Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 8, No. 6, 7782-7790 2024 Publisher: Learning Gate DOI: 10.55214/25768484.v8i6.3687 © 2024 by the authors; licensee Learning Gate © 2024 by the authors; licensee Learning Gate * Correspondence: omarin@unfv.edu.pe Mathematical modeling of global covid-19 fatalities Marín-Machuca Olegario1*, Humala-Caycho Yuri Esquilo2, Chinchay-Barragán, Carlos Enrique3, Yataco-Velásquez, Luis Andrés4, Rojas Rueda, María del Pilar5, Bonilla-Ferreyra, Jorge Luis6, Luis Adolfo Perez-Ton7, Marín-Sánchez Obert8 1School of Food Engineering, Faculty of Oceanography, Fisheries, Food Sciences, and Aquaculture. Research Group on Environmental Sustainability (GISA), Graduate School (EUPG). Universidad Nacional Federico Villarreal (UNFV), Lima. Peru. omarin@unfv.edu.pe (M.M.O.). 2School of Aquaculture Engineering. Faculty of Oceanography, Fisheries, Food Sciences, and Aquaculture. Universidad Nacional Federico Villarreal. yhumala@unfv.edu.pe (H.C.Y.E.). 3Professional School of Food Engineering, Faculty of Fisheries and Food Engineering, Universidad Nacional del Callao. Callao, Peru. cchinchayb@unac.edu.pe (C.B.C.E.). 4Public Administration and Management Program, Faculty of Business. Universidad Privada del Norte. Lima, Peru. luis.yataco@upn.pe (Y.V.L.A.). 5School of Human Medicine, Norbert Wiener University, Lima, Peru. maria.rojasr@uwiener.edu.pe (R.R.M.D.P.). 6Graduate School in Public Management, Universidad Autonoma del Perú. Lima, Peru. jbonillaf@autonoma.edu.pe (B.F.J.L.). 7Professional School of Food Engineering, Faculty of Fishery and Food Engineering, National University of the Callao, Callao, Peru. laperezt@unac.edu.pe (L.A.P.T.). 8Faculty of Medicine, Universidad Nacional Mayor de San Marcos. Lima, Peru. omarins@unmsm.edu.pe (M.S.O.). Abstract: Objective. Determine was mathematically modeled using the expression 𝑁 = 𝑀 (1 + 𝑄 × 𝑒−𝑘×𝑡)⁄ , which is a predictive equation. Using this model, the number of deaths due to COVID-19 worldwide was estimated.Design. Correlational, prospective, predictive and transversal study. Participans. The data on deceased individuals due to the COVID-19 disease up to November 5, 2022, was considered. Main measurement. This data was used to analyze the pandemic dispersion, which was determined to exhibit logistic sigmoidal behavior. By deriving Equation 3, the rate of deaths due to COVID-19 worldwide was calculated, obtaining the predictive model represented in Figure 3.Results. Using Equation (5), the critical time 𝑡𝑐 = 447 𝑑𝑎𝑦𝑠 and the maximum speed ( 𝑑�̂� 𝑑𝑡 )𝑚á𝑥 = 1 525 028,553 𝑝𝑒𝑟𝑠𝑜𝑛𝑠/𝑑𝑎𝑦 and the date when the global death rate due to COVID-19 reached its maximum was July 6, 2021. The Pearson correlation coefficient between the elapsed time (𝑡) and the number of deceased individuals (𝑁) worldwide, based on 33 cases, was 𝑟 = −0,9365. Conclusions. This indicates that the relationship between elapsed time and the number of deceased individuals is real, with no significant difference, showing that the predictive model provides a high estimation of the correlated data.There is a "very strong correlation" between elapsed time (𝑡) and the number of deceased individuals (𝑁) with 87,7 % of the variance in 𝑁 explained by 𝑡, ue to the COVID-19 disease. These models help us predict the behavior of disease like COVID-19. Keywords: COVID-19 disease, Estimation, Global fatalities, Logistic modeling, Validation. 1. Introduction The 2019 coronavirus is a virus that causes a respiratory disease, spreading from person to person. It was first identified at the end of 2019 during an investigation of an outbreak in Wuhan, China. It is now known as Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2), responsible for causing COVID-19. In open environments, it remains suspended in the air and can travel greater distances due to atmospheric turbulence1 remaining viable for less than three hours. Experimental https://orcid.org/0000-0002-0515-5875 https://orcid.org/0000-0003-4363-5930 https://orcid.org/0000-0003-0053-4865 https://orcid.org/0000-0003-0502-5808 https://orcid.org/0000-0003-3812-7579 https://orcid.org/0000-0003-2704-8066 https://orcid.org/0000-0001-7040-1502 https://orcid.org/0000-0003-2912-1191 7783 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 8, No. 6: 7782-7790, 2024 DOI: 10.55214/25768484.v8i6.3687 © 2024 by the authors; licensee Learning Gate studies have shown