Page 114 - 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

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