Generalized models and the impacts of population density on COVID-19 transmission

Objective: to analyze epidemic curves based on mathematical models for the state of Mato Grosso do Sul and the impacts of population density on COVID-19 transmission. Method : the linear, polynomial and exponential regression model was used to make the numerical adjustment of the respective curves empirical. Result : it was found that the models used describe very well the empirical curves in which they were tested. In particular, the polynomial model is able to identify with reasonable reliability the appearance of the inflection point in the accumulated curves, which corresponds to the maximum point of the respective daily curves. The analysis indicates a weak positive correlation between infection, mortality, lethality and deaths from COVID-19 with population density, as revealed by the correlation and analysis of R 2. Conclusion : the models are very effective in describing the COVID-19 and epidemic curves in the estimation of important epidemiological parameters, such as peak case curves and daily deaths, allowing practical and efficient monitoring of the evolution of the epidemic. Descriptors


INTRODUCTION
Anastassopoulou et al 5        The linear and non-linear regressions of the cumulative number of cases and deaths as a function of time were both significant.For the cumulative number of cases, the best fit was achieved using the second-degree linear regression, while for the cumulative number of deaths, the exponential regression with 2 parameters was the best model (Table 2).The curvilinear shape of the total cases and accumulated deaths (Figure 3).The parameters β1 and β2 of the second-degree linear regression represent the linear and quadratic effects, respectively, which shows that the accumulation of cases and deaths had a higher rate of increase in the periods between July and October, with a slight decrease before a more expressive new rate, starting in November.
From the second week of May 2020, there was a significant increase in the

DISCUSSION
The state of Mato Grosso do Sul

Participação dos autores:
Since the first case of infectionwith the new coronavirus (Sars-Cov-2), which causes COVID-19, in Wuhan, China, in December 2019, the virus has already spread to virtually every country, leading to one of the biggest global health crisis in the last 100 years.In Brazil, Sars-Cov-2 infection was first confirmed in the city of São Paulo on February 26, 2020.Since then, the epidemic has spread throughout the country, which has forced several Brazilian states and municipalities to adopt measures of social isolation and other mitigation measures to contain the spread of the virus.Mathematical models have received unprecedented attention and have been widely used during the current pandemic as a strategic tool to predict the incidence, prevalence and mortality rate of COVID-19 worldwide.Popular statistical methods currently in use for studying and forecasting COVID-19 pandemic are based on the classical SIR model which consider Susceptible, Infectious and Recovered individuals 1 , and its various modifications, in particular the incorporation of Exposed but non-contagious individuals producing the SEIR model 2 .Roda et al 3 , for example, correlated the standard SIR and SEIR structures to the COVID-19 model in Wuhan, China.Fanelli 4 have incorporated the number dead individuals' data within a simple susceptible-infected-recovered-deaths (SIRD) model to studiy the temporal dynamics of the COVID-19 pandemic in mainland China, Italy and France.

Figure 1 -
Figure 1 -Number of daily new and accumulated cases of COVID-19 in Mato Grosso do Sul in the period from March 14, 2020 to January 31, 2021.

Figure 2 -
Figure 2 -Moving average of the last 7 days for the number of new and new deaths due to COVID in Mato Grosso do Sul in the period from March 14, 2020 to January 31, 2021.
Figure 3 -Linear and non-linear regressions for temporal characterization of the number of accumulated cases and number of accumulated deaths in Mato Grosso doSul in the period from March 14, 2020 to January 31, 2021.

Figure 4 -
Figure 4 -Variation in the rate of a) infected, b) mortality, c) lethality and d) deaths due to COVID-19 with population density in the municipalities of Mato Grosso do Sul. 1

Table 1 -Non-parametric tests for verifying trends in the moving average of cases and deaths by COVID in Mato Grosso do Sul in the period from March 14, 2020 to January 31, 2021.
The scatter plot of the total (cumulative) of cases of infection, mortality, lethality and deaths of people in relation to population density for the declared municipalities is shown in Fig.4.It was found that the rate of infection and mortality is higher in metropolitan cities with high population density.On the other hand, it is noted that the spread of COVID-19 and related deaths are low in districts with low population density.The situation is not very clear in districts with moderate density; data points spread across the graphics area with a slight tendency to increase infection and death with density.
number of cases of COVID-19, mainly until 07/22 where it reached a value of 1503 cases.Later, a decrease to 968 cases on 07/29 was observed, rising again until 08/22 with 1177 cases, decreasing on 11/11 to 138 cases, rising again until 12/31 with 1220 cases.For deaths, there was also variation, but to a lesser degree.The highest growth rates occurred mainly in the first half of the analyzed period (08/16) with 28 deaths, then there was a fall from 11/13 to 11/30, with greater stabilization in this period, SARS-CoV-2 virus is carried out using real-time RT-PCR techniques (considered the gold standard for the identification of the new coronavirus) or rapid serological test validated by reference institutions 23 .

Table 2 -Adjustment parameters and statistics for linear and non-linear regressions in Mato Grosso do Sul in the period from March 14, 2020 to January 31, 2021.
Os autores declaram que não houve financiamento.
25ndemic in Mato Grosso do Sul, the contingency of the virus was effective.Reports in which the increase in cases of COVID-19 in Brazil occurred since April are extensive25.In the case of COVID-19, there is Financiamento: