Page 117 - 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

expectation, the second person would have been in close • During any particular day, any two people in the
contact with more than one infected people. Thus, tak- city meet each other with a probability of 0.01.
ing the number of contacts with all people into con- Thus, on average, a person meets around 10 people
sideration could significantly improve the tracing. The per day in expectation. When two people meet, and
simulation in this section also confirms our claim. one of them is infected while the other is not, the
These two policies can be mathematically described as virus will spread with a probability of 3/(14 × 10);
follows. hence an infected person spreads the virus to an
average of = 3 people before being removed.
• Policy 1: Fix a time frame of a duration say 2 weeks,
and call the time duration composed of the previous • Each day the community chooses 20 people to quar-
two weeks as the “tracing window”. At any given antine by using its policy. If quarantined persons
time we only take into account those contacts that are found to be infected, then they will be isolated
occurred during the tracing window. Let be the until they are removed. Otherwise, they will be

probability that the virus spreads from an infected quarantined for 14 days, and then will be back to
person to a healthy person during a contact. We the normal schedule.
assume that is constant and known. For any per- • We assume that the community as a whole knows

son , given that person contacted confirmed all the contacts between all of its people, and when-
infected persons during the tracing window, we use
ever a person is removed the community gets to
ℙ ({ got infected}) = 1 − (1 − ) (17) know this information at the beginning of the next
day. Also, we assume that the spreading probabil-

to measure the risk that person is infected. We ity is known to the community. We note that,

then choose to test those persons who have the with the knowledge of and assuming the value of

highest probabilities of being infected. , the community is able to compute Eq. (17) and

Eq. (18).
• Policy 2: It additionally utilizes the contact graph,
and checks the number of contacts of each person We perform simulations for 150 consecutive days, and
∈ . Hence, if is the number of contacts of in record the cumulative infections in the population for
the tracing window, we let the following 5 policies and parameters:
• No contact tracing of any sort is utilized.

ℙ({ got infected}) = 1 − (1 − ) (1 − )

(18) • Policy 1 (Eq. (17)).
in order to measure the risk that person is in- • Policy 2 with = 0.02, where 0.02 is a well tuned

fected. Over here, is the so-called base infection value.

probability, which can either be a constant or de-
pend on the proportion of confirmed cases of the • Policy 2 with = 0.2, where 0.2 is an example of

population (i.e., adaptive). Note that we are as- a not well tuned value of .

suming that the infection status of these people • Policy 2 with adaptive = /1000, where “rr”
rr

are unknown. denotes “recently removed” and rr means the
Our simulations results are depicted in Fig. 2, and number of people removed in the tracing window
(i.e., the last two weeks).
clearly show the superior performance of Policy 2 as
compared to that of Policy 1. More details on the sim- Our simulation results are summarized in Fig. 2. We
ulation setup are as follows: explicitly state the number of total infections in Table 1.
• The population size is 1000 people, and a single tracing policy parameter total infections
person (that is chosen uniformly at random from no tracing — 987
the population) is infected by the virus at day zero. Policy 1 — 617
Policy 2 0.02 540
• Regarding the transmission capability of the virus, Policy 2 0.2 669
we assume that a person will be able to spread the Policy 2 adaptive 569
virus 1 day after getting infected. Moreover, a per-
son remains infected for at least 7 days. After this Table 1 – Total number of infections of the virus under different
duration, on each day the person will change his tracing policies.
state (to either isolated due to its symptoms, recov- We summarize our findings as follows.
ered, or deceased) with a probability of 1/7. Thus,
in expectation, the virus lasts for 14 days. A per- • Contact tracing and quarantine facilities are essen-
son whose state has changed to removed, will not tial in order to control the spread of virus. Without
spread the virus or get infected. these, the total number of infections are around 987,

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