10.17843/rpmesp.2020.372.5405
ORIGINAL ARTICLE
Estimated
conditions to control the covid19 pandemic in peruvian pre and postquarantine scenarios
Charles Huamaní ^{
1,2}, Neurologist, Master of Science in Epidemiological Research;
Raúl TimanáRuiz ^{
3},Physician specialized in Public Management
Jairo Pinedo ^{
4,5}, Mechanical fluid Engineer
Jhelly Pérez ^{
5}, Bachelor’s degree in Scientific Computing, Master of Applied Mathematics with mention in Computer
Science
Luis Vásquez ^{
5}, Bachelor’s degree in Mathematics, Master of Applied Mathematics
^{1} Hospital
Nacional Adolfo Guevara Velasco, Cusco, Perú.
^{2} Universidad Andina del Cusco, Cusco, Perú.
^{3}
Instituto de Evaluación de Tecnologías en Salud e Investigación, EsSalud,
Lima, Perú.
^{4} Politécnico de Milán, Italia.
^{5} Universidad
Nacional Mayor de San Marcos, Lima, Perú.
ABSTRACT
Objectives: To determine the probability of controlling the outbreak of COVID19 in Peru, in a pre and postquarantine scenario using mathematical simulation models.
Materials and methods: Outbreak simulations for the COVID19 pandemic are performed, using stochastic equations under the following assumptions: a prequarantine population R0 of 2.7 or 3.5, a postquarantine R0 of 1.5, 2 or 2.7, 18% or 40%, of asymptomatic positives and a maximum response capacity of 50 or 150 patients in the intensive care units. The success of isolation and contact tracing is evaluated, no other mitigation measures are included.
Results: In the prequarantine stage, success in controlling more than 80% of the simulations occurred only if the isolation of positive cases was implemented from the first case, after which there was less than 40% probability of success. In postquarantine, with 60 positive cases it is necessary to isolate them early, track all of their contacts and decrease the R0 to 1.5 for outbreak control to be successful in more than 80% of cases. Other scenarios have a low probability of success.
Conclusions: The control of the outbreak in Peru during prequarantine stage demanded requirements that were difficult to comply with, therefore quarantine was necessary; to successfully suspend it would require a significant reduction in the spread of the disease, early isolation of positives and followup of all contacts of positive patients.
Keywords: Coronavirus Infection; Outbreaks; Surveillance; Decision Modelling (source: MeSH NLM).
INTRODUCTION
Controlling
an epidemic depends, among other factors, on the current knowledge about the disease
and how this information is used in decisionmaking. Therefore, knowing the
contagion periods, the number of people susceptible, the spread speed, among
others, is necessary to predict the progression of the disease. The problem
with the coronavirus disease (COVID19) pandemic is that such new information
is being generated constantly and decisions are based on highly uncertain
assumptions ^{(1)}.
Once the
epidemic in China was first reported, preventive measures took several weeks to
be stablished worldwide. In Peru, social distancing was implemented once the
first cases were detected ^{(2)}. Other mitigation measures followed,
but due to their low effectiveness, the Government was forced to decree
national quarantine on March 16, 2020. These measures (mitigation and
suppression strategies) were possibly implemented based on the recommendation
of experts who generated mathematical models to simulate the impact of the
epidemic ^{(3)}. However, when the national quarantine was decreed,
some local groups rejected the idea.
Mitigation and suppression measures proposed by the Government of Peru required citizen participation; nonetheless, there have been societal difficulties in complying with these. Other measures directed towards the health sector included increasing the number of hospital beds and health personnel, as well as the timely detection of people with COVID19. Early diagnosis is intended to promote isolation in order to cut off the spread of disease and carry out contact tracing. Our study aims to determine the probability of controlling the COVID19 outbreak in Peru, in a pre and postquarantine scenario with mathematical simulation models, and without the effect of social mitigation measures. Considering only the isolation of positive cases and the tracing of their contacts, in scenarios with greater or lesser supply of beds in intensive care units (ICU).
KEY MESSAGES 
Motivation for
the study:
Mathematical modeling at the beginning of the COVID19 pandemic was carried
out to estimate the number of cases, but not the conditions for starting or
suspending quarantine.
Main findings: The COVID19 pandemic would only
have been controlled if all patients were detected and isolated from the
start. To be successful in controlling the postquarantine pandemic, the
spread of the virus must be significantly reduced, all cases must continue to
be isolated, and the percentage of contacts traced must be close to 100%.
Implications: Control of the pandemic is not
possible without slowing the spread of the disease. This is a matter of a
societal nature. In the health sector, it is necessary to identify all cases,
isolate them and trace their contacts. Scenarios with less active
participation have a high probability of failure. 
