Page 114 - ITU Journal, Future and evolving technologies - Volume 1 (2020), Issue 1, Inaugural issue
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ITU Journal on Future and Evolving Technologies, Volume 1 (2020), Issue 1




             The first step is to infer the type or level of con-  the pandemic. Note that this objective is quite differ-
             tacts between two individuals. Have they stayed   ent from focusing on testing individuals with the highest
             closer than 6 feet or stayed in the same room for a  probability of infection, which is what current systems
             while? The second step is to deduce the link proba-  try to do. Rather our focus must be on testing individu-
             bility. Accurate characterizations of the link prob-  als that have the highest expected impact on viral spread.
             abilities could come from exposure data studies to  Consider the following example as an illustration.
             the virus. However, a reasonable model would be   Example: Assume that two individuals    and    are in-
             to use a concave function of time to estimate the  fected with probabilities 0.1 and 0.3, respectively. How-
             link probability.                                 ever, assume that the expected number of individuals
                                                               that    encounters is 50 times larger than the expected
           • Testing results. For an individual, if this individ-  number of individuals that    comes in contact with. In
             ual has taken a virus test and got the result, then  this case, it makes more sense to prioritize testing indi-
             we know whether this individual has the disease or  vidual    over individual   . This is another reason why
             not (with a certain confidence).                  we should test healthcare workers more often, because
                                                               of their frequent contact with a large number of individ-
          3.3 Data Integration                                 uals. Based on this key insight, our goal will be to:
          In real-world scenarios, there are multiple data sources.
          For example, different contact tracking data sources as  • Develop learning based approaches that result in
          described earlier (Bluetooth or ultrasound contact trac-  smart testing capabilities which balance the ex-
          ing data, WiFi logs, GPS, etc.) could be integrated to   ploration and exploitation subject to testing con-
          greatly improve the quality of contact tracing. The in-  straints. Isolate individuals who have been tested
          tegration could be done by using filtering techniques,   positive and quarantine their contacts.
          in which we compute the probability of an edge condi-
          tioned on the (multi-source) information available to us.  • Our model will also incorporate practical issues
          We would typically rely upon generative models of the    such as inaccurate estimates, testing errors, pool
          data in order to compute these conditional probabilities.  testing, etc.
          With multiple data sources, we need to deal with incon-
          sistent data. For instance, Bluetooth gives relative loca-  • Develop efficient rules of thumb that can be eas-
          tion information whereas WiFi gives absolute location    ily implemented in practice. This could mean test-
          information, and the information of two sources may      ing asymptomatic individuals who have not encoun-
          be inconsistent. We can deal with this issue by assum-   tered a confirmed infected person, but have made
          ing that the data collections of the sources are random  a large number of contacts.
          and independent and assign probability distributions to
          them. Probabilistic description allows “soft recovery”  4.1 Suspicious Infection Inference
          of data after we use filtering algorithms. Bayesian up-
          dates can be used to merge or pool information from  One significant task is to find the most likely infected
          various source. We can use Kalman filtering or some  individuals from the partial observations, i.e., the test
          other filtering algorithm.                           results of some individuals. To do this, one way is to
          Such an integration can yield us the following kind of  interpret the probability that a person is infected given
          improvements:                                        the partial observations, such as (“noisy”) contact graph
                                                               or test results of a few individuals from the graph etc.
           • Reduced inaccuracies and better estimates of the  These algorithms could be based upon the susceptibil-
             link probabilities. Consider for example the case  ity graph constructed by using the methods stated in
             when people could have social contact by virtue of  Section 3.
             being located in a crowded facility such as students
             in the same classroom or people in the same flight.  4.1.1 Partial Observed Markov Decision Pro-
             However, data sources such as building information,       cess (POMDP)
             WIFI access might be noisy. In this case, one could
             combine GPS data (collected from probably smart-  We formulate the problem of sequential testing for
             phone usage) in order to yield an accurate estimate  COVID-19 as a Markov Decision Process (MDP). Pop-
             of social contacts.                               ulation is composed of    individuals, and the state
                                                               evolves at discrete times    ∈ [1,   ]. Let    (  ) ∈ {0, 1}
                                                                                                       
          4.  TESTING        UNDER         RESOURCE            denote the hidden state of individual    at   , where
              CONSTRAINTS                                         (  ) = 0 means that    is free of disease at    and
                                                                   
                                                                  (  ) = 1 indicates that    is infected. We use the vector
                                                                   
          The goal here is to leverage the information contained in    (  ) ∶= (   (  ),    (  ), … ,    (  )) ∈ {0, 1}     to represent
                                                                               2
                                                                                         
                                                                         1
          the susceptibility graph in order to sequentially choose  the state of the entire system. Let    ∶= {0, 1}     de-
          individuals for testing so as to minimize the spread of  note the state-space of the network. Note that the state


          94                                 © International Telecommunication Union, 2020
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