Page 113 - ITU Journal, Future and evolving technologies - Volume 1 (2020), Issue 1, Inaugural issue

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.

© International Telecommunication Union, 2020 93