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Introduction:  On December 2019, the province of Hubei in the city of Wuhan, China, was the epicenter of a new type of pneu-monia that did not respond to known treatments (1), in a few days the infections rose exponentially not only in the place of origin but also in different countries. The cause of the disease was a new type of coronavirus, the severe acute respiratory syndrome coronavirus type 2 or SARS-CoV-2, initially called the new coronavirus of 2019 or 2019-nCoV. On March 11, 2020, the World Health Organization declared this disease a pandemic that in just a few months has spread rapidly to practically almost the entire world.

This disease, epidemiologically linked to a wholesale market for live and unprocessed fish, shellfish and animals in Hubei province (2) rapidly spread due to the unappropriated management of infected patients and international air traffic (3). Covid 19 presents symptoms such as: fever, dry cough, loss of smell or taste and tiredness, but also other less common ones such as: aches and pains, nasal congestion, headache, conjunctivitis, burning and sore throat, including in some cases diarrhea, skin rashes or color changes in the fingers or toes. The symptoms are usually mild and come on gradually, in fact some of the infected people have only mild cold-like symptoms. Approximately between 80% and 90% of those infected recovers from the disease without being hospitalized, but around 20% of people who get infected ends up presenting a severe condition and ex- periences difficulties in breathing, requiring intensive care and a mechanical respirator. Older adults and patients with previous medical conditions such as: high blood pressure, heart or lung problems, type 2 diabetes mellitus, chronic kidney disease, obesity (body mass index 30 or higher), COPD (chronic obstructive pulmonary disease), immunosuppressed (weakened immune system) from solid organ transplantation or cancer, are more likely to have severe conditions leading to death.

The first confirmed case has been traced back to 17 November, 2019 in Hubei. As of 9 July, 2020, more than 11.9 million cases have been reported across 188 countries and territories, resulting in more than 547,000 deaths. The COVID-19 pandemic in Mexico began on February 27, 2020. The first confirmed case was detected in Mexico City (a Mexican who had traveled to Italy and had mild symptoms); a few hours later, another case was confirmed in the state of Sinaloa and a third case, again, in Mexico City. Thus, on March 18, 2020, the first death by Covid in Mexico was documented. In the state of Veracruz, the first two cases of Covid 19 were registered in the metropolitan area Veracruz, Boca del R??o on March 17, 2020, and the first death from Covid 19 in the state of Veracruz was reported in Veracruz Port on 29 March, 2020. On March 23, 2020, the national healthy distance campaign begins in Mexico, where recommendations are issued to society such as: teaching the citizen to identify Covid symptoms, covering coughs, frequent hand washing, use of disinfectant gel on the hands, avoiding handshakes and kisses, maintaining physical distance from others, classes were suspended at all educational levels as well as economic-productive activities were reduced to a group of essential activities.

Veracruz is a major port city and municipality on the Gulf of Mexico in the Mexican state of Veracruz. The city is located along the coast in the central part of the state coordinates 19o 11’ 25’’ N, 96o 09’ 12’’ W, Veracruz municipality is settled on a hot, low, and barren sandy beach along the Gulf of Mexico only about 50 feet (15 meters) above sea level. Veracruz is the chief seaport on the east coast of Mexico and is a communications center for the gulf littoral and the tropical and highland hinterlands of Veracruz State. Despite its hot humid climate, Veracruz is an important domestic tourist destination, particularly attractive to weekend visitors from Mexico City. A major commercial fishing port, also offers sport fishing, beaches, and water sports. The city is linked by highway, railroad, and air (international airport) to other major population centers. According to the 2015 census by INEGI (4), the population of the municipality represents the 7.51% of the total population of the state of Veracruz, its area constitutes only the 0.33% of the total area of the state, however up to November 1st, 2020, the municipality contributes respectively with a 22.15% and 20.65% to the total of confirmed and Covid deaths in the state of Veracruz. Several mathematical models have been defined in order to get a better understanding of the Covid transmission process. The vast majority are deterministic, based on compartments (4) and defined as nonlinear systems of ordinary differential equations. (5-9) These models are in fact variants of the famous model due to McKendrick and Kermack (10) . Epidemiological quantities such as: the basic reproduction number (11), transmission, latency and recovery rates are estimated by fitting the models to historical data (12). De- terministic models assume an initial state at and allow the computation of the state of the variables at time by using the state of the variables at the previous time , they also assume that the populations are perfectly mixed, with no spatial or social aspect to the epidemic. The work is organized as follows: section 2 describes the main assumptions and the models employed to estimate Covid spread in this mu- nicipality. Those include: Pearson correlation coefficients, Richards model and machine learning projections. Section 3 shows some numerical calculations. Finally at section 4 we include some conclusions of this work.

