1. Introduction

The new coronavirus (COVID-19), discovered in China's Wuhan province in late December 2019, is characterized by a flu-like condition of fever and cough, which can progress to a stage of pneumonia and dyspnea in more severe cases. From that time on, the virus spread worldwide, and the World Health Organization (WHO) declared, on 11 March 2020, a pandemic. Because of large variations in testing, the COVID-19 points out to an underestimation in the number of confirmed cases for some countries. The continental ones tend to have higher numbers, both of cases and deaths.

The disease incubation period varies from two to fourteen days. There are many factors that explain cases and deaths in a country such as the population density, percentage of the urban population, number of beds per hundred thousand inhabitants, human development index, Gini coefficient, poverty index, income per capita and life expectancy. The risk of dying from COVID-19 increases rapidity with age and it is higher to males than to females, but the factors associated with sex differences remain unclear. Hypertension, obesity, organ transplantation, respiratory diseases, blood cancer and diabetes are the most common comorbidities among infected patients.

The coronavirus pandemic had already affected more than 480 million people worldwide, leading to about 6.14 million deaths by 26 March 2022. Europe remains the continent most affected in the world by the coronavirus pandemic up to this date, with over 175 million infected people and more than 1.76 million deaths ^[1]. It has 36% of the confirmed cases worldwide, and 29% of all deaths recorded globally, despite adding only 7.9% of the world population. The large proportion of deaths is due to high life expectancy, greater spread of the virus due to intense mobility, and several cities with very high population density.

Among the fourth-five countries with death rates higher than 2,000 deaths/million in the world (among 222 countries), there are seven in South America: Peru, Brazil, Chile, Argentina, Colombia, Paraguay and Uruguay. Brazil, on 26 March 2022, registered cases totaled 29 millions, its death toll is more than 658,000, and an overall lethality rate of 2.2%, while 28 million people have recovered from the virus so far according to data registered from Ministério da Saúde (Brazil) ^[2]. In addition to Brazil, Argentina, Colombia, and Chile have highlights when considering the absolute records of notified cases. This happens for obvious reasons, since Brazil, Argentina, Colombia and Chile have large populations corresponding to populations greater than 209, 444, 496 and 187 millions of inhabitants, respectively.

Considering the percentage of lethality in the countries of South America, Brazil is in the position 6th of greater lethality. Countries such as Peru, Ecuador, Colombia, Paraguay and Bolivia have a lethality percentage above Brazil, with lethalities of 8.33%, 4.14%, 2.96%, 2.87% and 2.39%, respectively. In the case of Venezuela, it is clear that because it is a country with a closed regime, its statistics regarding confirmed cases and deaths may be far below the reality faced. The record of 5,673 deaths and a lethality rate of less than 1%, more precisely 1.09%, does not seem consistent for a country with several serious problems in the areas of health, supply and the economy. Thus, a cautious look at Venezuela's data is important.

The pandemic came to Brazil through the arrival of foreigners and the return of Brazilians from Europe who disembarked at the ports and airports in Brazil, mainly those of São Paulo, Rio de Janeiro, Fortaleza, Recife and Salvador. It has gone from the rich to the most vulnerable poor people. Slum-dwellers, homeless people, drug users, elderly in nursing homes and riverine communities—and also from coastal cities to the interior—were all affected by the pandemic. It has reached devastatingly almost all 5,568 Brazilian cities. For some time, the spread of the virus has been restricted in more affluent areas. However, the transmission has gradually been spread to cities further away from large urban centers, where their populations are more exposed to intense social vulnerability. Thus, it is not by chance that most Brazilian cities are suffering so much from the pandemic, because of a large number of cities in metropolitan regions and capitals of high population density, and marked by an increase of social vulnerability. It is very known that the North and Northeast regions in Brazil have the most vulnerable cities

The highest number of deaths from coronavirus occur in areas that have always suffered from poverty problems, such as lack of decent housing, water and sewage and soil pollution. As stated by the World Health Organization (WHO), the amount of cases reported is highly dependent on each country’s testing policy. In this matter, testing is crucial to understanding the spread of the pandemic and responding appropriately ^[3]. The number of tests carried out for coronavirus in Brazil was quite small concerning the population size during the pandemic's first year. The number of COVID-19 vaccination doses administered per 100 people in Brazil rose to 192 as of Mar 26, 2022.