that the virus can remain viable for at least three hours in aerosols, 24 hours on cardboard, and up to 72 hours on plastic or stainless-steel surfaces. The virus has been detected in the gastrointestinal tract, feces, saliva, and urine, representing potential transmission routes that require further evaluation in the near future2. Existing studies on the influenza virus have shown that its airborne transmission is sensitive to climatic conditions3. Its transmission increases in the presence of cold air and low humidity4; as observed when saliva droplets expelled by infected individuals while speaking or breathing remain suspended in the air, potentially spreading the disease5. It is believed that the virus originated in bats and was transmitted to humans in a seafood and live animal market in Wuhan, China, through an intermediate host sold as an exotic species. Approximately 55% of the initial cases were reported in that location. Subsequent transmission occurred through various human activities, with the incubation period being less than 14 days in 95% of cases, supporting the implementation of a 14-day quarantine period6,7. In March 2020, the World Health Organization (WHO) declared the COVID-19 outbreak a pandemic8. After nine weeks of sustained transmission, officials from Hubei province reported 64,084 confirmed cases, with 2,346 deaths. The actual number of cases is likely much higher, as only the most severe cases were included in the reports due to a shortage of testing kits. The rapid spread of the virus is significantly higher compared to the 2003 SARS-CoV outbreak, suggesting that SARS-CoV-2 is much more transmissible9. Chinese authorities responded on January 23, 2020, by placing millions of people in Hubei province under quarantine. It is estimated that five million people left Wuhan before the lockdown began, leading to a sudden increase in cases in the surrounding Chinese provinces10. On January 30, 2020, the WHO Director-General reconvened the Emergency Committee (before the 10-day deadline) and just two days after the first cases of person-to-person transmission of the coronavirus outside China were reported. This time, the Emergency Committee reached a consensus and recommended to the Director-General that the outbreak constitutes a Public Health Emergency of International Concern (PHEIC), marking the sixth time the WHO has declared a PHEIC since the International Health Regulations (IHR) came into effect in 200511. On March 18, 2020, the WHO and its partners launched the "Solidarity" trial, an international clinical trial aimed at generating robust data worldwide to identify the most effective treatments against COVID-19. It was acknowledged that transmission among asymptomatic individuals had been the primary cause of the SARS-CoV-2 pandemic's spread12. Wang and Cowled10 mention that fever is the most common symptom, while Guan¹³ indicate that only 43.8% of patients had a fever at the time of admission, although the majority developed it during their hospital stay. Yang14 refers to the fact that 11% of critically ill patients did not present with fever at the onset of symptoms, with alveolar infiltration being the most common radiological pattern. In China, 80% of confirmed cases exhibited mild to moderate symptoms, 13.8% had a severe clinical course (dyspnea, tachypnea ≥ 30/min, O2 saturation ≤ 93%, and pulmonary infiltrates in ≥ 50% of radiological fields within 24–48 hours), and 6.1% presented a critical course (respiratory failure, septic shock, and/or multiorgan failure). However, the number of asymptomatic individuals remains unknown11. The possible risk factors include age, sex, smoking, chronic obstructive pulmonary disease, coronary disease, diabetes, hypertension, carcinoma, chronic kidney disease, and other comorbidities. In a univariate study, the variables significantly associated with higher mortality were age, coronary disease, diabetes, and hypertension11. The global evolution of COVID-19 fatalities up to November 5, 2022, the mathematical statistical modeling, the critical time (in days), the rate at which fatalities occurred, and the validation of the estimated data, along with other global public health indicators, represent a significant prevention challenge. These factors undoubtedly serve as reference data for addressing similar issues of mortality in the future. A logistic-type