Mean Squared Error (MSE) between y (which is generated by the simulator) and the prediction nd
We treat each agent as sample in batch to obtain the sample loss L; MSE(y., }!) =
dmaz Ed (v6" "(l) )2. The net loss is the sum of L over all agents i.
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8
Cloozz
F
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Figure 2: PCT model architecture. Diagram showing Left: The embedding network combining pre-existing conditions O day offsets O risk message clusters O O, and symptoms information O to be fed into a stack self-attention block featuring Multi-Head Dot Product Attention (MHDPA), Fully-Connected layers with ReL.U (FC + R) and residual connections. Right-bottom: (DS) set processing block. Here, the denotes concatenation and the addition operation.
either Deep-Set (DS) or Set Transformer (ST) blocks O. Right-top: (ST)
3.2 TRAINING PROCEDURE
Unlike existing contact tracing methods like BCT and the NHSx contact tracing app (Briers et al.) 2020) that rely on simple and designdd heuristics to estimate the risk of infection, our core hypothesis is that methods using a machine-learnnng based predictor but noisy signals that might be available locally on a smartphone. In order to test this hypothesis prior to deployment in the real world, we require simulator built with the objective serve testbed for app-based contact tracing methods. We opt to use COVI-Agente which features an agent specific virology model together with realistic agent behaviour, mobility, contact and app-usage patterns. With the simulator, we generate large datasets of O(10") samples comprising the input and target variables defined in sections 2.1 and 3.1 Most importantly for our prediction task, this includes a continuous-valuee infectiousness parameter as target for each agent.
learn from patterns in rich
(Gupta et al. 2020).
We use 240 runs of the simulator to generate this dataset, where each simulation is configured with parameters randomly sampled from selected intervals (See Appendix (5.2). These parameters include the adoption rate the contact tracing app. initial fraction of exposed agents in the population, the likelihood of agents ignoring the recommendations, and strength of social distancing and mobility restriction measures. There are two reasons for sampling over parameter ranges: First, the intervals these parameters sampled from reflect both the intrinsic uncertainty in the parameters, well as the practical setting and limitations of an app-based contact tracing method (e.g. we only care about realistic levels of app usage). Second, randomly sampling these key parameters significantly improves the diversity of the dataset, which in turn yields predictors that can be more robust when deployed in the real world. The overall technique resembles that of domain-randominn fomain-randomizztion randomizationn (Tobin) et al. 2017 Sadeghi & Levine 2016) in the Sim2Real literature, where its efficacy is well studied for transfer from RGB images to robotic control, e.g. (Chebotar et al. 2018 OpenAl et al. 2018).
We use 200 runs for training and the remaining 40 for validation (full training and other reproducibility details are in Appendix 55. The model with the best validation score is selected for online evaluation, wherein we embed it in the simulator to measure the reduction in the R as function of the average number of contacts per agent per day. While the evaluation protocol is described in section 4 we now discuss how mitigate fundamental challenge that share with offline reinforcement learning methods, that of auto-induced distribution shift when the model is used in the simulation loop
(Levine et al. 2020 Krueger al. 2020).
To understand the problem, consider the case where the model trained on simulation runs where PCT is driven by ground-truth infectiousness values, i.c. oracle predictor. The predictions made by an oracle will in general differ from ones made by trained model, as will resulting dynamics of spread of disease. This leads to distribution contacts and epidemiological scenarios that

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the model has not encountered during training. For example, oracle-driven PCT might even be successful in eliminating the disease in its early phases - scenario unlikely to occur in model-driven simulations. For similar reasons, oracle-driven simulations will also be less diverse than model- ones. To mitigate these issues, we adopt the following strategy: First, we generate an initial dataset with simulations driven by noisy-oracle, i.e. we add multiplicative and additive noise to the ground- truth infectiousness to partially emulate the output distribution resulting from trained models. The corresponding noise levels are subject rannainranddmizztiion (as described above), resulting in dataset with some diversity in epidemiological scenarios and contact patterns. Having trained the predictor on this dataset (until early-stopped), we generate another dataset from simulations driven by the fhus-far trained predictor, in place of the noisy-oracle. We then fine-tune the predictor on the new dataset (until early stopped) to obtain the final predictor. This process can be repeated multiple times, in what we call iterative retraining. We find three steps yields good trade-off between performance and compute requirement.
EXPERIMENTS
We evaluate the proposed PCT methods, ST-PCT and DS-PCT, and benchmark them against: test- based BCT; a rule-based FCT Heuristic method proposed by Gupta et al. (2020 and a baseline No Tracing (NT) scenario which corresponds to recommendation level (some social distancing).