Besides lacking in doing tests, Brazil is one of the countries with the worst income distribution in the world ^[4]. In other words, the pandemic affected people who were already in expressive social vulnerability due to unemployment, poor housing conditions and difficulty in accessing health services. Under these circumstances, it is possible to identify which factors contribute to a fast spread of the virus: they are linked not only to their pathogenic characteristics but also to social and economic factors ^[5]. So, in this context, anyone can get the virus, but its impacts are not equal. However, low socioeconomic status is associated with low adherence to preventive measures as well—either through ignorance or having to take risks surviving ^[6].

Another fact to address is that the poorest people live in places with high population density, in small houses and with several people altogether, which facilitates the spread of the virus. In addition to that, they already suffer from a burden of other infectious pathologies, such as HIV/AIDS and tuberculosis, as well as chronic non-communicable diseases, like diabetes, hypertension and obesity, to mention some—these are risk factors for the worsening of the pandemic ^[7][8].

2. The Challenges of the Brazilian Unified Health System and the Coronavirus Economic Impact

The Unified Health System (SUS, acronym in Portuguese) of the Brazilian Ministry of Health guarantees access to health actions and services in this pandemic to the great majority of Brazilians. However, its management to combat the coronavirus was inefficient because it reached much higher levels than expected. About 94.4% of the individuals, who constitute the poorest 20% of the population, are dependent on the SUS.

The capacity of the SUS to perform its functions during the pandemic required not only the creation of new hospitals and ICUs but also a new operational organization within the health system, including the creation of new accesses, mainly by remote route ^[9]. So, in this context, all the modalities of call centers (consultation, counselling, monitoring and control of beds) have become vitally important in this process ^[10].

Indeed, remote patient care has proven to be an excellent tool in the fight against coronavirus and, at the same time, it reduced crowding in health services, making them safer and more efficient. In addition, patients with other pathologies can use remote care in the safety of their homes. In addition, despite all its problems, the SUS has been a vital piece in facing the pandemic. Now it becomes clear the need for more resources for the system to function well. In other words, the COVID-19 further exposed the problems of the unified health system, especially the uneven distribution of medium and high complexity infrastructure, as well as the limited ability to perform diagnostic tests.

Even after the start of vaccination in January 2021, the critical scenario of the pandemic persisted due to obstacles in vaccination strategies. A critical point to consider is the situation of health professionals because Brazil has kept practically the same professionals on the front line since 2020. Thus, these professionals are exhausted due to excessive workloads and lack of adequate infrastructure.  On the front line of combating the pandemic, researchers have about 3.5 million health professionals working in hospitals and health units that are presented in 5,570 Brazilian municipalities ^[11]. In addition to the insufficiency of hospitals and ICUs beds, several “field hospitals” were created with the hiring of professionals with precarious employment ties and without labor rights. In addition, many of these professionals were inexperienced and came from health courses that anticipated graduation to meet the demand ^[11]. In summary, it is necessary to recognize the importance of health professionals who work even under adverse conditions and at high risk.

Before the worsening of the pandemic, the prospects for the Brazilian economy were of an average growth for the Gross Domestic Product (GDP) of 2.5% for the biennium in 2019–2020. The impacts of the pandemic on the Brazilian economy were very heterogeneous. The most affected sector was services that represent 70% of the national GDP. It was followed by the industrial transformation sector, while the industrial sector agriculture continued to maintain positive growth.

According to data released in March 2022 by the Brazilian Institute of Geography and Statistics (https://agenciabrasil.ebc.com.br/en/economia/noticia/2022-03/gdp-grows-46-2021-and-exceeds-pandemic-losses), Brazil’s gross domestic product (GDP) went up 0.5 percent in the fourth quarter of 2021 and closed out the year up 4.6 percent. The surge was enough to cover the losses of 2020, when the Brazilian economy shrank 3.9 percent as a result of the pandemic.

3. General statistics in Brazil

Several updated statistics about COVID-19 in Brazilian states and municipalities can be easily accessed at https://pedro-rafael.shinyapps.io/shinydashboard/  and https://brasil.io/home/ developed by a co-author of this work. The database adopted to obtain COVID-19 information in Brazil consists of almost 3 million records from more than 5,550 municipalities that notified at least one confirmed case in each city. The complete database tends to increase significantly over time.

