Page 113 - 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




           • Node infection state. For each individual    and      needs to be investigated. If time is discretized, then
             time   , we use    (  ) to denote its infection state,  the duration of a discrete time-slot could be any-
                               
             where    (  ) = −1 means that this individual does    where from several minutes to one day. Using time
                       
             not have the disease,    (  ) = 0 denotes that it has  slots can help reduce the storage and computation
                                    
             the virus but cannot spread the virus, and    (  ) =  resources required.
                                                       
             1 denotes that it has the virus and is able to spread
             the virus. For individual    and time   , we use    (  )  3.2 Graph Construction
                                                         
             to denote its test results at time   .    (  ) = 0 means
                                               
             individual    does not take a test at time   ,    (  ) =  As discussed earlier, the graph    consists of a set of
                                                       
             −1 means it is tested as negative at time   , and  nodes and a set of edges, where each node holds a base
                (  ) = 1 means it is tested as positive at time   .  infection probability and each edge holds a spreading
                                                               probability. The nodes, edges, and the probabilities all
                 
           • Edges. For every two nodes    and   , If persons  need to be deduced from the data, and the data can be
               ,    have direct contact, then there is an undirected  multi-sourced, for example wifi access logs of all users,
             edge (  ,   ) between them. We are free to choose the  CCTV cameras, or Bluetooth scanning based contact
             way in which we define “contact”: for example if  tracing. More details on how to construct such a graph
             these people are staying less than 6 feet apart for  are as follows:
             at least a certain duration of time co-occurrence in  • Individual identification. Identifying the indi-
             a narrow space (e.g., a room and a bus), or par-      viduals and avoiding duplication are necessary for
             ticipating in the same event. The contact informa-    the success of graph construction. How to do these
             tion can be deduced by the techniques introduced      may depend on the data collection methods. For
             in Section 2. We use ℰ to denote the set of undi-     instance, in the university WiFi logging system, an
             rected edges and that (  ,   ) is in ℰ means there is a  individual has and only has one access ID, and thus,
             contact between    and   .                            this ID can be used to identify an individual. How-
           • Base infection probabilities.  Given the fact         ever, in general WiFi systems, an individual may
             that we cannot test every individual, each untested   have multiple devices, and removing the duplication
             individual has a base probability of being infected.  is significant in this case. One method is restricting
             This probability can be helpful for some tasks like   the tracking to one type of device such as mobile
             finding a suspected infected individual.  For in-     phones. When using the Bluetooth contact tracing,
             stance, a person who contacted 500 people yester-     we can use the IDs of the mobile phones to iden-
             day could be more likely to be infected than some-    tify the individuals, which is also applicable when
             one who was in contact with a confirmed positive      using Bluetooth contact tracing and WiFi logging
             person; and we can use the base infection proba-      simultaneously.
             bilities to deduce this probability. The simulations  • Edge detection. If there is a possible contact
             in Section 5 also indicate that take the base infec-  between two individuals, then an edge should be
             tion probabilities into account can find and isolate  generated to connect these two individuals. The
             more infected people. The base infection probabil-    contact can have multiple types. For instance, the
             ity could be time-varying (e.g. abrupt changes due    contact can be staying less than 6 feet, co-occurring
             to certain events), and we use    (  ) to denote the  in the same room at some time period, or connected
                                            
             base infection probability at time   .                to the same access point during some time period.
           • Spreading probabilities. In case two individu-        This information can be deduced from the collected
                                                                   data.
             als   ,    have been in contact, and one of them, say
             user   , was a positive case, then there is a chance  • Base infection probabilities. The base infec-
             that individual    got infected by the contact. This  tion probability can be deduced from the positive
             chance may also be time-variant. We let the spread-   rate per test or the number of confirmed posi-
             ing probability be denoted as      →  ,   (  ), which is the  tive cases per randomly tested individuals. For in-
             probability that    got infection from a contact with  stance, a university randomly tested 1,000 students
               . The calculation of the probability will be dis-   and found 20 positive cases, then we can assume
             cussed later.                                         that each student of the university has 2% proba-
                                                                   bility to be positive. If we do not have this infor-
           • Time. The time can either be continuous or dis-       mation, we can use the number of newly detected
             crete. Continuous time better fits the reality, but   infections in a period with a multiplier as the esti-
             such an assumption also needs more storage and        mate.
             computation power to process the graph. Besides,
             given the fact that there are delays, or the occur-  • Spreading probabilities (link probabilities).
             rence time of events or contacts are not known pre-   Deducing the spreading probabilities is a relatively
             cisely, how to construct an accurate timely graph     harder task, which can be divided into two steps.





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