{'fraction_non_alphanumeric': 0.030810717769235184, 'fraction_numerical': 0.018647082448792242, 'mean_word_length': 4.87858347386172, 'pattern_counts': {'":': 0, '<': 1, '<?xml version=': 0, '>': 1, 'https://': 6, 'lorem ipsum': 0, 'www.': 6, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Prediction of the propagation of SARS-CoV-2 in Amapá State, Amazon Region, Brazil, by mathematical modeling

This article presents an analysis of the spread of SARS-CoV-2 in Amapá using three approaches. In the first, the ICL model for the pandemic applied to Brazil was used to implement a comparative linear projection for the Amapá population. The second approach was developed with the short-term solution of the standard SIR model where it was shown that the typical exponential behavior satisfactorily describes the data for the first weeks of the epidemic, but soon after there are early discrepancies due to a sudden slowdown in the temporal evolution number of cases due to isolation measures. This new regime is appropriately described with the third approach which is based on the vSIR model which is a variant of the SIR model. The results presented enable, on the one hand, a better understanding of the scenarios already faced by the population and on the other hand provide short-term projections that will be constantly updated on the link[11].


INTRODUCTION
Tangenced by an unrestrained spread of the new coronavirus in Amapá, let us think of families alienated from the labor force and in social isolation, prevented from carrying out their profession. Under these conditions, the only solution is to wait for the illness to pass, causing other problems such as anxiety, depression, post-traumatic stress, irritability, among other psychological impacts of the quarantine. For their response to the negative impacts, people also suffered from predictive facts such as: fear, sadness, guilt, confusion, for not being able to find a work or hobby solution on their own. Part of these psychological contexts mentioned is perceptible in all classes and social levels of the State of Amapá, starting mainly with health professionals who work and are always at the forefront of care centers that have been inadequate and insufficient for years lived behind of an alarming political system of democratic inequality (BROOKS, 2020).
In the existing cataloging at the different levels of urban and peripheral social groups in the state of Amapá, a city like Macapá and Santana are the two municipalities where the disease is most concentrated. According to the Superintendence of Health Surveillance SVS, this researched statement was based on the period from April 14th to 27th, always showing the concentrating characteristics of COVID-19 in the city center of Macapá, where it all started, this is due to people who traveled abroad state and returned. It is concluded that then the effect of the expansion of contamination is given by imported people that we will call Class A and B (Socioeconomic Classification https://www.nucleodoconhecimento.com.br RC: 50449 Disponível em: https://www.nucleodoconhecimento.com.br/health/prediction-of-the-propagation Criterion). Partly opposed to the confirmations of the under pressure epicenter of COVID-19 in downtown Macapá, Santana is ratifying its concentration statistics in all possible urban and peripheral areas of necessary intercity commuting for family reasons, residential or not (direct contact), even with the containment measures applied by sanitary barriers. This panorama will be presented by the group of people of Class C, D, E, framed in the dependence on the use of public and private transportation (SVS, 2020).
In this idea commented above, we have integrated a framework model for the relations of classes or social groups of isolation, measured by income and well-being among Amapá people (IN LOCO, 2020). the classes A and B willing to fulfill isolation, part of this fulfillment is due to these people having companies, jobs and fixed salaries of public servants in career. Contrary to the other remaining social classes C, D and E, there is a criterion of the combined wage pattern between contributing parts of the family fixed income (financial dependence), and formal and informal temporary jobs for the expected well-being, regardless of whether or not he is a public career employee. or academic training. This is the reason for the growing breach of social isolation, which reaches 60% with a tendency to grow even more during the current months (IBGE-AMAPÁ, 2020).

AIM
This research aims to analyze the incidence of confirmed cases of COVID-19 in Amapá / AP /Brazil using statistical methods and mathematical models in order to understand the dynamics of contagion of the virus, providing information to promote a more effective combat strategy against the covid-19.
Among other driving specifications, it is intended to verify the forced behavior of social restriction in the public and domestic environment, given as one of the priority care conditions for the proliferation reduction of contagion by Coronavirus.