Brazil consists of five geographic regions, North, Northeast, South, Southeast, and Central-West. Among them, the Southeast and South regions have the highest lethality rate (deaths/confirmed cases in percentage), both equal to 2.70%, where for the other regions are: Northeast (2.07%), North (2.02%) and Central-West (1.96%). Seven Brazilian states have lethality rates higher than the overall lethality rate of 2.20%, namely: Rio de Janeiro (3.50%), São Paulo (3.20%), Maranhão (2.56%), Amazonas (2.44%) and Pará (2.41%). For the COVID-19 mortality rates (deaths/resident population per one million residents), the states the states of Rio de Janeiro, Goiás and São Paulo have the highest mortality rates in Brazil ^[2].

In the Northeast, the municipalities in the state of Pernambuco with the highest rates, in general, are closer to the land-sea coastal. In the state of Rio de Janeiro, located in the Southeast region, 40% of the municipalities have a lethality rate above the state rate of 3.5%. On the other hand, 58% of the municipalities of Pernambuco have a lethality rate above the state rate of 3.2%, which is a very worrying situation, although the number of confirmed cases has been declined in both states in the last months. For Pernambuco, 71.43% of the municipalities with a population above 100,000 inhabitants have a lethality rate higher than the state rate. For the state of Rio de Janeiro, this percentage is close to 61.29%.

4. Application of GAMLSS to Forecast Coronavirus in Brazil

The GAMLSS models are regression methods adopted in several studies ^[12]. Researchers use GAMLSS models to provide forecasts about new cases and new deaths by coronavirus in the Brazilian states and their capitals. The GAMLSS modeling framework is currently implemented in a series of packages of the R statistical software (www.r-project.org). The gamlss package allows to explain real data by considering more than fifty different distributions. For example, the exponential power distribution of Box–Cox ^[13] used by the World Health Organization to build the world standard growth curves ^[14], and the Poisson and negative binomial distributions. The last distribution is studied in several technical reports on coronavirus from the Imperial College COVID-19 Response Team in London ^[15].

It is considered that in the case of coronavirus, the growth of confirmed cases and deaths will necessarily decrease over time after some period. Therefore, it is justified that these confirmed cases and deaths registered over time can be fitted using a regression. Let y be the response vector denoting the number of confirmed daily cases or the number of daily deaths. For this response variable, researchers can consider the two-parameter logistic distribution, which is widely used to model population growth data. The choice of the logistic distribution to model the confirmed cases and deaths caused by coronavirus, via GAMLSS, is justified by the behavior of similar respiratory syndromes, which have a period of accelerated growth at the beginning of an epidemic and a slower period of decrease at the end of it that takes into account the logistic distribution, which is adequate for growth data.

Two GAMLSS regressions are chosen under the logistic distribution. The first regression considers the number of COVID-19 confirmed cases as a response variable, and the time as explanatory variable plus a dummy variable that corrects the effect of the under reporting identified on weekends. The historical series was considered from the reported 100th confirmed coronavirus case. The second regression follows the same structure to analyze the death data by considering the historical series from the 50th death recorded.

In order to provide forecasts related to new cases and new deaths caused by COVID-19 in Brazil, the UFPB Respiratory Syndromes observatory has developed web applications which can be easily accessed through the following links  http://obsrpb.com.br/ufpb/ and http://shiny.de.ufpb.br/st_pred/

Based on data registered until 25 March 2022, it is possible to show evidence that new cases of COVID-19 are increasing in the following states: Ceará, Rio Grande do Norte and Sergipe. By performing the predictions for the new confirmed cases in these states, there is evidence that the numbers of new cases are increasing, requiring a constant review of rules imposed on the population, as a way to prevent the transmission of the coronavirus.

In relation to the state capitals, it is possible to show evidence that new cases of COVID-19 are increasing in the following capitals: Macapá, Fortaleza, São Luís, Cuiabá, Belo Horizonte Rio de Janeiro, Natal, Porto Alegre and Porto Velho. Furthermore, when they analyze the data about new deaths, there is evidence that the number of new deaths are increasing in the following states: Acre, Amapá, Alagoas, Bahia, Ceará, Minas Gerais. In relation to capital cities, there is the evidence that the number of new deaths by COVID-19 are increasing in the following capitals: Rio Branco, Maceió, Recife, Campo Grande and Belo Horizonte.

This entry is adapted from the peer-reviewed paper 10.3390/epidemiologia2030018