Discussion

Notably, the epidemiologic picture is changing daily. While Brazil is facing a challenging scenario, especially considering people under social vulnerability, mostly blacks, other countries in Africa are predicted to be significantly affected by the ongoing COVID-19 outbreak (Lone and Ahmad, 2020). A pandemic status like the one we are experiencing brings lots of concerns. The clinical and laboratory characteristics of Covid-19 are non-specific and similar to other viral infections, particularly respiratory diseases (Prasitsirikul et al., 2020). As the number of COVID-19 patients is increasing dramatically (Han et al., 2020), it is crucial to predict the number of infected cases and deaths considering local health assistance availability. The real number of COVID-19 infected cases is difficult, if not impossible, to obtain since most of the patients presenting mild symptoms are not accounted for. However, the number of patients that present moderate or acute symptoms is particularly important and possible to be estimated. They are the ones that will need sustained medical attention in hospitals and will potentially overburden the health system.
Several diseases can vary from fully asymptomatic to severe symptoms until clinical intervention, demanding for hospitalization and leading to death, which demonstrates the importance of the measurements of the case fatality ratio (CFR) to understand epidemic dynamics and disease burden (Cauchemez et al., 2019).The initial saturation of the number of infected cases observed throughout the third week of April in Figure 1(a), particularly visible in the curves of daily projected cases and deaths, is due to the reduction of social distancing. The social distancing index was about 30 % before the COVID-19 epidemic started in the state, then, it rapidly peaked at about 53 % just before the first reported death. However, the continuous social distancing decrease until now (~38 %) has produced a new rise in infected cases and deaths, clearly observed in the curves of daily projected cases and deaths. The CFR calculated from governmental data and plotted in Figure 1 (b) increased from 1 % to 4.2 % at the end of April, when it slowly decreased to 2.1 % in the second week of July. The model predicts a further decrease to about 1.5 % until the end of the year. In comparison, in the second week of July, Brazil exhibited a CFR=3.8 % and that rate varied between 16.8 % and 2.3 % among the ten countries with the largest reported COVID-19 disease (SUS, 2020). This rate is calculated considering the tested infection cases and deaths only, mainly of hospitalized patients. Therefore, it should be considered biased, non-realistic, and not necessarily an upper limit.
COVID-19 epidemic significantly increased the mortality rate in 2020. Nevertheless, the number of deaths by other causes should decrease due to social distancing and the closing of non-essential economic activities. Deaths caused by transport accidents and assaults were responsible for 52 % of all deaths in Minas Gerais in 2018 (DATASUS, 2020), percentage that should heavily decrease due to the cited reasons. Deaths related to complications in hospital interventions, which are now postponed due to the epidemic, are also expected to decrease. In the same way, the decrease in the economic activities should reduce the number of deaths related to work accidents. Those reductions are clearly visible from the start of the COVID-19 epidemic in Figure 2, except for SARS and COVID-19 related deaths.
We interpret the rise of SARS related deaths as an excess mortality not explained by the officially COVID-19 deaths reported in 2020. The governmental number of deaths is even considerably lower than that reported by the registry office. The projected COVID-19 sub-notification of deaths shows stabilization until the end of the year with a lower bound of about 30 % and upper bound of about 57 %, regarding governmental data. These numbers can be affected by a reduction of the social distancing index which as shown in Figure 1(c), has been continuously decreasing since the epidemic started in Minas Gerais.
The same methodology applied to estimate a more realistic number of deaths can also be applied to retrieve a more realistic estimate of COVID-19 infected cases, as shown in Figure 4(a) and 4(b). Our methodology indicates that in the 28th epidemiological week of 2020, the excess of moderate and severe infection cases was approximately 25 % higher than the officially reported number, with a prevalence of 2.6 %, leading to a projected sub-notification of around 42 % by the end of the year. A recent survey of COVID-19 infected cases (Hallari et al., 2020) reported a prevalence of 0.4 %, with 95 % CI between 0.2 % and 0.7 %, in the southeast region of Brazil. This number is 13 times lower than the value found in our study. Once calculated the excess of deaths and cases, a more realistic CFR was also calculated. This rate increased from about 11 % in week 13th to around 32 % in week 18thand decreased to a saturation of around 2.4 % at the end of 2020. It is important to note that this CFR, calculated with more realistic data (excess of deaths and excess cases data) actually represents an upper limit. A recent estimation of the total number of COVID-19 infected people in the state capital (city of Belo Horizonte) indicates a number 75 times larger than the official one (Aguas, 2020). Applying this factor to the whole state and considering the excess of deaths calculated by our methodology, we can estimate a CFR lower bound of 0.03 % by the end of the year.
