Predicting Infectiousness for Proactive Contact Tracing

1 INTRODUCTION . Until pharmaceutical interventions such as a vaccine become available , control of the COVID-19 pandemic relies on nonpharmaceutical 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 ) , a technique to track the spread of the virus among individuals in a 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 to all recent contacts of a person after a positive test result . While BCT is simple 1All bolded terms are defined in the Glossary ; Appendix 1 . * , † , ‡ Equal contributions , alphabetically sorted ; aMila , Québec ; bUniversity of Oxford ; cMax-Planck Institute for Intelligent Systems Tübingen ; dUniversity of Ottawa ; e McGill University ; fUniversité de Montreal ; gÉcole Polytechnique de Montreal ; hThe Alan Turing Institute ; iHEC Montréal and fast to deploy , and most importantly can help curb spread of the disease ( Abueg et 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 number of reasons : ( i ) Tests have high false negative rates ( Li et al. , 2020 ) ; ( ii ) Tests are administered late , only after symptoms appear , leaving the asymptomatic population , estimated 20 % -30 % of cases ( Gandhi et al. , 2020 ) , likely untested ; ( iii ) It is estimated that infectiousness is highest before symptoms appear , well before someone would get a test ( Heneghan et al. , 2020 ) , 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 . ( 2020 ) propose a rule-based system leveraging other input clues potentially available on a smartphone ( e.g . symptoms , pre-existing medical conditions ) , an approach they call feature-based contact tracing ( FCT ) . Probabilistic ( nonbinary ) 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 a 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 to 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 ) . 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. , 2017 ) 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 our 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 an ML infectiousness predictor on the domain-randomized output of an agent-based epidemiological model , in several loops of retraining to mitigate issues with ( i ) non-stationarity 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 to binary contact tracing and rule-based methods ( see Sec . 4 ) 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 a smartphone ( including information about symptoms , preexisting conditions , age and lifestyle habits if willingly reported ) to compute proactive estimates of an individual ’ s expected infectiousness . These estimates are used to ( 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 . 1 ) . 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 are incompatible with privacy constraints in many societies . Further , the estimator runs locally on the individual ’ s device , such that any sensitive information volunteered does not need to leave the device . In Section 2.1 , 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 in Section 4 to outperform DCT baselines by a large margin . 2.1 PROBLEM SETUP . We wish to estimate infectiousness yd ′ i of an agent i on day d ′ , given access to locally observable information Odi now on day d ≥ d′ and over the past dmax days ( d′ ≥ d − dmax ) 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 hdi of reported symptoms and known test results . Finally , O d i also includes information about encounters in the last dmax days , grouped in edi for day d. Thus : Odi = ( gi , h d i , e d i , h d−1 i , e d−1 i , . . . h d−dmax i , e d−dmax i ) ( 1 ) The information ed ′ i 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 to estimate their past infectiousness a posteriori . Our goal is thus to model the history of the agent ’ s infectiousness ( in the last dmax days ) , which is what enables the recommendations of PCT to be proactive and makes it possible for an infected asymptomatic person to 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 Pθ ( y d i |O d i ) , where y d i = ( y d i , y d−1 i , . . . , y d−dmax i ) is the vector of present and past infectiousness of agent i and θ specifies the parameters of the predictive model . In our experiments we only estimate conditional expectations with a predictor fθ , with ŷdi = ( ŷ d i , ... , ŷ d−dmax i ) = fθ ( O d i ) an estimate of the conditional expected per-day present and past infectiousness EPθ [ ydi |O d i ] . The predicted expected values are used in two ways . First , they are used to generate messages transmitted on day d to contacts involved in encounters on day d′ ∈ ( d− dmax , d ) . These messages contain the estimates ŷd ′ 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 ŷdi is also used to form a discrete recommendation level ζdi ∈ { 0 , 1 , ... , n } regarding the behavior of agent i at day d via a recommendation mapping ψ , i.e . ζdi = ψ ( ŷ d i ) . 2 At ζdi = 0 agent i is not subjected to any restrictions , ζdi = 1 is baseline restrictions of a post-lockdown scenario ( as in summer 2020 in many countries ) , ζdi = n is full quarantine ( also the behaviour recommended for contacts of positively diagnosed agents under BCT ) , and intermediate levels interpolate between levels 1 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 , or as number of cases,3 and minimizing the degree of restriction on agents , e.g. , measured by the average number of contacts between agents . Managing this tradeoff is a 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 Odi of agent i depend on the predicted infectiousness histories and the pattern of contacts generated by the behavior ζj 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 .

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.