Introduction
Coronavirus disease 2019 (COVID-19) pandemic is vastly spreading worldwide, with more
than 7.4 million confirmed cases and 418,294 deaths (5.64% mortality rate) on 12 June
2020 (WHO, 2020). Understanding the COVID-19 behaviour is fundamental for combating
the dissemination of the virus while an effective vaccine or medicine is not available.
At this moment, preventive measures and social distancing are the most efficient strategies
to combat the COVID-19 pandemic [1]. Because this pandemic is unprecedented, models
to predict the outbreak are scarce, mathematically complex [2] or not available.
In Brazil, the COVID-19 pandemic started on 26 February 2020, and rapidly spread into
the country, starting in Sao Paulo and Rio de Janeiro states and disseminating to
other Brazilian states a few weeks later. Three months after the first COVID-19 case,
several Brazilian states already are in critical condition, with their health systems
overloaded, most of them above 80% occupancy or even collapsing. Nowadays, Brazil
is considered the epidemic centre of Latin America, occupying the second place in
total number of cases and more recently in total number of deaths.
Situation in Brazil is critical and authorities require a general scenario and the
developing trend of the Covid-19. By using a simple mathematical model described previously
[3], we present herein the Sars-Cov-2 epidemiology in Brazil and in the five most
affected Brazilian states: Sao Paulo, Rio de Janeiro, Amazonas, Ceara, and Pernambuco.
We are able to predict the outbreak peak and the decreasing tendency of the pandemic
with this model. Our results are important for the comprehension of the COVID-19 outbreak,
estimation of the affected population size, and temporal evolution of the disease.
This knowledge may help Brazilian authorities make critical decisions and direct new
strategies for controlling the COVID-19 pandemic, as well as predict when life may
be safely returned to normal, at least in part.
The mathematical model
The methodology of exponential decay proposed by Tang and Wang [3] is applied. The
infected numbers, including cumulative number and daily change number, were collected
from several publicly available online Brazilian sources. Then, the decay factors
for each location were obtained by simulating the growth rate. Finally, the predictions
of cumulative number and daily change number were calculated and the figures were
plotted.
Analysis and discussion of the results
While no specific vaccine or treatment against COVID-19 is available, the best strategy
to combat the disease is preventive measures and social distancing. The Brazilian
government is making important decisions to avoid the Sars-CoV-2 spread. Different
mechanisms and levels of social distancing have been imposed, including 1.5 metres
of distance among people (in lines, public spaces, and transportation), quarantine,
and lastly, lockdown. Most Brazilian cities adopted quarantine with only essential
services allowed to work. In some critical cities, lockdown was imposed. Other preventive
measures include sanitation (hands, personal objects, and public spaces), face mask
usage, complete isolation of infected people, and flu vaccination. Nowadays, according
to our results, Brazil and the five analysed Brazilian states are crossing by the
worst moment of the COVID-19 epidemic and any easing of the preventive measures and/or
social distancing will probably have a negative impact on the disease curve.
Sao Paulo state, the epicentre of the COVID-19 in Brazil, was the first state to adopt
several measures to avoid the fast virus spreading [4]. The occupation rate of intensive
care units is ∼70% in state and 89% in Sao Paulo city (the main city and the capital
of the Sao Paulo state). Quarantine started on 24 March and it was prorogated until
28 June in the last update. Transmissibility index or reproduction number (R
0) was ∼2.2 before quarantine (17–23 March), dropping to ∼1.4 after one month (14–20
April) and to ∼1.2 after 2 months (12–18 May). Isolation rate, evaluated by monitoring
cell phone mobility, was 27.8%, 51.7%, and 48.8% before and after one, and two months
of quarantine, respectively. Mandatory use of face masks in any public space was established
on 7 May 2020. Our mathematical analysis shows that Sao Paulo state is at the peak
of daily new cases (∼4000 daily cases), which would persist for some days before starting
to drop. Daily new cases would drop to ∼3000 by the end of 30 June, to ∼1300 by the
end of July, and to ∼450 by the end of August. Total confirmed cases would reach ∼225,000
by the end of June, ∼287,000 by the end of July, and ∼311,000 by the end of August
(Figure 1).
Figure 1.
(A), (D), (G), (J), (M), (P): Cumulative COVID-19 cases; (B), (E), (H), (K), (N),
(Q): Growth rate of COVID-19; and (C), (F), (I), (L), (O), (R): Daily change COVID-19
cases in Brazil, Sao Paulo, Rio de Janeiro, Amazonas, Ceara, and Pernambuco, respectively.
The first case of Covid-19 in Rio de Janeiro was confirmed on 5 March 2020. Nowadays,
Rio de Janeiro is the second state in the number of positive cases and deaths for
COVID-19. Main affected cities in Rio de Janeiro state are Rio de Janeiro (capital
of the state) with 40,504 confirmed cases and Niteroi with 4413 cases. Occupation
rate of intensive care units is ∼90% in state and 83% in Rio de Janeiro city. Quarantine
started on 24 March and it was prorogated until 10 June in the last update. Isolation
rate was 41%, 53.2%, and 57.4% before and after one and two months of quarantine,
respectively. Use of face masks is mandatory in any public space since 23 April 2020.