EXP1: In Figure 3 we plot the Pareto frontier between spread of disease (It) and the amount of restriction imposed. To traverse the frontier at 60% adoption rate, we sweep through multiple values of the simulator's s global mobility scaling factor, a parameter which controls the strength of social distancing and mobility restriction measures. Each method uses 3000 agents for 50 days with 12 random seeds, and we plot the resulting number of contacts per day per human. We fit a Gaussian Process Regressor to the simulation outcomes and highlight the average reduction R obtained in the vicinity of R ~ 1, finding DS-PCT and ST-PCT reduce R to below 1 at much lower cost to mobility on average. For subsequent plots, we select the number of contacts per day per human such that the no-tracing baseline yields realistic post-lockdown I of around 1.2 (Brisson & et al. 2020 5
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Figure 3: Pareto frontier of mobility and disease spread: reproduction number R as function of mobility. In boxes, average difference +/- standard error, p-value under null hypothesis of no difference. Note that small differences in R over time produce large changes the number of cases. Gist: All methods span a wide range of ft values in their Pareto frontier, including values for the No Tracing scenario which have R below 1, achieved by imposing strong restrictions on mobility (e.g. a lockdown). However DCT methods are able to reduce R at much lower cost to average mobility. Compared to NT. BCT has 12% advantage in R. DS-PCT (left) 31% and ST-PCT 25% (right).
EXP2: Figure compares various DCT methods in terms of their cumulative cases and their fraction of false quarantine: the number of healthy agents the method wrongly recommends quarantine.
'While did experiment with additional methods like linear regression and MLPs, they did not improve the performance over the rule-based FCT heuristic proposed by Gupta al. (2020).
'To estimate this number, we use the GP regression fit in figure 3 and consider the x value for which the mean of the NT process is at 1.2. We find an estimate at 5.61, and select only the runs yielding effective number of contacts that lie within the interval (5.61 0.5, 5.61 + 0.5).

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Again, all DCT methods have clear advantage the no-tracing baseline, while the number of agents wrongly recommended quarantine much lower for ML-enabled PCT.
Thacing
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Figure 4: Left: Cumulative case counts for each method, 60% adoption, 50 days, with all runs normalized to 5.61 + 0.5 effective contacts per day per agent. Right: Mobility restriction for the same experiments (fraction quarantines). Gist: For similar number of cumulative cases to other DCT methods (left), PCT methods impose very little mobility restriction (right), close to NT.
EXP3: Figure Left we plot the bootstrapped distribution of mean R for different DCT methods. Recall R is estimate of how many other agents an infectious agent will infects, i.e. even numerically small improvement f could yield an exponential improvement in the number cases. We find that both PCT methods yield clear improvement over BCT and the rule-based heuristic, all of which significantly improve over the no- no-tracing baseline. We hypothesize this is because deep neural networks are better able capture the non-linear relationship between features available the phone, interaction patterns between agents, and individual infectiousness.
EXP4: In Figure 5 Right investigate the effect of iterative retraining the machine-learning based methods, DS-PCT and ST-PCT. We evaluate all iterations of each method in the same experimental setup in Figure and find that DS-PCT benefits from the 3 iterations, while ST-PCT saturates at the second iteration. We hypothesize that this a form of overfitting, given that the set transformer (ST) models all-to-all interactions and is therefore expressive than deep-sets (DS).
lleration
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Distribution (median and quartiles) of R at 60% adoption where the ML methods outperform the Heuristic and BCT methods proposed by Gupta et al. (2020). Right: Iterative re-training significantly improves model performance. Upon the second re-trnin however, it seems that ST-PCT begins to overfit.
Figure 5: Method Comparison and Retraining. Left:
'Note that the haseline no tracing method also has false quarantines, because household members of an infected individual also recommended quarantine, irrespective of whether they infected.
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EXP5: In Figure analyze the sensitivity of the various methods adoption rate, which measures what percent the population actively uses the CT app. Adoption rate is an important parameter for DCT methods, it directly determines the effectiveness of app. We visualize the effect of varying the adoption rate on the reproduction number R. Similarly to prior work (Abueg et al. 2020), find that all DCT methods improve over the no-tracing baseline even at low adoptions and PCT methods dominate at all levels of adoption.
Adoption
1.4
1.3
30%
45%
1.2
60%
1.1
c
1.0
0.9
0.8
0.7
BCT
Heuristic
ST-PCT
DS-PCT
Method
Figure Adoption rate comparison. We compare all methods for adoption rates between 0% (NT) and 60%. Gist: All methods are able to improve over NT, even at low adoption rates. At 30% and 45% ST-PCT performs the best by a relatively wide margin while DS-PCT outperforms 60%.
