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Global Health Econ Sustain Implication of close contact

It is possible that new viruses with enhanced versions of model. Another difference is that we considered a closed
these characteristics may emerge in the future. Therefore, it total population without accounting for birth, death
is of great importance to develop new measures to contain processes, or migration, meaning that no new susceptible
an outbreak or at least to mitigate its impact. While general individuals were born, died, or changed the population
quarantine measures and social distancing have proven due to migration. This decision was motivated by the fact
effective in curbing the spread of epidemics, they are also that the analyzed regions exhibited minimal population
extremely costly. Testing of close contacts has been another change over the studied time period. In addition, as
measure employed during the COVID-19 pandemic, previously discussed, births and deaths are unlikely to
yielding varying results. This raises the question of whether be significant factors contributing to the stability of daily
it is feasible to stop a pandemic if governments allocate all COVID-19 cases. In all observed situations, the number
their efforts to implementing this control mechanism. of daily births is lower than the number of new COVID-
19 cases per day. Therefore, including birth and death
With this in mind, we have developed a CM that processes would introduce unnecessary parameters that
introduces a simple approach for tracing close contacts could hinder our understanding of the mechanisms
of symptomatic individuals who tested positive and were involved in the evolution of the epidemic.
placed in quarantine. Consequently, many other infective
individuals, both symptomatic and asymptomatic, can be As is typical for CM, we set a population S of susceptible
identified and quarantined promptly. As a result, there individuals who can contract the disease through contact
may be an increase in the number of individuals entering with asymptomatic individuals capable of transmitting the
quarantine, creating the false impression that the measure disease (A) or infectious individuals exhibiting symptoms
implemented leads to an increment in the number of cases. (I). Once an individual is infected, they enter the exposed
However, in reality, the number of infected individuals stage (E), unable to transmit the disease. A couple of days
present in society capable of transmitting the disease has later, the infected individual becomes infectious, exhibiting
decreased, eventually reducing the total number of cases. symptoms (I), or remaining asymptomatic (A) based on a
Therefore, it is possible that, depending on the level of effort certain probability p. It is worth noting that infectiousness
invested in contact tracing, the number of daily positive begins before the appearance of symptoms. Thus, within
tested individuals initially increases but subsequently the infected population I, there are individuals who do
decreases and eventually reaches a balance, as observed not present symptoms yet but will eventually exhibit
in many countries or cities. Our model demonstrates this them. Finally, all infected individuals enter the removed
outcome and successfully reproduces the case evolution stage (R) through various possible mechanisms, including
observed in South Korea and New York City. Most of the placement in quarantine on testing positive, a natural
parameters in our model were chosen based on clinical reduction in infectiousness as the disease progresses, or
observations, with adjustments made to reflect different death.
scenarios resulting from social distance measures. The equations that describe the evolution of these
Furthermore, our model can also account for situations populations are as follows:
where health-care systems have limited capacity, providing
potential outcomes for the epidemic in South Korea based dS = -µ SI -ν SA (1)
on varying maximum testing capacity. dt N N
2. Methods dE = µ SI +ν SA −δ E (2)
dt N N
2.1. Mathematical model
As mentioned earlier, many CM have been proposed dA = pE −δ α A − () (3)
θ
t AI
to study the evolution of a pandemic in the absence of dt
external interventions. In our study, we built on the model dI
t I
pE −δ
θ
proposed by Wang et al. (2020). Wang’s model implements dt =(1 − ) β I − () 2 (4)
ideas previously proposed by Kim et al. (2020) and later
expanded by Liu et al. (2021). Specifically, it employs a dR A + () 2
tI + ()
Susceptible-Exposed-Infectious-Removed (SEIR) scheme dt = β I +α θ θ tAI (5)
along with a new population for asymptomatic individuals.
However, as we were only interested in the evolution of Most of the terms and parameters introduced
daily epidemic cases, we did not consider hospitalized, correspond to the typical SEIR model. Here, N represents
recovered, or quarantined populations, unlike Wang’s the total population of the system, μ and ν are the

Volume 1 Issue 1 (2023) 3 https://doi.org/10.36922/ghes.0873