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 individuals, and cost-eficiency, are not necessarily aligned with each other. Pareto optimization of the corresponding inherent trade-ofs, especially at the early stages of infection, is typically unrealistic due to insuficient 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).
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 [
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 diferent risk profiles [
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The Exposure Monitoring System (EMS) monitors “accumulated exposure to infection” for each participating individual , ℰ [0,] (defined in the next section) in near real time , and feeds this informa tion into the RS. RS also gets available information on demographic and risk factors of participating (1) as well as health status of both participating and not participating individuals who (2) . 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 () , i.e., the average number of new infections produced by one infected individual during his/her lifetime: ( )̃ ≈ () . Estimate ( )̃ 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: () < 1 . Due to numerous uncertainties in the () estimation: ( )̃ ≈ ()
, the infection suppression condition is ( )̃ ≤ 1 − , where “safety margin” < 1 depends on the confidence level of the corresponding estimate. The reward of the RS supported Contact Tracing ℰ̂ : is quantified be the negative loss
−() , where () = () + () . Here economic loss due to lost productivity and cost of testing/treatment is () , and “social cost” quantifying sufering and, most importantly, deaths due to the infection () . 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 () = ( ()) , where component () describes the health status of participating individual , i.e., “non-infected,” “infected,” “deceased.” “Non-infected” and “infected” states may not be observable which makes process () partially observable. The decision to test a participating individual reveals his/her infected or not-infected status at a certain cost due to limited testing capacity. RL employs DRL to make testing decisions on the basis of ℰ [0,] Constraints on the infection reproduction number can be incorporated through penalty function ℎ(( )̃) , (2).
(1) , which is flat for ( )̃ ≤ 1 −
and sharply increases for ( )̃ > 1 − .
Our conjecture is that (near) optimal notification strategy is threshold-based: individual should be notified at the first moment
= > 0 when this individual’s accumulated exposure reaches threshold
where threshold ℰ̂ = Δ(ℰ , ) depends on the history of former testing decisions/results combined
with medical and demographic data of these individuals. The function Δ(ℰ , ) 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 [
For each participating individual , the contact tracing system identifies “accumulated exposure” to another participating individual during time interval [0, ] as follows: where the corresponding instantaneous exposure rate () is an increasing function of > 0 , the distance between individuals and at moment is ( ) , and ̃ > 0 , ≥ 1 are some parameters. Individual accumulated exposure to infection during time interval [0, ] is defined as the aggregated exposure to all known spreaders during this time interval: (1) (2) (3)
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 [
≥0 = inf{ ∶ ℰ [0,] ≥ ℰ̂ }, 0 0 ℰ [0,] = ∫ [(/̃
( )) ] , ℰ [0,] = ∑ ∫ ( ) [(/̃ ( )) ] , where () = 0 if ≤ 0 and () = 1
24 individual is assumed exposed if ℰ [0, ] = ∫0 (2/()) > 15 min. where ( ) = 1 if individual is infected at moment and ( ) = 0 otherwise.
Consider some examples. As currently defined by the CDC [