5 CONCLUSION
Our results demonstrate the potential benefit of digital contact tracing approaches for saving lives while reducing mobility restrictions and preserving privacy, independently confirming previous reports (eerrttt et al. 2020 Abueg et al. 22000) Of all methods in our study, we find that deep learning based PCT provides the best trade-off between restrictions on mobility and reducing the spread of disease under a range of settings, making a potentially powerful tool for saving lives in safe deconfinement. This area research holds many interesting avenues of future work in machine learning. including: (1) The comparison of methods for fitting parameters of the epidemiological simulator data using spatial information (not done here to avoid the need for GPS), (2) Using reinforcement learning to learn (rather than expert hand-tune) the mapping from estimated infectiousness and individual-level features (number of contacts, age, etc.), and thereby target desirable outcomes for hetcrogencous populations.
Accurate and practical models for contact tracing are only a small part of the non-pharmaceutical efforts against the pandemic, response which is complex venture necessitating cooperation between public health, government, individual citizens, and scientists of many kinds epidemiologists, sociologists, behavioural psychologists, virologists, and machine learning researchers, among many others. We hope this work can play role in fostering this necessary collaboration.
ACKNOWLEDGEMENT
We thank all members of the broader COVI project http:: www.c//aa..ca..acccc org for their ded- ication and teamwork; it was a pleasure and honour work with such great team. We also thank the Mila and Empirical Inference communities, in particular Xavier Bouthillier, Vincent Mai, Gabriele Prato, and Georgios Arvanitidis, for detailed and helpful feedback on early drafts. The authors gratefully acknowledge the following funding sources: NSERC, IVADO, CIFAR. This project could not have been completed without the resources MPI-IS cluster, Compute Canada & Calcul Quebec, in particular the Beluga cluster. In gratitude have donated to project to help understand and protect the St. Lawrence beluga whales for whom the cluster is named https: / //ba e nesendi rect. .ect.org//

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APPENDIX 1: GLOSSARY OF BOLDED TERMS
Contact tracing Finding the people who have been in contact with an infected person, typically using information such as results and phone surveys, and recommending that they quarantine themselves to prevent further spread of the disease.
Manual contact tracing Method for contact tracing using trained professionals who interview diagnosed individuals to identify people that have come into contact with an infected person and recommend a change in their behavior (or further testing).
Digital contact tracing (DCT) Predominantly smartphone-based methods of identifying individu- als at high risk of contracting an infectious disease based on their interactions, mobility patterns, and available medical information such as test results.
Binary contact tracing (BCT) Methods which use binary information (e.g. tested positive or negative) to perform contact tracing, thus putting users in binary risk categories (at-risk or not-at- risk).
Proactive contact tracing (PCT) DCT methods which produce graded risk information to mitigate spread of disease, thus putting users graded risk categories (more-at-risk less-at-risky potentially using non-binary clues like reported symptoms which are available earlier than test results.
Agent-based epidemiological models (ABMs) Also called individual-based this type of simu- lation defines rules of behaviour for individual agents, and by stepping forward in time, contact patterns between agents are generated in a "bottom up" fashion. Contrast with Population-level epidemiological models.
Risk of infection infectious agent given qualifying contact (15+ minutes at under 2 meters).
Expected infectiousness, or probability of infection for susceptible agent by an
Contact An encounter between 2 agents which lasts least 15 minutes with distance under meters (Health Canada 2020).
Risk Level A version of the risk of infection quantized into 16 bins (for reducing the number of bits being exchanged, for better privacy protection). The thresholds are selected by running the domain randomization with separate seeds and grouping risk messages such that there are an approximately uniform number in each bin.
Risk mapping A table which maps floating point risk scalars into one of 16 discrete risk levels.
Recommendation mapping A table of which recommendation level should be associated with given risk level. Each recommendation level comes with a series of specific recommendations (e.g. "Limit contact with others", "wash hands frequently", "wear a mask when near others" "avoid public transportation", etc) which should be shown for given risk level. Reminders of these recommendations may be sent via push notification more or often depending on the recommendation level.
Population-level epidemiological models This type of model fits global statistics of a population with mathematical model, typically sets of ordinary differential equations. The equations track some statistics over time, typically counts of people in each of few "compartments" e.g. the number of Infected and Recovered, and the parameters of the equations are often tuned to match statistics collected from real data. It does not give any information about the individual- contact patterns which give rise to these statistics.
Compartment model (SEIR) A compartment model tracks the counts of agents in each of several nuuuualy--xxlusiig categories called "compartments". In an SEIR model, the 4 compartments are Susceptible, Exposed, Infectious, and Recovered (see entries for each of these words).
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Susceptible
At risk of catching disease, but not infected.
Exposed or infected Infected with the disease, (i.e. potentially carries some viral load).
Infectious
Carries sufficient viral load to transmit the disease to others. In real life, this typically means that the virus has multiplied sufficiently overwhelm the immune system.
No longer carries measurable viral load, after having been infected. In real life this is typically measured by two successive negative lab tests.
Recovered
Viral load Viral load is the number of actual viral RNA in person as measured by lab test.
Effective viral load A term introduce representing a number between 0 and 1 which we a proxy for viral load. could be converted to an actual viral load via multiplying by the maximum amount of viral RNA detectable by lab test.
Infectiousness Degree to which agent is able to transmit viruses to another agent. A factor in determining whether an encounter between a susceptible and an infectious agent results in the susceptible agent being exposed (it is property of the infector agent; this does not consider environmental factors or the other agent's ' susceptibility; see Transmission probability).
Attack rate
The proportion of individuals in population who are infected over some time period.
Contamination duration How long location remains infectious after infected person has visited it and shed viruses there.
Transmission probability The chance that one agent infects another during an encounter. Infec- tiousness of the infected agent, susceptibility of the other agent, both their behaviour (e.g. usage of masks) and other environmental factors all play a role determining this probability.
PCR Test Also, colloquially referred to as lab test. In this context, this means a Polymerase Chain Reaction (PCR) test used to amplify viral DNA samples, typically obtained via nasopharangeal swab.
Asymptomatic
When an infected person shows symptoms, For COVID-19, many people remain asymptomatic for the entire course of their disease.
Incubation days The number days from exposure (infection) until an agent shows symptoms. In real life this is the average amount of time takes the viral RNA multiply sufficiently in / burst out of host cells and cause an immune response, which is what produces the symptoms.
Reproduction number (R) The average numher of other agents an agent infects, measured over a certain window of time. We follow Gupta et al. (2020) and approximate R by computing the infection tree and taking the ratio of the number of infected children divided by the number of parents who are recovered infectors.
Serial interval The average number of days between successive symptom onsets (i.e. between the incubation time of the infector and the infectee).
Generation time The number of days between successive infections (i.e. between the exposure of the infector and the infectee). Generation time is difficult to measure directly so one can estimate from the serial interval.
Domain randomization A method of generating training dataset by sampling from several distributions, each corresponding to a different setting of parameters of simulator. This allows to generate dataset which covers potentially wide range of settings, improving generalization to
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environments which may not be well covered by the simulator in any particular setting chosen priori.
Oracle Predictor Baseline for the Set Transformer which uses ground-trute infectiousness levels as "predictions". Provides an expected upper-bound performance for the predictors and can be used to provide risk level inputs when pre- pre-training a predictors.
Multi-Layer Perceptron (MIP) A risk prediction model which concatenates all inputs (after heuristically aggregating to a fixed size vector the set-valued inputs), feeds these through several fully-connected neural network layers and is trained to predict infectiousness. See Section S.1
Set Transformer (ST) Model A risk prediction model which uses modified set transformer to process and attend inputs, and is trained to predict infectiousness. See Section 5.1
Deep Set (DS) Model Similar structure as the Set Transformer, but using pooling instead of self-attention. This allows to use less memory and compute as compared the Set Transformer.
Heuristic (HCT) Model A rule-based method for predicting risk histories and corresponding current behavior levels developed in Gupta et al. 2020).
Adoption rate tion.
The proportion of the total population which uses digital contact tracing applica-
The technique of varying the parameters a simulation environment to create broad distribution of training data.
Domain randomization
The process of matching anonymous data with publicly available data so as to determine which person is the owner.
Re-identification
Big brother attacks "Big brother" is reference to the 1984 book by George Orwell where highly regulated government surveilled and controlled its citizenry. The term "big brother attacks" references the idea that an organized group (e.g., state, federal, academic or financial institution) may try to gain control of your data.
Little brother attacks Little brother attacks references the idea that potential security threats also posed by smaller actors like individuals, criminals, and data brokers.
Vigilante attacks Extra-judicial violence by an individual. In the context of this paper, specifically as result of recommendation shown to the user or gained through other means.
Degree of Restriction Ratio between the number of people given a recommendation in the highest level of restriction (i.e. quarantine) relative to other categories.
Global mobility scaling factor simulator parameter enabling us to vary the amount of contacts which may lead to infection in the simulator. It allows scale the mobility to simulate pre- lockdown or post-lockdown environments.
Auto-induced distribution shift change in distribution of data observed by an agent or algorithm as result of the agent algorithm's 's actions.
Iterative re-training The process generating data using some method a simulator, training model on this data in supervised manner, then evaluating the model in the simulator to produce more data.
Pareto frontier The Pareto frontier is a way of evaluating tradeoff's in a set of policies and environments with multi-dimensional outputs (e.g., viral spread and mobility).
