Estimation and prediction of COVID-19 cases in Brazilian metropolises

Objective to estimate the transmission rate, the epidemiological peak, and the number of deaths by the new coronavirus. Method a mathematical and epidemiological model of susceptible, infected, and recovered cases was applied to the nine Brazilian capitals with the highest number of cases of the infection. The number of cases for the 80 days following the first case was estimated by solving the differential equations. The results were logarithmized and compared with the actual values to observe the model fit. In all scenarios, it was considered that no preventive measures had been taken. Results the nine metropolises studied showed an upward curve of confirmed cases of COVID-19. The prediction data point to the peak of the infection between late April and early May. Fortaleza and Manaus had the highest transmission rates (≥2·0 and ≥1·8, respectively). Rio de Janeiro may have the largest number of infected people (692,957) and Florianópolis the smallest (24,750). Conclusion the estimates of the transmission rate, epidemiological peak, and number of deaths from coronavirus in Brazilian metropolises presented expressive and important numbers the Brazilian Ministry of Health needs to consider. The results confirm the rapid spread of the virus and its high mortality in the country.


Introduction
The new coronavirus (SARS-CoV-2) belongs to a family of viruses that cause diseases in the human respiratory system. Previous outbreaks of coronavirus (CoVs) include Severe Acute Respiratory Syndrome (SARS)-CoV and Middle East respiratory syndrome (MERS)-CoV as major threats to public health (1) .
The COVID-19 disease pandemic began in December 2019 in Wuhan, Hubei province, People's Republic of China. It quickly spread to other Chinese provinces (2) . Due to its high spread rate, China declared COVID-19 a second-class infectious disease, with management measures for a first-class infectious disease (the most dangerous category of infection) (3) .
The spread of COVID-19 was rapid and global. United Kingdom (January 31 st ) (4) , and the geographical expansion of this pandemic continues.
In this scenario, it remains to be established that the ongoing pandemic of COVID-19 is devastating, despite the extensive implementation of control measures. On January 30 th , 2020, the World Health Organization (WHO) characterized the disease as a pandemic, being declared a Public Health Emergency of International Importance. As of April 1 st , 2020, 823,626 cases of Covid-19 were confirmed, with 40,598 deaths worldwide (5) .
Brazilian data are alarming. In this sense, research is urgent to estimate the risk of this pandemic in Brazilian macro-regions. To know the most exposed urban centers that face the heaviest disease burden, it is imperative to closely monitor changes in epidemiology, the effect of public health strategies, and their social acceptance. Given the above, this research aimed to estimate the transmission rate, epidemiological peak, and the number of deaths by COVID-19 in the nine Brazilian capitals with the highest number of cases.

Method
The first case of COVID-19 was diagnosed on February 27 th , 2020 in São Paulo. On February 3 rd , a public health emergency was decreed in the country, and on March 20 th , 2020, community transmission of the disease was announced in the country (7) .
Thus, to understand this disease's dynamics in the population, the SIR epidemiologic model proposed by Kermack and McKendric (8) was applied. This model rests on the idea that there are three groups of individuals: susceptible (S), infected (I), and recovered (R). The mathematical expression of the model uses three differential equations, where β is the parameter that controls the transition between S and I, and γ is the parameter of the transition between I and R.
In this article, the first third of Brazilian capital cities with the highest number of cases until March 27 th , 2020 was investigated, which corresponds to nine capital cities (out of twenty-seven). According Salvador and Fortaleza in the Northeast. Brasilia, in the Midwest, would be added, but was removed from the pool of investigated cities due to difficulties to find official data.
Data were extracted from the daily epidemiological reports since the first day of confirmed cases until March 30 th , 2020 and the capital's population was according to the IBGE (9) . Initially, graphs were created with the actual number of confirmed cases in each city until the end date, followed by their logarithmic transformation to show growth patterns. Then, the differential equations were solved for each of the nine scenarios and the number of cases was predicted until the 80 th day of infection since day one. To test the model's fit, the natural logarithm of the observed and predicted number of cases was used. They were graphically presented for the sake of a better understanding.
healthy people an ill person can infect. The predicted number of cases, the day of peak, and the possible number of deaths were also investigated, considering the maximum number of people who can be sick and 1% lethality. These values were considered as if no prevention measure had been taken. Data were analyzed in R software, using the package deSolve.
This work did not require Ethics Committee approval because the state health department freely distributed the data on the internet. Yet, the authors complied with Brazilian resolution 466/2012 on ethics for research.