Social inequalities in Brazil are intrinsically associated with ethnicities where most black people are among the poorest. A considerable number amount of black people lives in crowded communities, with reduced access to health care. Noticeably, Minas Gerais has 60 % of the population self-declared black, against 39.7% of self-declared white persons and 72 % of black persons are also in the group with 10 % lower incomes (IBGE, 2020). The data presented in Figure 5 shows that 60 % of COVID-19 cases are in black patients, fitting the demographic profile. Nonetheless, in the second half of April, only 55% of deaths corresponded to black patients, which is 5% below the demographic profile. Therefore, we understand that SARS-Cov-2 does not affect differently black and white populations in Minas Gerais. For unknown reasons, deaths among black patients are 5% lower than expected. A recent study suggests that a certain degree of cross protection can exist from previous infection by another coronavirus (Grifoni et al., 2020). We speculate that the self-declared black population can be partially protected, due to being previously infected by another coronavirus. However, further studies are necessary to understand this discrepancy.
The geographic distribution of cases and deaths in Minas Gerais is also notable. The distributions throughout the state are non-uniform, demonstrating high incidence in large urban cores, with several municipalities showing a considerable number of cases and a reduced number of deaths. The large number of deaths seem to be concentrated not only in the capital, but also in cities closer to the state borders. The geographical distribution of cases and deaths in white and black patients follows the geographical distribution of both populations in the state, where the white population is concentrate in the southwest and richer region of the state, while the black population is more concentrated in the northeast and poorer portion of the state. It is striking that even knowing that most of the black population lives in the lowest Human Development Index (HDI) regions of the state, our calculated CRF for black patients is 3.7 % points lower than for white patients.
Mathematical modelling is necessary to predict the behaviour of epidemic variables and to assist authorities in appropriate policies. Several mathematical models have been used to assess deaths and infected cases such as outbreak analytics (Polonsky et al., 2019), data-driven (Ranjan, 2020), stochastic simulations of early outbreak trajectories (Riou and Althaus, 2020), SAIR (Monteiro, 2020) and the spatiotemporal dynamics of a spread applying machine learning (Siettos and Russo, 2013; Science et al., 2020). We applied the Gompertz function and showed how this simple technique can considerably contribute to the analyses of epidemiological data collected during COVID-19 pandemic. Herein, we used a proved, simpler, and intuitive mathematical model that successfully demonstrated our results. This model well reproduced the time evolution data however, has been reported to have systematically overestimated the COVID-19 related prediction in China (Yang et al., 2020). Uncertainties are also present in the used data from public resources, mainly due to collection efficiency and update delays. Therefore, caution is required in the consideration of the absolute predicted number of deaths and cases.
COVID-19 cases increase several folds every 24 h. The increasing number of patients and victims makes it even difficult to maintain a real-time track of the numbers, also due to notification delays and updates of the public databases. In countries with severe inequalities, such as Brazil, a considerable part of patients receives suboptimal attention in the public health system (Villela, 2020). Between the Influenza virus subtype (H1N1) pandemic (2009) and COVID-19, Brazil lost about 34.500 hospital beds (Marson and Ortega, 2020) impairing access of the more vulnerable populations to health assistance.
Notwithstanding, national and regional priorities need to be identified considering the rational use of limited healthcare resources. The resume of non-essential economic activities as well as changes in social distancing drastically alter the epidemic evolution. The social distancing index has dropped below the 40 % level since June in Minas Gerais, approaching the pre-epidemic baseline, accompanied by an increase of 163 % in the number of infected cases and 172 % in the number of deaths, reported by governmental agencies, just in the first half of July. Of course, it is expected that, with improved testing coverage, more cases of COVID-19 will be detected and the clearest picture of the disease burden in Minas Gerais will become evident.