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APPENDIX 2: MOTIVATING EXAMPLE
Manual onlyy
Tor met
Biraary traciing
Our approso
Ter
Figure 7: Motivating example comparing manual, binary, and proactive contact tracing: This example shows the potential effectiveness of early warnings in controlling the spread of the infection. Manual tracing is delayed because of the time between diagnosis and calling all contacts. Both manual and digital contact tracing are sending late signals because they only make use of the strongest possible signal (positive diagnosis). The proposed ML approach takes advantage of reported symptoms and the propagation of risk signals between phones to obtain much earlier signals.
APPENDIX 3: COMPARISON OF APPROACH TO RELATED WORK
Epidemiological Modeling and Simulations. Given that modeling contact- tracitg requires captur- ing past interactions, mathematically complicated to consider the dynamic nature network interactions. An agent-based model (simulator), the other hand, gives maximum flexibility to incorporate real data and/or assumptions easily and emulate the effect of personalized policies (such as resulting from the proposed app). Models with binary contagion and random-walk mobility are ubiquitous (Stevens, 2020). The appeal of such models is their simplicity; they are easy to code, fast run, and can give general picture of some aspects of disease spread. There are other models with increasing complexity of either the mobility model, contagion model, agent demographics,
some Vespignani et al., 2020 Wood et al.) 2020 Lorch et al.,
combination of these, e.g. (Verity al. 2020
2020 Hinch et al.) 2020).
GLEAM (Global Epidemic And Mobility model) (Vespignani et al. 2020 is an off-the-shelf simula- tion platform for epidemics which offers mobility patterns and demographic information, and uses generic format for defining how a disease depends on these two things. Similarly. FRED (Framework for Reconstructing Epidemiological Dynamics) provides realistic social networks and US demographics. JJ et al. (2013), and (Wood et al. 2020) build an ceerveetioo-planninn tool top of this simulator. These works comparable our simulator only; they do not do any contact tracing or individual risk prediction.
open-source, agent-based model with
The work presented in (Lorch et al. 2020) and (Ferretti et al. 2020) is closely related detailed mobility model for interactions is presented in (Lorch et al. (2020), but the epidemiological model of the disease is much simpler there. First, the contact graph built based on their mobility model. The next step is an implementation of various policy interventions by health authorities, which includes contact tracing. This is done instead of building a contact graph that takes into account policy interventions and contact tracing apps at an individual level. Next, most similarly to our work, (Ferretti al. 2020) proposes an baseb tracing and recommendations. However, their epidemiological model is a very simple differential-equatior model, and interventions for controlling the disease are computed analytically.
A
Risk estimation approaches. While the applications deployed so far are based primarily on binary contact tracing as discussed above, some probabilistic risk estimation approaches, similar to ours, have been developed for other discases
applications, and have begun to be applied to COVID-
19. For example, (Baker et al., 2020) uses the wewptiill--ffeeed-reeeeeeo deseribes the dynamical process of infection propagation using the dynamical message passing equations from (Lokhov et al.] 2014); the probability of each node (person) to be a specific state (S,1 R) is estimated via the dynamic message-passing (DMP) algorithm, which belongs to the
(SIR) model and
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family of local message- paasiing methods similar to belief propagation (BP) algorithm (Yedidia et al. 2000) for estimating marginal probability distributions over the network nodes; despite BP being only an approximate inference method, not guaranteed to converge the correct marginals when the underlying graphical model has (undirected) cycles, it demonstrated remarkable performance in various applications. A similar approach based on BP was also discussed in (Murphy) (220)) Furthermore, there are recent extensions of belief propagation approach graph neural nets (Satorras & Welling 2020). Also, another recent work uses Gibbs sampling and SEIR model for their test-trace- isolate approach (Herbrich et al. 2020). However, such approaches typically rely on the knowledge of the social interaction graph, which is not available in our case due to privacy and security constraints.
To the best of our knowledge, our work is the first to use an approach based on detailed agent-based based epidemiological model together with a model of phone app messaging to generate simulated data for training an MI.-based predictor of individual-level risk.
Digital contact tracing for COVID-19 (Hinch et al. 2020 Hellewell et al., 2020 Aleta et al. 2020
Grantz et al. (020) study, either via simulations mathematical models, s. the conditions under which BCT can be effective. Toward addressing the issues with BCT, (Hinch et al. 2020) show in simulation that using self-reported symptoms in addition to test results can greatly help control an outbreak. Probabilistic minnrbinary) approaches to the problem of contact tracing (c.g. [aker iet al. (020); (atorras& & Welling (2020) Briers et al. (2020) typically assume full access to location histories and contact graph, an unacceptable violation of privacy in most places in the world. As a result, these methods most often used for predicting overall patterns of disease spread.