Results
In total, 2,829 confirmed cases of COVID-19 were analyzed in nine Brazilian capital cities. In the Regarding the number of predicted cases, the observed cases were superior to the modeled number.
In BH, some degree of stability was observed since day 14, with the number of cases remaining inferior to the model (Figure 1).

Discussion
Brazil is marked by intense socioeconomic inequalities and health conditions, with relevant geographical differences, whether in the levels of health risks or the access to the resources available in the country's health system (10) .  (12) .
It is worth noting that the unequal distribution of COVID-19 cases among Brazilian regions is also influenced by underreporting. The North and Northeast regions are marked by a worse assessment of the health status, greater restriction of activities, and lesser use of health services, despite the greater coverage of public programs (13) .
Representing the North region, Manaus, the state capital of Amazonas, is the main financial, corporate and commercial center of the region. It is the most populous city, with 2.1 million inhabitants and one of the largest tourist destinations in Brazil. The growth of cases in the city is expressive and linked to a social scene where asymmetry, verticality, competitiveness, and weak relations between the cities prevail, in addition to an insufficient health service network with difficulties to maintain human resources (14) .
In the Northeast region, the cases of COVID-19 were analyzed in Salvador and Fortaleza, cities with for consumers (15) . The establishment of hubs in several airports has enhanced the entrance of foreigners in different countries of the world.
The economic advantages of tourism in Brazil are undeniable, however, the issues of travel and health are an existing concern. The profiles of travelers differ in terms of origin and destination, which can directly influence the occurrence of epidemics and pandemics, often of unexpected magnitude and severity (16) , such as COVID-19. Also, limited coverage and access to health services in the country can corroborate the spread of diseases.
While a small portion of the Brazilian population has access to health services, many people face a decrease in the availability of hospital beds (17) . This factor, linked to COVID-19's pandemic potential, put the response capacity of epidemiological surveillance services at the center of attention and required preventive measures from the Brazilian government, such as confinement and social distancing.
Extensive measures are needed to reduce the interpersonal transmission of COVID-19 (1) . Some of the measures adopted, such as spraying disinfectant and alcohol in the air, on roads, vehicles, and people have not been effective though (3) . More expanded measures include isolation of cases, identification and monitoring of contacts, environmental disinfection, and use of personal protective equipment (4) . Regarding the control strategies, social distancing stood out as a strategy that limits human-to-human transmission, as well as reducing secondary infections between close contacts and health professionals, preventing transmission amplification events, and reducing or delaying the dissemination of the virus.
Moreover, epidemics and pandemics paralyze the economic, social, political, and cultural development, interfering in the demographic trajectory of the locations where they spread (18) . The emergence of COVID-19 and its consequences has left the worldwide population with feelings of fears, concerns, and anxiety, which can further expand the disease data (19) .
The biological, mental, emotional, social, and The main limitation of this study arises from the use of a secondary database, as data for some cases were incomplete. Furthermore, underreporting and/or insufficient testing might influence the predicted peak.
It is also important to highlight that the results did not consider social distancing measures that aim to reduce the transmission rate of the virus.

Conclusion
The estimates of the transmission rate, epidemiological peak, and number of deaths by COVID-19 in the Brazilian metropolises presented expressive and important numbers which the Brazilian Ministry of Health should take into account. All metropolises showed an exponential growth in the number of cases.
The transmission rate was higher in Fortaleza and in Manaus, where many deaths are expected. Thus, the results confirm the rapid spread of the virus and its high mortality in Brazil.