=Paper=
{{Paper
|id=Vol-3823/7_Marbukh_position_8
|storemode=property
|title=Towards Recommender System Supported Contact Tracing for Cost-Efficient and Risk Aware Infection Suppression
|pdfUrl=https://ceur-ws.org/Vol-3823/7_Marbukh_position_8.pdf
|volume=Vol-3823
|authors= Vladimir Marbukh
|dblpUrl=https://dblp.org/rec/conf/healthrecsys/Marbukh24
}}
==Towards Recommender System Supported Contact Tracing for Cost-Efficient and Risk Aware Infection Suppression==
https://ceur-ws.org/Vol-3823/7_Marbukh_position_8.pdf
Towards Recommender System Supported Contact Tracing
for Cost-Efficient and Risk Aware Infection Suppression⋆
Vladimir Marbukh1,∗
1
National Institute of Standards & Technology, Information Technology Laboratory, 100 Bureau Dr., Gaithersburg, Maryland, USA
Abstract
In public health, contact tracing is the process of identifying people who may have been exposed to an infected
person. Contact tracing performance criteria, which include infection suppression, protection of high-risk indi-
viduals, and cost-efficiency, are not necessarily aligned with each other. Pareto optimization of the corresponding
inherent trade-offs, especially at the early stages of infection, is typically unrealistic due to insufficient information
on infection propagation, risk factors, prevention and treatment options, etc. We suggest that contact tracing
performance can be significantly improved with the support of a specialized Recommender System (RS). Based
on the combination of up-to-date contact tracing and medical data, RS can identify and test through Exposure
Notification System (ENS) not only high-risk individuals but also potential superspreaders to suppress infection
propagation. Due to incomplete information, the dynamic nature of the problem, and a large state and action
spaces, the RS should be supported by Deep Reinforcement Learning (DRL) for solving the corresponding Partially
Observable Markov Decision Process (POMDP).
Keywords
contact tracing, exposure notifications, recommender system, deep reinforcement learning, partially observable
Markov decision process
1. Introduction & Motivation
In public health, contact tracing is the process of identifying people who may have been exposed to an
infected person, subsequent testing them for infection, and isolating or treating the infected [1]. Contact
tracing performance criteria include infection suppression, protection of high-risk individuals, and
cost-efficiency. These criteria are not necessarily aligned with each other, e.g., given testing capacity,
infection suppression requires high priority testing for the potential super spreaders, while protection of
high-risk individuals requires testing them with higher priority. Given the testing priorities, the existing
Google/Apple Exposure Notification (GAEN) technology [2] can support an Exposure Notification
System (ENS) by allowing public health authorities to quickly notify people for subsequent testing.
GAEN is a framework and protocol specification developed by Apple Inc. and Google to facilitate digital
contact tracing during the COVID-19 pandemic to augment more traditional contact tracing techniques
using Android or iOS smartphones.
Extensive research on COVID-19 has revealed that while risk-aware, multi-criteria optimization of
contact tracing has significant potential, realization of this potential requires deep knowledge of the
infection propagation mechanisms, medical prognoses and treatment options for infected individuals
with different risk profiles [3]. Even though COVID-19 originated almost five years ago, such knowledge
is still lacking [4, 5], which suggests that a contact tracing system should have the ability to collect
and make sense of all up-to-date available information on infection. This can be achieved with the
HealthRecSys’24: The 6th Workshop on Health Recommender Systems co-located with ACM RecSys 2024
⋆
Official contribution of the National Institute of Standards and Technology; not subject to copyright in the United States.
Certain equipment, instruments, software, or materials are identified in this paper in order to specify the experimental
procedure adequately. Such identification is not intended to imply recommendation or endorsement of any product or
service by NIST, nor is it intended to imply that the materials or equipment identified are necessarily the best available for
the purpose.
Envelope-Open marbukh@nist.gov (V. Marbukh)
© 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
Figure 1: Recommender System supported Contact Tracing.
support of a specialized Recommender System (RS). Given testing capacity, the RS should utilize the up-
to-date contact tracing, medical, and all other available relevant data to identify and through Exposure
Notification System (ENS) notify individuals to be tested [2, 6]. Due to incomplete information, the
dynamic nature of the problem, and a large state and action space the RS should be supported by Deep
Reinforcement Learning (DRL) for solving the corresponding Partially Observable Markov Decision
Process (POMDP) [7, 8]. POMDP describes the evolution of health status of each participating individual,
where infectious status may not be observable and testing decisions are constrained by available testing
capacity. Since a positive test result for some individual may reveal increased accumulated exposure for
other individuals due to proximity to the newly discovered infection spreaders, the problem cannot be
decoupled. These interdependencies significantly complicate the problem. The paper is organized as
follows. Section 2 outlines operations and flow of information in the proposed RS supported contact
tracing, and section 3 provides some technical details on accumulated exposure evaluation.