Data Analysis and Models for COVID spread: All the data (Covid confirmed cases and deaths) employed in this study were obtained at the official website of public health ministry of the state of Veracruz (12). Figure 1 shows the geographical location of the municipality of Veracruz, Figures 2 and 3 respectively show the number of confirmed cases and Covid deaths biweekly reported. Figure 4 shows the weekly evolution of lethality also called Case fatality rate (number of deaths/over number of confirmed cases), the mean case fatality rate for the analyzed data is 13.24% .

Numerical computations: Weather information was obtained from Chowell (13), and from the reports of Ministry of Public Health of the State of Veracruz (14). Monthly data (March to October 2020) for: mean temperature (Celsius), maximum temperature (Celsius), minimum temperature (Celsius), mean wind speed (Km/h), average sunshine hours, sea level pressure (hPa), rainfall (mm), humidity comfort, average sea water temperature (Celsius), solar energy (Kwh), clouds cover percentage and relative humidity. All these weather variables together with the number of confirmed and death cases were tested for correlation. Here Pearson correlation coefficients between the variables x and y are calculated with the formula. Here x , y denote the mean of x and y  respectively. We base the humidity comfort level on the dew point, as it determines whether perspiration will evaporate from the skin, thereby cooling the body. Lower dew points feel drier and higher dew points feel more humid. Table 1 reports the number of monthly confirmed positive and deaths for the municipality of Veracruz from March to October 2020. Four variables turned out to be correlated with the number of confirmed Covid cases (Statistical significance). Table 2 shows their correlation coefficients (cloud cover percentage negatively correlated). Figure 5 shows these correlated variables.  The more people get sick, the number of deaths increases. In this particular case the mean case fatality rate for the analyzed data is 13.24% mainly related to comorbidity risk factors (15), which makes mandatory to implement more restrictive measures to reduce infections in order to avoid more deaths. The found correlation of confirmed Covid cases with humidity and sea water temperature does not conflict with previously reported results. As concluded by Mecenas et al (17), who reviewed the existing scientific evidence, concluding that warm and wet climates seem to reduce but do not avoid the spread of Covid-19. They suggest that these variables alone could not explain most of the variability in disease transmission. Consequently the countries most affected by Covid-19 should focus on health policies, even with climates less favorable to the virus.

In SIR and SEIR models were used to calculate the basic reproduction number for the state of Veracruz, here we employed a SIRD to estimate the basic reproduction number for the municipality of Veracruz (19). In this model S, I, R, D respectively represent the com- partments: Susceptibles, Infected, Recovered and Deaths. The constant is assumed 0.13 from the historical data, while are obtained by fitting the SIRD model to biweekly Covid data. The basic reproduction number in this case is R0=1.22. Figure 8 shows the fitted graph for the infected curve and the data. Figure 8 shows Curve of Covid infected obtained by a SIRD model fitted to biweekly data. Making accurate predictions is quite a difficult task, instead a monitoring system can be very useful in order to make decisions such as: reduce human mobility, mandatory rules as wearing mask o closing public places, business etc. For monitoring purposes machine learning can be valuable tools. Machine learning is an application of artificial intelligence (AI) that provides systems the ability to automatically learn and improve from experience without being explicitly programmed. Figure 9 shows the curve of infected by using a simple machine learning function of Mathematica Wolfram (19). Here we notice an oscillatory behavior of the curve in the last weeks, thus this monitoring suggests that more drastic measures must be taken in order to reduce the number of infected and avoid the oscillatory behavior that would extend the epidemic indefinitely (20). 

Discussion:  There is no perfect mathematical model that can accurately predict the spread of Covid, however different models can be used to promptly answer particular questions about the spread of Covid such as: does the weather affect the spread of Covid favorably or unfavorably? What is the average rate of infections that we have? How many people could become ill in the course of the illness?, how many could die?, how can we monitor and make short-term projections (2 weeks) that help us to make decisions? The employed models have provide us with some estimates and projections of the Covid spread at the municipality of Veracruz, the information they generate can be useful for decision-making at different stages of the disease. 

Conclussion: Statistical analysis on environmental data and data from the Covid epidemic has shown that confirmed cases are posi- tively correlated (Pearson coefficient) with number of Covid deaths, sea water temperature, and humidity comfort while negatively correlated with clouds cover percentage. The basic reproduction number was obtained by fitting data of cases to a SIRD ode model. Estimates for the number of confirmed cases and deaths projected to a few weeks ahead were provided by fitting a modified Richards growth models to historical data. While machine learning functions may be useful for monitoring and assisting in decision-mak- ing during the course of the disease.

Palabras clave: Covid-19 SIRD Modelo Richards Correlación Pearson

2021-08-21   |   336 visitas   |   Evalua este artículo 0 valoraciones

Vol. 15 Núm.2. Julio-Diciembre 2020 Pags. 25-30 Rev Invest Cien Sal 2020; 15(2)