mathematical model is a tool that helps analyze and estimate disease cases, aiming to describe, explain, and predict epidemics in defined geographical areas. It is used to understand the 7784 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 8, No. 6: 7782-7790, 2024 DOI: 10.55214/25768484.v8i6.3687 © 2024 by the authors; licensee Learning Gate dynamics of dispersion and, in this case, mortality caused by the disease across various scenarios. Modeling requires the use of tools from infinitesimal calculus15. Marín16 mentions that modeling for COVID-19 was based on determining the relationship between the variation in the number of reported cases (𝑑𝑁) and the variation in elapsed time (𝑑𝑡), referred to as the rate of reported cases with respect to elapsed time. To estimate COVID-19 infections, the corresponding predictive logistic model was developed. Manrique17 highlights that mathematically modeling cases and phenomena involving the exponential function of the form 𝑁 = 𝑀 (1 + 𝐴𝑒𝑘×𝑡)⁄ is essential. Failing to apply statistical, mathematical, logistic, and parameter validation knowledge, as well as variation factors, to relate, estimate, predict, or correlate data of a dependent variable such as mortality in terms of one or more independent variables, such as elapsed time or event dates, leads to an imminent scientific preventive gap. The objectives of this study were to analyze mortality behavior due to COVID-19, compare representations between actual and estimated fatalities, estimate the critical time (in days) to determine the maximum mortality rate, and statistically validate the reliability of the models. 2. Methods 2.1. Statistical Data The methodology used was based on the specific growth constant (k), where the conditions of the process impose constraints on the number of deaths caused by COVID-19 worldwide, considering that the constant k decreases as the number of deaths increases. This assumes that the k of the deceased (growth or decline) depends solely on the number of individuals and not on time-dependent mechanisms, such as non-seasonal phenomena. This led to the determination of a logistic equation whose solution is a logistic function. A mathematical model is a mathematical description, often through a function or equation, of a real-world phenomenon, such as the number of global fatalities caused by COVID-19. Its purpose is to understand deaths and, potentially, make predictions regarding future behavior. The stages covered included: 1) the problem of modeling the number of infections as a function of time; 2) formulating and selecting the logistic model through data dispersion analysis; 3) determining the model, analyzing it, and drawing mathematical conclusions; and 4) making predictions (estimations) about the number of deaths caused by COVID-19 worldwide. It is acknowledged that a mathematical model is never a completely accurate representation; it is an idealization that simplifies the reality of the number of global fatalities caused by COVID-19, yet it is sufficiently precise to support valuable conclusions and foster relevant discussions. As of February 25, 2023, around 6,832,204 fatalities due to the coronavirus (SARS-CoV-2), caused by COVID-19, have been recorded worldwide. The virus initially originated in the city of Wuhan (China) and has since spread to every country in the world. The accumulated cases of fatalities worldwide as a function of elapsed time (days) are presented in Table 1. Table 1. Statistical data on the number of fatalities due to COVID-19 worldwide as a function of elapsed time (days). Date Time, t (days) N (Number of fatalities) 03/31/2020 0 47205 04/14/2020 13 144532 05/26/2020 42 384344 06/17/2020 63 489619 07/05/2020 84 576857 08/16/2020 126 825733 09/20/2020 161 1 021 306 10/18/2020 187 1 174 969 11/29/2020 229 1 528 933 12/15/2020 243 1 707 231 7785 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 8, No. 6: 7782-7790, 2024 DOI: 10.55214/25768484.v8i6.3687 © 2024 by the authors; licensee Learning Gate 01/18/2021 278 2 124 707 02/09/2021 299 2 431 542 03/24/2021 342 2 852 496 04/27/2021 376 3 260 857 05/07/2021 387 3 400 028 06/18/2021 429 3 862 475 07/16/2021 457 4 087 826 08/13/2021 485 4 345 952 09/25/2021 527 4 745 551 10/23/2021 561 4 948 224 11/06/2021 575 5 048 856 12/30/2021 631 5 436 623 01/29/2022 659 5 665 031 02/26/2022 687 5 946 761 03/25/2022 715 6 115 681 04/08/2022 728 6 168 449 05/20/2022 770 6 262 426 06/17/2022 798 6 302 937 07/31/2022 842 6 382 570 08/30/2022 873 6 454 522 09/16/2022 889 6 488 025 10/18/2022 921 6 534 601 11/05/2022 947 6 563 777 12/15/2022 987 6 625 253 01/20/2023 1023 6 761 565 02/25/2023 1059 6 832 250 Note: Pan american health organization18. Figure 1. Representation of the number of fatalities due to COVID-19 worldwide as a function of elapsed time (days). In Figure 1, the evolution of accumulated cases over time is plotted, showing that the number of accumulated cases increases as time progresses. 