2. RS Supported Contact Tracing
Figure 2 presents a highly aggregated view of a Recommender System supported Contact Tracing
System.
The Exposure Monitoring System (EMS) monitors “accumulated exposure to infection” for each
[0,𝑡]
participating individual 𝑖, ℰ𝑖 (defined in the next section) in near real time 𝑡, and feeds this informa-
tion into the RS. RS also gets available information on demographic and risk factors of participating
(1)
individuals 𝑥𝑖 as well as health status of both participating and not participating individuals who
(2)
went through Health Care System 𝑥𝑖 . Note that participating individuals are likely to consent to
revealing their health information since they would benefit from accounting for their risk factors, e.g.,
advanced age, preexisting conditions, etc. For not participating individuals, some relevant information,
which does not require revealing individual identity, can be obtained without violating their privacy.
RS is also fed the estimate of the infection reproduction number 𝑅(𝑡), i.e., the average number of new
infections produced by one infected individual during his/her lifetime: 𝑅(𝑡) ̃ ≈ 𝑅(𝑡). Estimate 𝑅(𝑡) ̃ may
combine information from EMS, the Health Care System, and possibly from other tracing mechanisms
not shown in Figure 1, e.g., from manual tracing. Infection suppression requires keeping the infection
reproduction number less than one: 𝑅(𝑡) < 1. Due to numerous uncertainties in the 𝑅(𝑡) estimation:
̃ ≈ 𝑅(𝑡), the infection suppression condition is 𝑅(𝑡)
𝑅(𝑡) ̃ ≤ 1 − 𝜀, where “safety margin” 𝜀 < 1 depends on
the confidence level of the corresponding estimate. The reward of the RS supported Contact Tracing
is quantified be the negative loss −𝐿(𝑡), where 𝐿(𝑡) = 𝐿𝑒𝑐 (𝑡) + 𝐿𝑠𝑐 (𝑡). Here economic loss due to lost
productivity and cost of testing/treatment is 𝐿𝑒𝑐 (𝑡), and “social cost” quantifying suffering and, most
importantly, deaths due to the infection 𝐿𝑠𝑐 (𝑡). The cost estimates are provided to RS by the Health Care
System and Agencies collecting and processing economic data.
System evolution is described by POMDP 𝛿(𝑡) = (𝛿𝑖 (𝑡)), where component 𝛿𝑖 (𝑡) describes the health
status of participating individual 𝑖 , i.e., “non-infected,” “infected,” “deceased.” “Non-infected” and
“infected” states may not be observable which makes process 𝛿(𝑡) partially observable. The decision
to test a participating individual reveals his/her infected or not-infected status at a certain cost due
[0,𝑡] (1) (2)
to limited testing capacity. RL employs DRL to make testing decisions on the basis of ℰ𝑖 , 𝑥𝑖 , 𝑥𝑖 .
Constraints on the infection reproduction number can be incorporated through penalty function ℎ(𝑅(𝑡)) ̃
̃ ̃
which is flat for 𝑅(𝑡) ≤ 1 − 𝜀 and sharply increases for 𝑅(𝑡) > 1 − 𝜀.
Our conjecture is that (near) optimal notification strategy is threshold-based: individual 𝑖 should be
notified at the first moment 𝑡 = 𝜃𝑖 > 0 when this individual’s accumulated exposure reaches threshold
ℰ𝑖̂ :
[0,𝑡]
𝜃𝑖 = inf{𝑡 ∶ ℰ𝑖 ≥ ℰ𝑖̂ }, (1)
𝑡≥0
where threshold ℰ𝑖̂ = Δ(ℰ , 𝑥) depends on the history of former testing decisions/results combined
with medical and demographic data of these individuals. The function Δ(ℰ , 𝑥) can be evaluated by
employing a Deep Supervised Learning (DSL) algorithm. Note that in practice, notification strategy may
operate on the basis of a small number of risk groups [3], which may be defined and then redefined by
an on-line clustering algorithm. Assumptions of homogeneity and large number of individuals within
each group, simplifies optimization of group-specific thresholds in (1).
3. Accumulated Exposure
For each participating individual 𝑖, the contact tracing system identifies “accumulated exposure” to
another participating individual 𝑗 during time interval [0, 𝑡] as follows:
𝑇
[0,𝑡] ̃ 𝑖𝑗 (𝜏 ))𝛼 ] 𝑑𝜏 ,
ℰ𝑖𝑗 = ∫ 𝜙 [(𝑑/𝑑 (2)
0
where the corresponding instantaneous exposure rate 𝜙(𝑧) is an increasing function of 𝑧 > 0, the
distance between individuals 𝑖 and 𝑗 at moment 𝜏 is 𝑑𝑖𝑗 (𝜏 ), and 𝑑̃ > 0, 𝛼 ≥ 1 are some parameters.
Individual 𝑖 accumulated exposure to infection during time interval [0, 𝑡] is defined as the aggregated
exposure to all known spreaders during this time interval:
𝑇
[0,𝑡] ̃ 𝑖𝑗 (𝜏 ))𝛼 ] 𝑑𝜏 ,
ℰ𝑖 = ∑ ∫ 𝜋𝑗 (𝜏 )𝜙 [(𝑑/𝑑 (3)
𝑗 0
where 𝜋𝑗 (𝜏 ) = 1 if individual 𝑗 is infected at moment 𝜏 and 𝜋𝑗 (𝜏 ) = 0 otherwise.
Consider some examples. As currently defined by the CDC [1], a high-risk COVID-19 exposure is a
contact with a person who tests/tested positive for SARS-CoV-2 which takes place at a distance of less
than two meters for a total of 15 minutes or more over a 24-hour period. In this case, 𝑑̃ = 2 m, 𝛼 → ∞,
24
𝜙(𝑥) ≡ min(𝑥, 1), and thus an individual is assumed exposed if ℰ [0,𝑇 ] = ∫0 𝟙(𝑑(𝑡) − 2 m)𝑑𝑡 > 15 min,
where 𝟙(𝑥) = 0 if 𝑥 ≤ 0 and 𝟙(𝑥) = 1 otherwise. In another example [9], 𝑑̃ = 2 m, 𝜙(𝑥) ≡ 𝑥, and thus an
24
individual is assumed exposed if ℰ [0,𝑇 ] = ∫0 (2/𝑑(𝑡))𝛼 𝑑𝑡 > 15 min.
Finally note that available information on accumulated exposure to specific individuals can be used to
identify “infection superspreaders” who otherwise could be unidentified, e.g., due to being asymptomatic
or for any other reason. This can be done with known algorithms [10] on undirected exposure graph 𝐺
where nodes 𝑖 and 𝑗 are connected if ℰ𝑖𝑗[0,𝑡] ≥ ℰ ̆[0,𝑡] , and ℰ ̆[0,𝑡] > 0 is a properly defined threshold.
References
[1] CDC, Contact tracing, 2024. URL: https://www.cdc.gov/museum/pdf/
cdcm-pha-stem-lesson-contact-tracing-lesson.pdf.
[2] C. Nebeker, D. Kareem, A. Yong, R. Kunowski, M. Malekinejad, E. Aronoff-Spencer, Digital
exposure notification tools: A global landscape analysis, PLOS Digital Health 2 (2023) 1–16.
doi:10.1371/journal.pdig.0000287 .
[3] D. Acemoglu, V. Chernozhukov, I. Werning, M. D. Whinston, Optimal Targeted Lockdowns in
a Multigroup SIR Model, American Economic Review: Insights 3 (2021) 487–502. doi:10.1257/
aeri.20200590 .
[4] C. F. Manski, F. Molinari, Estimating the COVID-19 infection rate: Anatomy of an inference
problem, Journal of Econometrics 220 (2021) 181–192. doi:10.1016/j.jeconom.2020.04.041 .
[5] W. Rauch, H. Schenk, N. Rauch, M. Harders, H. Oberacher, H. Insam, R. Markt, N. Kreuzinger,
Estimating actual SARS-CoV-2 infections from secondary data, Scientific Reports 14 (2024) 6732.
doi:10.1038/s41598- 024- 57238- 0 .
[6] X. Chen, L. Yao, J. McAuley, G. Zhou, X. Wang, Deep reinforcement learning in recommender
systems: A survey and new perspectives, Knowledge-Based Systems 264 (2023) 110335. doi:10.
1016/j.knosys.2023.110335 .
[7] X. Xiang, S. Foo, Recent advances in deep reinforcement learning applications for solving partially
observable markov decision processes (POMDP) problems: Part 1—fundamentals and applications
in games, robotics and natural language processing, Machine Learning and Knowledge Extraction
3 (2021) 554–581. doi:10.3390/make3030029 .
[8] X. Xiang, S. Foo, H. Zang, Recent advances in deep reinforcement learning applications for
solving partially observable markov decision processes (POMDP) problems part 2—applications in
transportation, industries, communications and networking and more topics, Machine Learning
and Knowledge Extraction 3 (2021) 863–878. doi:10.3390/make3040043 .
[9] K. Sayrafian, B. Cloteaux, V. Marbukh, Impact of using soft exposure thresholds in automatic
contact tracing, in: 2022 IEEE International Conference on E-health Networking, Application &
Services (HealthCom), 2022, pp. 1–6. doi:10.1109/HealthCom54947.2022.9982790 .
[10] D. Zhang, Y. Wang, Z. Zhang, Identifying and quantifying potential super-spreaders in social
networks, Scientific Reports 9 (2019) 14811. doi:10.1038/s41598- 019- 51153- 5 .