Agent-Basee Brent-Based Models as a generative process Our use of an agent-based simulator GGupa et al. 2020) as generative model allows us to generate fine-grained (continuous) values for expected infectiousness with realistic contact patterns. Most works performing probabilistic inference for disease modeling use a simple differential equation generative model, which does not characterize individual behaviour but rather the dynamics of transition between each of several mutually exclusive disease states. Such models make many simplifying assumptions, such as contact patterns based on random walks, which make them unsuitable for individual-level prediction of infectiousness; they are typically used instead to infer latent variables such as infectiousness that would be consistent with the population-level statistics generated by the differential equation model, and/or to predict statistics of spread of the disease in population, e.g. (ref, ref). While agent-based models are widely used in epidemiological literature to model the spread of disease (see e.g. (ref) for review), to our knowledge we are the first to use an ABM as a generative model for training a deep learning-bast based infectiousness predictor.
Distributed inference and belief propagation Belief propagation in graphical models is often used for disease spread modeling, e.g. Fan et al. (2016). Some recent works have applied this to COVID-19; for example, Baker et al. (2020) use the susceptible-infeet inffected-reoovered (SIR) model and describe the process of infection propagation using the dynamical message passing equations from Lokhov et al. (2014), A work concurrent with ours follows a similar justification for modeling a latent parameter of expected infectiousness, using an SEIR model with inference via (Herbrich et al., 2020). However, these approaches rely on a centralized social graph or a large number of bits exchanged between nodes, which challenging both in terms of privacy and bandwidth. This challenge motivated our particular form of distributed inference where we pretrain the predictor and do not assume that the messages exchanged are probability distributions, but instead just informative input to the node-level predictor.
APPENDIX 4: EXPERIMENTAL DETAILS
5.1 ML ARCHITECTURES AND BASELINE DETAILS:
Binary contact tracing quarantines app-users who had high-risk encounters with an app-user who receives positive PCR test. Under BCT1, if Alice gets a positive test result, then every user who encountered Alice within 14 days of her receiving the positive test result is sent a message which places them in app-recommendatioo level 3 (quarantine) for 14 days. Formally, ç² (/() 3.
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Set Transformer Recall that in Section 3 we proposed two parameterizations of the model (DS and ST in Figure 2) In the first proposal, we use a set transformer (ST) to model interactions between the clements in the set DV UUE UE We now describe the precise architecture of the model used.
The model comprises 5 embedding modules, namely: the health status embedding @hs health profile embedding @hp- day offset embedding @do. risk message embedding &e and an embedding de the number of repeated encounters.
(n) of
The model was trained for 160 epochs domain randomized dataset (see below) comprising 10 samples. We used a batch-size of 1024, resulting ~ 80k training steps. The learning rate schedule is such that the first 2.5k steps used for linear learning- raatt warmup, wherein the learning rate linearly increased from to x 10 10-4, followed by a cosine annealing schedule that decays the learning rate from 2 x 10 to 10 in 50k steps.
5.2 DOMAIN RANDOMIZATION
Inspired by research in in deep reinforcement learning (Tobin et al.) (001)) we created the transformer's training data by sampling uniformly in the following ranges:
search (Bergstra & Bengio, 2012) and recent advances
1. Adoption rate [30 60]
2. Carefulness E [0.5 - 0.8]
3. Initial proportion of exposed people E [0.002, 0.006]
4. Oracle additive noise E [0.05 - 0.15]
5. Oracle multiplicative noise [0.2 0.8]
6. Global mobility scaling factor [0.3 0.9]
7. Symptoms dropout: Likelihood of not reporting some symptoms E [0.1, 0.6]
8. Symptoms drop-in: Likelihood of falsely reporting symptoms E |00.0001, 0.001]
9. Quarantine dropout (test) E [0.01, 0.03]: likelihood of not quarantining when recommended quarantine due positive test
10. Quarantine dropout (household) [0.02, 0.05]: likelihood of not quarantining when recom- mended to quarantine because household member got a positive test
All-levels dropout [0.01, 0.05]: likelihood not following app-recommended behavior and instead exhibit pre-pandemic behavior
5.3 TRAINING TIME
Our MI. experiments use approximately 250 days training time on GPUs while simulations required approximately 41 days of CPU time. All CPU time run compute using renewable resources.
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APPENDIX 5: RELEVANT BACKGROUND ON COVI-AGENTSIM
Details on the simulator can be found in Gupta et al. 2020), and the code is open-source at httpps:/ github. com/mn /m 1a- iiaa/iia/ COVI Agent Si Here we summarize some of the most relevant details about the simulator for ease of reference.
5.4 APP ADOPTION
CoVI-AgentSim models app adoption proportional to smartphone usage statistics, shown Table
of population with app
Uptake required get that %
1.50
42.15
40
56.18
84.15
70
98.31
Table I: Adoption Rate vs Uptake: The left column show the total percentage of population with the app, while the right column shows the proportion of smartphone users with the app.