METHOD
In general, two modeling approaches have been used to gain insights into the epidemic evolution related to Sars-CoV-2. On the one hand, there is an effort to develop sophisticated models that take into account several variables that can describe the epidemic dynamics. Such an approach was used, for example, in Zhang (2020) with a system of 15 differential equations. On the other hand, a mathematical vision has also been adopted focusing on the main epidemic characteristics of the contagious process of success for the epidemic curve of the coronavirus through primary or extended versions of the SIR models (TODA, 2020;KATUL, 2020;ZHONG, 2020). The SIR epidemiological model proposed by Kermack andMcKendrick in 1927 (HETHCOTE, 2000) is one of the classic models used to describe the evolution of the infectious disease contagion process. This model composed of differential equations employs the compartment strategy and divides, in relation to the disease, the population into individuals who can contract, individuals who can transmit and https://www.nucleodoconhecimento.com.br RC: 50449 Disponível em: https://www.nucleodoconhecimento.com.br/health/prediction-of-the-propagation individuals who have recovered and are not subject to new contamination called susceptible (S), infected (I) and recovered (R) respectively.
Mathematically, a SIR model can be represented using the following differential equations: where β is the disease transmission rate, is the recovery rate of individuals, both are positive and characteristic parameters of the data under analysis.
In order to optimize and estimate these parameters so that the reported and simulated cases are approximately equal, initial values are used for the three-state variables (0), (0) and (0).
The initial value (0) is the population community affected by the outbreak, while (0) is the number of confirmed cases that can have any value, but not zero. We can set (0) to zero if the spread and simulation start times are the same. The transmission rate reduces monotonically over time (HARKO, 2014).
Solving the system (1) we determine the solution function for the susceptible population and we obtain (BATISTA, 2020). According to Ghani and Fergunson (2020), the R0 value for COVID-19 has varied between 1 and 7 (more precisely 1.1 to 6.95) throughout the development of the epidemic. As indicated by Delamater et al (2019), an R0 <1 shows that the number of infected people decreases with time and the epidemic tends to eradicate, for values of R0> 1 it is assumed that the epidemic must persist in the population for a long term.
Thus, taking the limit when t tends to infinity, the number of susceptible people obtained is: Where is the final amount of recovered. Considering that the final number of infected people is zero, we have: From (03) we get D and E) Suppression -we explore different epidemiological triggers (deaths per 100,000 inhabitants) for the implementation of large-scale intensive social detachment (modeled as a 75% reduction in interpersonal contact rates) with the aim of quickly suppressing transmission and minimizing short-term cases and deaths.
For these scenarios, we do not produce final size estimates, but we illustrate their impact on representative configurations. For Tardia, it is considered conducting mass tests, isolating positive cases and monitoring people close to those diagnosed from 1.6 deaths per 100 thousand inhabitants per week. For Precoce, the same measures as before, but adopted from 0.2 deaths per 100 thousand inhabitants per week (GHANI; FERGUSON, 2020). The scenarios exposed by ICL for a population in Brazil of more than 200 million people at the present time, are extrapolated (due to the fundamental premise of minimizing impacts for the population) are as follows: Scenario A -No mitigation measures; Scenario B -With social distance from the entire population. In Scenario A, the Brazilian situation is reckless, and depending on the scenario, with percentages of infected people ranging from 88% and lowering up to 5% of the population, to the number of deaths ranging from 1% to 0.02%. There is also a third scenario -C -that It is important to reiterate the concern with the obvious adaptations of ICL modeling in relation to the socio-cultural and socio-economic characteristics of our country. At the same time, the data from the ICL modeling scenarios are extrapolated numbers and may, in this sense, constitute an exaggeration. In this sense, in a preventive way, verifying the propensity for the next days of multiplication of national cases and the still current implantation of the local testing system and the imminent arrival of rapid testing exams -which are likely to be under-sufficient and will be focused on symptomatic population, which delays the improvement of any projection due to the immediate incubation period to contagion and, therefore, muddies the real perception of the epidemiological picture -it is considered probable that the transition from Scenario D to C is possible. If this transition is confirmed, prospects of securitization of the city through traffic zoning of people and goods will be inevitable (Wuhan model of confinement reinforced by restriction to intrazonal traffic) to reach the desirable 60% -75% restriction, noting that case mapping by region would be positively determinant in helping to contain community transmission more accurately and observe both contaminated and elderly people. The advance and massification of tests, social distance, prioritization of the location of elderly and co-morbid patients, as well as the isolation of those diagnosed, are decisive in this regard (ZORZETTO, 2020).

ACCUMULATED CASES OF COVID-19 IN AMAPÁ
The time series with confirmed cases of covid-19 for the State of Amapá belongs to the section from March 25 to May 12. In this period, the referred State presented the following evolution of individuals tested positive, mortality and recovered:  As seen in figure 2, in (A), Amapá took 50 days to leave 1 case for 2910 (03/25 to 05/12). As of the closing date of the study, the state had one of the highest relative rates of cases with around 355.3 per 100,000 inhabitants, drawing attention from the entire country because it is a state with less than 1 million inhabitants.
Based on this scenario, at the beginning of the epidemic temporal evolution for Amapá, we can assume S ≅ N. Thus, the equation for dI / dt in the system (1) becomes: Where R0 = β / ϒ . After a direct integration we obtain: To obtain a first estimate of R0 we apply a linearization of the above equation. In this way we obtain log (I (t)) = mt + lgo (I0), where we have the slope m = ϒ (R0-1). The fit Regarding the exponential growth phase of covid-19 cases, in Figure 3 there is a satisfactory agreement between the observed data and the theoretical forecast (red curve) until April 14. However, immediately afterwards there is an early discrepancy of the preliminary fit with the data, which raises questions about the reason for such