MATERIALS
AND METHODS
The Centre for Mathematical Modelling of Infectious Diseases at the London School of Hygiene & Tropical Medicine ^{(4)} designed a model available for free download in the Rproject software, based on the disease assumptions known up to 5 February 2020 (Table 1).
Table 1. Assumptions used in mathematical modeling
Concept 
Values 
Reference 
Patients with subclinical infection 
18% and 40% 
Mizumoto ^{ (9)}, Nishiura ^{(10)} 
Incubation time (days) 
5.8 ± 2.6 
Li ^{(11)} 
Isolation time (days) 


Early 
3.43 (2.025.23) 
Donnelly ^{ (12)} 
Late 
8.09 (5.5210.93) 
Hellewell^{ (4)} 
R0 


Prequarantine 
2.7 and 3.5 
Liu ^{(7)}, Chen ^{(6)} 
Postquarantine 
1.5, 2.0 and 2.7 

Number of ICU beds 
50 or 150 
Assumed 
Initial number of cases 


Prequarantine 
1, 5 or 10 
Assumed 
Postquarantine 
20, 40 or 60 
R0: nbasic reproductive number; ICU: intensive care unit
Stochastic
differential equations
The study
designed by Hellewel et al. ^{(4)} was
based on a mathematical model which originated from stochastic differential
equations, and has the following modeling concepts.
If x_{(}_{t)} is the number of infected persons in a day, the equation in linear stochastic difference associated with x_{(t)} is described in figure 1, where p+q=1. When in contact with an infected person; p represents the probability of a person becoming infected, while q is the probability of not becoming infected.
Figure 1. Disease spread according to the probabilities established in the stochastic difference equation model
This is one way of explaining the speed of the virus’ spread which is usually done using the R0 (basic reproductive number). That being said, the sequence for the number of new infections per day would be:
Infected
at the beginning
Among other
variables, the R0 varies according to the disease, the mechanism of contagion,
and the population interaction ^{(5)}. There are several R0 estimates
for the COVID19 epidemic, some studies indicate that it varies from 3.5 in
persontoperson contact, or 2.5 in persontoreservoir/fomite contact ^{(6)}.
R0 variability ranges from 1.4 to 6.5 ^{(7.8)}, with a median of 2.7.
When this study concluded, a Peruvian R0 was not yet available neither for the
prequarantine or quarantine stage.
Assumptions
for mathematical modeling
The study
by Hellewell et al. ^{(4)} used the
following assumptions for its mathematical modeling: 1) if a positive case was
detected, it was sent into early isolation for 3.43 days; 2) the incubation
period of the disease was 5.8 days; 3) the R0 was 2.5 in the community and 0 in
isolation; 4) the percentage of subclinical infected cases was 0%; and 5) most
importantly, they defined success in controlling an outbreak if the spread did
not exceed 5,000 cases. These assumptions were tested in scenarios where
positive case isolation measures were initiated after 5, 10 or 20 cases had
been detected.
We updated
the disease behavior data according to the new information available. While the
spread of the disease and the response of the health system are variables. In
Peru we do not have any data on this matter, so we carried out the modeling
based on the following assumptions:
Prequarantine
scenario: In which
the R0 would be 2.7 and 3.5. The R0 of 2.7 corresponds to the median of the R0
values calculated from 12 studies ^{(7)}. Nonetheless, a second R0 of
3.5 was posed^{ (6)}, which would correspond to an adverse scenario. In
this adverse scenario, the positive case isolation measures and the contact
followup, are assumed to begin with 1, 5 or 10 cases. Higher values for R0 are
not assumed, due to the fact that in such models, control of the outbreak would
be unsustainable.
Postquarantine
scenario: A
scenario where the R0 could be 1.5, 2.0 or 2.7. Starts with a R0 value of 1.5
because it would be the bestcase scenario after quarantine (assuming that the
learned and reinforced behaviors in quarantine will diminish the interaction
with the decrease in the spread dynamic). Another modeling with a R0 of 2.7 was
made, which would be the starting scenario with no learning from the pandemic.
In the latter modelling it is assumed that the quarantine is lifted when 20, 40
or 60 cases are registered per day.
The
percentage of patients with subclinical infection was modified in both
scenarios, the current being 18 ^{(9)}. This information originates
from what happened at the Diamond Princess Cruise, which was kept quarantined
and tested every passenger. In a real scenario, the subclinical or asymptomatic
infected cases would not be tracked, and could continue to spread the disease.
On the other hand, symptomatic cases would spread the disease until being
isolated. A second analysis is carried out, with 40% asymptomatic cases ^{(10)},
which corresponds to a pretty bad asymptomatic infection scenario.
The
incubation time estimates for the disease (5,8 ± 2,6 days) were maintained ^{(11)},
as well as the fact that 15% of the contagion occurred before the symptom
onset, and the assumption that isolation decreases the R0 to 0.
The
duration of the time to isolation was chosen based on findings from the severe
acute respiratory syndrome (SARSCoV) pandemic and
from the initial stage of the COVID19 pandemic, both of these measures were
used in the original study. The time to isolation in the SARSCoV 2003 outbreak was of 3.43 days (2.025.23) ^{(12)}
and it is referred to as “early isolation”. During the initial stage of the
COVID19 pandemic the time to isolation was of 8.09 days (5.5210.93) ^{(4)}
and is referred to as “late isolation”. Given that the first case in Peru was
isolated 10 days after being reported, baseline calculations are made
considering “late isolation”. In the postquarantine analysis, “early
isolation” is considered, as it is assumed that the epidemiological
surveillance and control measures were improved, thus reducing the delay.
Finally,
“outbreak control” was defined as the absence of new infections from 12 to 16
weeks after detecting the initial cases. The original study assumed that
outbreaks reaching over 5,000 cumulative cases were too large to be controlled. However,
this European assumption does not reflect the caseresolving capacity of Peru,
where there are a limited number of ICU beds for management of patients with
COVID19.
The
original study based the outbreak control on the maximum number of cases
detected, we made the modeling considering the maximum number of beds in the
ICU required, in scenarios where there are 50 or 150 beds in the prequarantine
stage, and 150 beds in the postquarantine stage. The modeling with 50 beds is
done to try to reflect what could happen in provinces or cities other than
Lima, with less caseresolving capacity.
RESULTS
Prequarantine
scenario
Two
scenarios are proposed according to the propagation dynamics, considering that the
basal R0 is of 2.7 and the unfavorable R0 is of 3.5 (Figure
2).
Figure 2. Probability of controlling simulated outbreaks according to different numbers of initial cases, different propagation scenarios (R0) and with different proportions of asymptomatic cases. The R0 used represents an ordinary (R0=2.7) or unfavorable (R0=3.5) scenario for Peru. Both scenarios are performed considering late isolation for positive cases (average 8.1 days), and 15% transmission before the onset of symptoms.
In the
baseline scenario, if measures are implemented from the first case onward, the
probability of success in controlling the outbreak is close to 80%, even
without the need for contact tracing. If isolation measures are implemented
when there are already 5 cases detected, 100% of the contacts should be traced
to obtain a success rate of 40%. Implementing measures when there are more than
10 cases detected, in all scenarios, shows a probability of success in
controlling the outbreak of less than 20%. The effect from the asymptomatic
people percentage barely changes the outbreak control scenarios when measures
are implemented from the first case detected.
In the
worstcase scenario (R0=3.5), if measures are implemented from the first case
onward, isolation measures by themselves would be enough to obtain a success
rate of at least 60% in controlling the outbreak. Contact tracing increases the
probability of success in controlling the outbreak up to 80%. But, if isolation
measures are implemented when there are 5 or 10 cases detected, success rate
decreases to less than 40%, even when tracing 100% of the contacts.
Postquarantine
scenario
It is
assumed that when quarantine ends the R0 decreases to 1.5, 2 or 2.7 in the
worstcase scenario, furthermore, the assumption of “late isolation” could be
updated and changed to “early isolation”.
From all of
the scenarios shown in Figure 3, the one with a success rate of 80% is the one
that integrates early isolation of positive cases, 100% of contacts traced, and
a R0 of 1.5; regardless if the quarantine ends with 20, 40 or 60 cases (Figure 3).
Figure 3. Probability of success in controlling the outbreak in different scenarios, starting with 20, 40 or 60 cases. In this differentiated propagation scenarios (R0), the percentage of asymptomatic people is 18%. It is differentiated according to early (average 3.4 days) or late isolation (average 8.1 days)
In a more
conservative scenario, where the R0 decreases to 2, quarantine could end with
20 positive cases; but 100% of contacts traced should be guaranteed to obtain
approximately a success rate of 60% in controlling the outbreak.
If early
isolation of positive patients is not yet achieved, there would still be a 60%
chance of success in controlling the outbreak if the R0 decreases to 1.5 and
quarantine ends with 20 positive cases and 100% of contacts traced.
DISCUSSION
Public
health decisions are recommended to be based on evidence and to have technical
support. At the onset of the COVID19 pandemic, information was either absent
or uncertain ^{(1)}, so several initiatives emerged to provide
epidemiological and clinical information to help make better decisions. In this
studies, mathematical modeling was used to simulate scenarios that predict the
pandemic development to be able to make decisions ahead of time ^{(13,14)}. We decided to show part of a scenario that is
still under development. This scenario evaluates, in an isolated way, the
effectiveness of epidemiological surveillance by identifying cases, isolating
them and tracing their contacts. All of this depends on the health system
logistics, so these would be scenarios where social participation would only be
reflected in the R0 variation.