5.5 RECOMMENDATION LEVELS AND CONTAINMENT PROTOCOL
Gupta al. 2020), the implementation binary contact tracing uses simple, binary containment protocol: quarantine at home for 14 days if in contact with someone who has had a positive test result, otherwise nothing. In contrast, the graded recommendation levels used by feature-based contact tracing methods including Heuristic and Proactive Contact Tracing are not binary, and do not model an explicit containment protocol. Instead, [uupta et al. (2020) models the effects of behavioural recommendations through reducing the number of daily effective contacts with respect to pre-confinement contact rates defined by Prem et al. (2017).
We denote by Cj the number of contacts that occurred location during pre-confinement. While operating under recommendation level 0, an agent visiting location will on average contact C other agents. Post-confinement contact patterns surveyed in Quebec during summer 2020 (Brisson & et al. (020)) are used to scale down the number of pre-confinement interactions across different locations, the percentage reduction per location are denoted ag. Table show the number of contacts and percentage reduction as a result of confinement.
Location
C
ag %
Household
2.7
0.30
Workplace
10
0.80
School
6
0.80
Other
3.1
0.50
Table Daily contacts per location type: This table shows for each location the pre-confinement mean number of daily contacts Cj and the reduction in number of contacts based on data collected the Region of Montréal.
There are 5 recommendation levels described by Table Bable3wiic with their corresponding expected number of contacts. When these recommendations are followed, they modulate the number of effective contacts that agents have while at locations. Recommendation level 3 scales down the contacts at location by ag. Levels and 2 are successively obtained by reducing the location dependent contacts by half from level 3, while level 4 is used to impose full quarantine i.e. contacts. Level 0 is not used except to represent the behavior when an agent does not adhere to the recommendations modeled by daily dropout parameter.
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Recommendation
Level
Description
Effective contacts
Level
Pre-pandemic behaviour
Cj
Level
Intermediate recommendations reducing contacts
1/4 (1 a.) C
Level
Stronger recommendations reducing contacts
1/2 * (1 ay) * Cj
Level
Post-confinement behaviour
(1 01) Ci
Level
Quarantine/seff-isllatte
Table 3: Recommendation level and corresponding effective contacts: Recommendation levels
and corresponding expected number of daily effective contacts for a location type I.
5.6 INFECTIVITY (TRANSMISSION) MODEL
Effective viral load (EVL) varies [O., 1.], and represents the 'severity' of viral load the agent is currently experiencing (which takes into account both the viral load and the interaction of the virus with the host's immune system), as shown in Figure & Each agent's disease progresses according to this curve, and the probability of transmission is also proportional to EVL.
Post
Post plateau 2
Effective Viral Load
Incubation
Onset
Plateau
plateau
Time
Figure 8: Effective Viral Load [Reproduced with permission from Gupta al. (2020)]: Schematic showing the viral load curve, and associated phases of symptoms with severity indicators: infectious- ness onset occurs on average 2.5 days after exposure, viral load peaks 0.7 days before symptom onset, which occurs an average of 5 incubation days after exposure. Symptoms are most severe after viral load peak and symptom onset, when the virus has had time infect many cells. Recovery takes on average 14 days from symptom onset.
5.7 TAILORING THE SIMULATOR REGIONAL DEMOGRAPHICS AND OTHER DISEASES
Many aspects of the simulator are customizable particular region's 's statistics, including individual agent features (pre-existing medical conditions, biological sex, etc.), contact patterns, and prevalence of other diseases (which affect the predictions of COVID-19 by introducing other reasons for agent to experience symptoms. The simulator provides details of to real data for the region of Montreal, producing conditions of flu, allergies, and colds. The process
Canada, with the confounding for tailoring the simulator to other regions is detailed in their work, but briefly, configuration files with the appropriate statistics need be provided in https: /ttpt/gtttttttttt//gg//gtttgot com/ mi la iiiia COVI - Swwenttiini im www.b/aattee/eeeeeoee www.er//rrrceeeeeeeeeeeeeeeeeeee covi d1 95 1 m/ conf gs/
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Reviews:
[{"review_id": "AB9wfl8-4qj", "reviewer": "AnonReviewer3", "summary": "", "questions": "", "limitations": "", "rating": 7, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "Summary: In this paper the authors propose a novel method of contact tracing which they dub Proactive Contact Tracing (PCT). PCT is aimed at detecting an individual's infectivity given locally observed information (and history), as can be carried on say a mobile device. As the name suggests, being able to estimate infectivity given this local information is useful in large part due to the fact that individuals can be asymptomatic, or they can have significant infectivity before demonstrating symptoms if they are to be symptomatic. Proactively estimating infectivity levels thus provides another tool in combatting viral spread through proper containment protocols. \n\nThe core methodology behind PCT lies in training a deep neural network offline with viral simulation data to estimate this very infectivity given local information / history. The purpose of this offline training is to preserve privacy of users, as they would only need to locally run the computation of their infectivity estimates (rather than send information to a centralised server for example for training). Furthermore, these infectivity estimates in practice can be used for