Reproduction number (R
0) was around 4.5 before quarantine and decreased to 1.7 on 19 May. According to our
analysis, Rio de Janeiro state is on the peak of daily new cases (∼2000 daily cases)
since the last week of May it would persist for around two weeks before starting to
drop. Daily new cases would drop to ∼1600, to ∼700, and to ∼250 by the end of June,
July, and August, respectively. Total confirmed cases would reach ∼110,500 ∼143,700,
and ∼156,400 by the end of June, July, and August, respectively.
Amazonas state is located in North of Brazil and it is crossing for critical situation
due to the fast spreading of COVID-19. The first case of COVID-19 in state was recorded
on 13 March 2020, in a 39-year-old woman who returned from England. Occupation rate
of intensive care units is 86% in state and 80% in Manaus city (most populous city
and the capital of the Amazonas state). Quarantine started on 24 March, and it was
prorogated until 2 July 2020. Mandatory use of face masks in any public space was
established on 11 May. Lockdown was adopted in four critical cities of the State:
Tefe (4 May to 22 May), Silves (11 May to 31 May), Barreirinha (5 May to 29 May),
and Sao Gabriel da Cachoeira (8 May to 25 May). Reproduction number (R
0) was ∼2.83 in beginning, 1.78 after one month, and 0.82 after two months of quarantine.
The mathematical model shows that Amazonas state is on the peak of daily new cases
since the last week of May (∼1600) and would last approximately three weeks before
starting to drop. Daily new cases would drop to ∼1200, to ∼500, and to ∼150 by the
end of June, July, and August, respectively. Total confirmed cases would be around
∼86,900, ∼111,100, and ∼119,400 by the end of June, July, and August, respectively.
COVID-19 cases in Ceara state started on 15 March 2020, where three people were diagnosed,
all in Fortaleza city (the capital and epidemic epicentre in Ceara state). Total case
number of confirmed COVID-19 patients is rapidly increasing, with the number of total
cases doubling each 10 days. Rapid advance of COVID-19 in Ceara is elevating the occupancy
rate of intensive care units; nowadays, this rate is ∼88% in state and ∼93% in Fortaleza.
Quarantine was initiated on 23 March and prorogated until 20 July. In addition, lockdown
was adopted in Fortaleza from 8 May 2020 to 31 May. Isolation rate was 28.6% one month
before the quarantine, 45.7% after one month of the quarantine, and 54.9% after two
months of quarantine and two weeks after lockdown restriction. On 5 May, Ceara made
mandatory to wear face masks while out in public, which was recommended by public
health agencies and the government, with the intension to reduce the Covid-19 transmission.
At the beginning of the quarantine period, R
0 was ∼2.5, dropping to ∼1.3 after approximately two months (21 May). Our results
show that Ceara state is on the peak of daily new cases (∼1900 daily cases) and it
would persist until the middle of June before starting to drop. This peak would drop
to ∼1200, to ∼460, and to ∼140 by the end of June, July, and August, respectively.
The number of confirmed cases would reach ∼101,000, ∼125,500, and ∼133,600 by the
end of June, July, and August, respectively.
Pernambuco state is located in Northeast region of Brazil and it has a fast spreading
of COVID-19. The first case of COVID-19 was on 12 March 2020, in a couple who returned
from Rome, Italy. Occupation rate of intensive care units is 67% in state and 81%
in Recife city (most populous city and the capital of the Pernambuco state). Quarantine
started on 17 March and it was prorogated until 30 June 2020. Isolation rate was 32.9%,
45.3%, and 58.9% before and after one, and two months of quarantine, respectively.
Reproduction number (R
0) was ∼1.49 after 2 months of quarantine (22 May) in the Pernambuco state and ∼1.43
in Recife city. Mandatory use of face masks in any public space was established on
16 May 2020, the same day of lockdown adoption in five cities of the State: Recife,
Olinda, Jaboatao dos Guararapes, Camaragibe, and Sao Lourenço da Mata; lockdown was
scheduled until 31 May 2020. After performing our evaluation, Pernambuco state would
have already reached the peak of daily new cases by the end of May (∼1000 daily new
cases), but it would persist by around three weeks. Daily new cases would drop to
∼490, to ∼150, and to ∼40 by the end of June, July, and August, respectively. Total
confirmed cases would reach ∼57,300 after one month, ∼66,100 after two months, and
∼68,600 by the end of June, July and August, respectively.
Some important limitations of our mathematical model have to be considered. First,
because our mathematical model is based on an exponential decay curve, small variations
in the system (social distancing, preventive measures, or re-opening of non-essential
services and stores, etc.) can lead to high alterations in the estimated prediction.
Therefore, our prediction is more accurate in the short term (weeks), as compared
to long term (months). Second, we used official data from the Brazilian Ministry of
Health and Municipal and State Health Secretaries, where data are released after some
days of delay. In addition, it is important to consider that in Brazil, only the hospitalized
people in moderate or severe conditions are tested for the diagnosis of COVID-19.
The number of positive cases may be 10–15 times higher than the reported cases. However,
this observation does not invalidate our analysis, since the most important sample
to be considered in this analysis is exactly the patients that require hospitalization
and consequently lead to the collapses of the public health systems. In addition,
similarly to Brazil, several countries have performed the diagnostics only in hospitalized
patients and therefore these countries would have resembling disease behaviour. Thus,
our results can be used for evaluating the effects of the preventive measures, social
distancing, and regulated policies on the disease evolution, as well as help country
authorities make critical decisions and direct new strategies for controlling the
COVID-19 pandemic.