Figure 4 vSIR simulation and confidence interval
The simulation of the vSIR model from 25.03 until 12.05.2020 shown in Figure 03 shows the confidence interval (CI) that defines the upper and lower limits of the simulated values in order to give a 95% probability of including the real value of predictive cases. There are two outlier points that occur on 01. May.2020 and 02.
May.2020, Friday and Saturday respectively. These dates that involve the national holiday of the labor day and whose number of infected people do not live up to expectations raise questions involving the procedural method of collecting information that will be investigated later from an analysis of data in loco. It is also noteworthy that the model was calibrated based on the actual data of infected people since the beginning of the pandemic in the state.  represents dates when the model is most effective in prediction (close dates), while the red area represents dates when the model can fail in prediction (BATISTA, 2020).
The estimated parameters for the Amapá data, using MATLAB's fminsearch programming, developed by Batista (2020), were as follows: Table 6 Estimated parameters in the vSIR model Figure 6 Daily evolution of R0.
The daily evolution of R0 shows that the lowest values occurred between April 26 (R0 26/04 = 1.12) to May 3 (R0 03/05 = 1.1) this period of low R0 may be indicating that the government decree of April 3 helped to reduce the basic reproduction rate, but not enough to lower its value below 1, which is ideal for controlling the epidemic. As of May 3, R0 rose again, being on the 12/5 at the level of 2.11, this increase may indicate relaxation of the quarantine by the population, whose relationship with R0 is inverse,

STUDY LIMITATIONS
While in the SIR model there are only two parameters to be estimated (namely the transmission rate β and recovery γ), in the vSIR model we have the possibility to estimate an additional parameter which is the effective size of the population N. With these three parameters {β , γ, N} we can satisfactorily describe the time series for the number of confirmed cases in the state of Amapá.
Our modeling can also be improved in future works considering the following limitations: • There is a limitation of the linear and general application of the ICL Model, on the one hand, and on the other, possible inaccuracies must be observed due to the interdependence and complexity of the specific conditions of human development in Brazil -already mentioned, such as concentration accentuated demographic in dozens of cities, precarious conditions of basic sanitation in needy communities, dwellings with inhabitants per room above the recommended by the World Health Organization (WHO), historical absence of other experiences of sanitary emergency with measures of this size and standard. In other words, Brazil has a specific proportion and demographic conditions, which makes the general models inaccurate.
• The underreporting of covid-19 cases is a factor that has been reported repeatedly around the world, which in the Brazilian case, due to the reduced number of tests, makes the incidence of this factor to be critical. For example, recently ~ 86% (95% confidence interval: 82-90%) of underreporting was estimated in the early stages of epidemic evolution when travel restrictions were not yet imposed (LI, 2020). For Amapá, there are estimates that project an underreporting rate of ~ 11.2%, according to a technical note published on April https://www.nucleodoconhecimento.com.br RC: 50449 Disponível em: https://www.nucleodoconhecimento.com.br/health/prediction-of-the-propagation • The vSIR model does not take into account the number of asymptomatic cases.
For example, in the review article by (BUITRAGO-GARCIA, 2020) an upper limit for the proportion of asymptomatic SARS-CoV-2 infections of ~ 29% (95% confidence interval: 23-37%) was estimated. One strategy to obtain an estimate of the fraction of asymptomatic cases in Amapá is to invest in testing a massive proportion of the population.

CONCLUSIONS
In the first approach, a comparative linear projection of the ICL model was developed for COVID-19 applied to Brazil for Amapá, whose conclusions point to the urgency of measures of social isolation as early as possible, considering the need to avoid massive contagion and accelerated in the locality. We also sought to observe the general conditions of the pandemic context. There is an inaccuracy with regard to the effective speed of transmission and infection, although surrounded by some degree of measurement, months after the beginning of a declared pandemic, it directly implies the observation of the respective local standards.
The second approach was mediated by the short-term solution of the SIR model equations. Such a solution provided the typical exponential growth that was shown to be in agreement with the data observed up to April 14th allowing the obtaining of a preliminary estimate of Ro between [1,340,3,271]. In the following days there is an abrupt and early discrepancy in the exponential fit due to the isolation measures adopted.
In the third approach, the vSIR model was applied to the actual infected data. It was verified that the basic reproduction rate R0 for Amapá is ~ 2.11, showing that the epidemic in this state is in full expansion, this fact is even worse with the information of social isolation that shows that the State, in the light the first quarantine decree reached 56% of its citizens isolated on April 5, however, that number dropped to 43% on April 12.