containment strategies. The authors propose truncating the infectivity values to 4 bits, and using this information by a centralised agent to recommend different distancing for agents. \n\nFinally, the authors back their results with simulations where they show that under some (unspecified) containment regime, the use of PCT can provide real gains over current contact tracing methods in terms of minimising the spread of the virus while simultaneously minimising the amount of containment required of a population. \n\n\nReasons for score: \n\nI think this work is well motivated and of great potential use to policymakers in what will be a long fight against COVID. In addition, the care given to preserving privacy (in terms of the messages sent from devices to centralised agents) is of utmost importance, and these very constraints are necessary in the solution space the authors are navigating.\n\n\nGeneral questions / Points to address:\n\n-I would like the authors to give more clarity on what the nature of the containment protocol they propose is. They mention that as a function of $y_i$, a centralised agent will propose $\\zeta_i$, a containment measure for an agent, but I am curious what this entails. Is it the case that an agent is isolated for a certain amount of time? Do they reduce their number of contacts by a proportional amount? The reason I ask this is that contact tracing measures are only as useful as the containment protocol that they are paired with.\n-I am also still a bit unclear as to what the infectivity is modelling specifically. The authors mention that $y_i$ is a positive real number, but what does this equate to in the underlying models used to train the DNN? I'm guessing this is an intrinsic parameter to the model generating data, but it would be useful to perhaps get an overview of the model itself if there is space. \n-Have the authors considered how the upcoming flu season might affect PCA, especially if there are common symptoms between diseases? In other developing countries, such as central Mexico, Dengue season is also just beginning, and the co-infection of diseases is an issue that local authorities are grappling with for their contact tracing applications\n-I also wonder if the authors have considered using the heterogeneity of the population to their advantage in terms of the underlying proposed containment protocol. Ultimately PCT is studying an individuals exposure data (albeit locally), and this very data can help understand the effictiveness of a proposed containment policy given their infectivity (such as an individuals propensity to listen to proposed containment, or whether this individual has a high baseline exposure to other individuals, and hence a possibility of spreading to many if they are infected). Recent work has focused on using heterogeneous population information to optimise pandemic policy (https://bfi.uchicago.edu/working-paper/socioeconomic-network-heterogeneity-and-pandemic-policy-response/), which could be of interest to the authors.\n", "extra_scores": {}, "extra_text": {}}, {"review_id": "8Dat44nN3TQ", "reviewer": "AnonReviewer2", "summary": "", "questions": "", "limitations": "", "rating": 9, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "This paper introduces a deep learning based digital contact tracing method to minimize the spread of COVID19. The proposed method is based on locally processed information collected on the mobile app. Unlike the most commonly used digital tracing approach that sends quarantine recommendations to all recent contacts of a newly diagnosed person, the developed method in this paper considers all the information related to the users and the ones who have been in contacts with them in order to make user specific recommendations. This is not an easy problem because of different conflicting factors involving in making recommendation decisions, i.e. user privacy, mobility restrictions, and public health. The proposed method, called proactive content tracing, is a set-based architecture (that uses attention) and perform distributed inference to preserve privacy.\n\nThe authors utilized a simulator called COVIsim (not sure whether it is COVAsim or COVIsim) to train the proposed deep learning model and showed that their proposed method outperforms two baselines on multiple different metrics. The use of simulated data is well-justified given how difficult it is to obtain relevant COVID19 tracing data. This paper advances the current digital contact tracing significantly and is a great contribution to the field. ", "extra_scores": {}, "extra_text": {}}, {"review_id": "6N1QD9BFP5P", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 7, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "In the manuscript entitled \"Predicting infectiousness from proactive contact tracing\" the authors present a sophisticated algorithmic approach to control of app-based quarantine advisories with regard to covid-19.  The methodology described covers multiple aspects of this practical problem: privacy preservation for the mobile phone data, trade-offs between reducing transmission & limiting constraints on personal freedom, synthesis of multiple data sources (e.g. test results, self-reported symptoms etc).  As an experienced epidemiological modeller I can say that the description of each component of this manuscript read as sensible to me and that no 'red flags' were raised.  However, I cannot comment on the details of the privacy preservation methods and I was left unsure of the necessity of a deep learning model for this problem over a simpler (and hence more readily interpretable for public health policy makers) parametric statistical approach.", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: The reviewers unanimously agree that the paper is timely, well motivated and correct, with potential to significantly impact digital contact tracing. 
Decision: Accept (Spotlight)