In Peru,
although the first positive case was isolated and the contacts were traced, the
process of identification and isolation of the case was late. In the ideal
scenario of “early isolation” from the first positive case, a low percentage of
contacts traced would have been required. But that ideal scenario would have
involved a more rigorous migration control from the beginning and having the
correct control of all possible suspects and their subsequent followup.
Changing the scenario to five cases to implement the isolation or tracing of
cases can be interpreted as if the detection measures were surpassed and five
cases went undiagnosed, in this scenario the probability of controlling the
outbreak would be less than 40%. Perhaps that is why countries such as Russia
and South Korea, both of which took very quick but different decisions, such as
closing borders or strictly monitoring confirmed and suspected cases ^{(15,
16)}, have had better results in controlling the pandemic.
European
models about propagation dynamics represented by the R0 could not be applied to
Peru, because it has greater social interaction and low healthcare
caseresolving capacity. This is why a greater number of cases for a reduced
supply of ICU beds is expected, therefore, the main objective would be to
minimize the number of cases that require mechanical ventilation ^{(17)}.
Taking action with only a few cases detected could seem less important.
Nonetheless, late decisionmaking has a low probability of success in
controlling the outbreak, even at 20 cases. In this context, from a
mathematical modeling perspective, a measure of mandatory social isolation such
as quarantine was the only option for timely control of the epidemic ^{(18)},
a measure that was finally adopted in Peru ^{(19)}. Since this scenario
is similar to several other countries with high social interaction and low
caseresolving capacity ^{(20)}, quarantine in countries like ours
would be the only viable way to control the epidemic.
However,
several questions remain. When is the right time to lift the quarantine or what
conditions must be met to lift the quarantine? It is foreseeable that after
quarantine ends many people will increase their social interaction
disproportionately; if the control measures are decreased, it is possible that
the postquarantine R0 could be higher than prequarantine.
A very
optimistic scenario is one where social interaction is reduced and accordingly
the capacity of contagion decreases with R0 values of 1.5 or even less, this
could be interpreted as a high probability of controlling of the epidemic
postquarantine. However, this optimistic scenario is not likely to take place,
as it implies reducing social interaction and increasing caseresolving
capacity in just a few weeks. In a more conservative scenario, where the R0 is
2, if we interrupt quarantine with 20 positive cases, we would need to track
all contacts and early isolate people who test positive for COVID19.
Therefore,
it is understood that measures taken after quarantine will result in the
control of the epidemic, or in the failure of the health system and the
epidemic reemergence. Everything will depend on how much the value of the
postquarantine R0 decreases.
This
analysis has several limitations, for example, it is based on a mathematical
model that assumes that the disease spreads in a single closed society. On the
contrary, Peru is divided into several regions that can be isolated from each
other and thus, each one can have a different type of propagation dynamics. For
each region, different problems arise when implementing and executing the
control measures in a differentiated manner, which could generate confusion and
inadequate preparation for the epidemic. Another limitation of this study is
that it is based on assumptions that may not actually be verified, such as the
number of cases. Without a mass screening test, the number of infected cases
may not be accurate; however, such approximation can be determined by
evaluating trends in epidemiological curves. This study recommends adequate
logistics to guarantee effective contact tracing. This type of logistics varies
in the case of a symptomatic or a nonsymptomatic contact. Due to the lack of
resources to guarantee such a measure, this is considered a limitation. Finally,
the spread dynamics of COVID19 in Peru is unknown, although the necessary
calculations could be made. However, given the high level of underreport of
COVID19 cases, we would obtain an underestimated result. This is why we need
to refer to values described in other studies.
The results
are intended to be applicable to Peru, but are relevant for any region or
country with similar caseresolving capacity, because the starting point is
considering the maximum number of cases that can be supported and not the
amount of affected population. Therefore, a region or country with less than
150 ICU beds will have to take more restrictive measures if it estimates
to have over 3,000 cases. Likewise, the postquarantine scenario we modeled
could be equivalent to a prequarantine scenario in places with a late
response.
In
conclusion, social isolation of positive cases and contact tracing required
many assumptions that were quickly exceeded, and if appropriate measures had
not been taken, the probability of failing to control the epidemic would have
been high.
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Citation: Huamaní C, TimanáRuiz R, Pinedo J, Pérez J, Vásquez L. Estimated conditions to control the COVID19 pandemic in peruvian pre and postquarantine scenarios. Rev Peru Med Exp Salud Publica. 2020;37(2):195202. doi: https://doi.org/10.17843/ rpmesp.2020.372.5405
Correspondencia: Charles Augusto Huamani Saldaña; Av. Arriba Perú 1154, Lima 42, Perú; huamani.ca@gmail.com
Received: 24/03/2020
Approved: 22/04/2020
Online: 28/04/2020
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