0 1000000 2000000 3000000 4000000 5000000 6000000 7000000 8000000 0 200 400 600 800 1000 1200 N u m b er o f fa ta lit ie s Time (days) 7786 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 8, No. 6: 7782-7790, 2024 DOI: 10.55214/25768484.v8i6.3687 © 2024 by the authors; licensee Learning Gate Statistical Treatment. Hernández19 mentions that in the statistical treatment of correlated data, the Pearson correlation coefficient is used, which provides a relative interpretation and indicates the magnitude of the relationship between the dependent and independent variables, with the sign only indicating the direction of the relationship. To validate the obtained models, the significance test of 𝑟, was performed using the correlation and determination coefficients, aiming to determine whether this value represents a real relationship between the two variables. The standard error of 𝑟 was calculated using the following expression: 𝑡𝑐𝑎𝑙 = |𝑟| √1−𝑟2 × √𝑁 − 2… (1) By comparing the student’s 𝑡 values, calculated (𝑡𝑐𝑎𝑙) and tabulated ( 𝑡𝑡𝑎𝑏) the relationship between elapsed time, 𝑡(days) and the number of fatalities (𝑁), was determined, along with the degree of difference and the estimation of the predictive model. 3. Results For modeling the number of fatalities worldwide (𝑁), due to COVID-19 as a function of elapsed time, 𝑡, (days), we relied on the Empirical Modeling Theory16. Analyzing the dispersion of statistical data (Figure 1 and Table 1), it was determined that the model is logistic, of the form 𝑁 = 𝑀 1+𝐴×𝑒𝑘×𝑡; where "𝑀" is the maximum quantity, "𝐴" is a pre-exponential quantity, "𝑘" is the proportionality constant, "𝑡" is the elapsed time of fatalities (days), and "𝑁" s the number of fatalities. The value of "𝑀” is calculated by considering three independent values and their corresponding dependent values from Table 1. Bronshtein and Semendiaev20 mention that, to evaluate the maximum value (𝑀), preference should be given to the first value (𝐴), which corresponds to the moment when the behavior exhibits an inflection point. The second value (𝐵) is the last data point, and the third value (𝐼) is an intermediate value between 𝐴 y 𝐵, specifically the mean of the first and last values. The formula is then applied as follows: 𝑀 = 𝐴×𝐵−𝐼2 𝐴+𝐵−2𝐼 …(2) First value: 𝑡1 = 387 𝑑𝑎𝑦𝑠, corresponding to: 𝐴 = 3 400 028 𝑓𝑎𝑡𝑎𝑙𝑖𝑡𝑖𝑒𝑠 Second value: 𝑡2 = 1 059 𝑑𝑎𝑦𝑠, corresponding to: 𝐵 = 6 832 250 𝑓𝑎𝑡𝑎𝑙𝑖𝑡𝑖𝑒𝑠 Third value: 𝑡3 = 387+1059 2 = 723 𝑑𝑎𝑦𝑠, corresponding to: 𝐼 = 6 149 819 𝑓𝑎𝑡𝑎𝑙𝑖𝑡𝑖𝑒𝑠 Now, replacing into Equation (1): 𝑀 = 3400028×6832250−61498192 3400028+6832250−2(6149819) = 7057519 𝑓𝑎𝑡𝑎𝑙𝑖𝑡𝑖𝑒𝑠 The model 𝑁 = 𝑀 1+𝐴×𝑒𝑘×𝑡 can then be written as: 𝑁 = 7057519 1+𝑄×𝑒𝑘×𝑡 Applying the method of least squares to the expression ln ( 7057519 𝑁 − 1) = 𝑄 + 𝑘 × 𝑡; the estimation model is obtained. �̂� = 7057519 1+18,9727×𝑒−0,0063×𝑡…(3) With a correlation coefficient of 𝑟 = −0,9728. By deriving Equation (3) the velocity equation for fatalities is obtained, expressed as Equation (4). 𝑑�̂� 𝑑𝑡 = 848304,4693×𝑒−0,0063×𝑡 (1+18,9727×𝑒−0,0063×𝑡)2…(4) By deriving Equation (4) and setting it equal to zero, the critical time (𝑡𝑐) is determined, at which the velocity of fatalities is maximum. 𝑡𝑐 = − 1 𝑘 × ln (1 𝑄⁄ )… (5) Therefore 𝑡𝑐 = 465 𝑑𝑎𝑦𝑠 and the maximum velocity is ( 𝑑�̂� 𝑑𝑡 )𝑚á𝑥 = 11 177,4525 𝑝𝑒𝑟𝑠𝑜𝑛𝑠/𝑑𝑎𝑦 According to the calendar, the maximum velocity of fatalities due to COVID-19 worldwide occurred on July 24, 2021. 7787 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 8, No. 6: 7782-7790, 2024 DOI: 10.55214/25768484.v8i6.3687 © 2024 by the authors; licensee Learning Gate Table 2. Number of fatalities, estimated fatalities, and estimated velocity of fatalities due to COVID-19 worldwide as a function of elapsed time (days). Time, t (days) N (Number of fatalities) �̂� 𝒅𝑵 𝒅𝒕⁄ (𝑷𝒆𝒓𝒔𝒐𝒏𝒔/𝒅𝒂𝒚) 0 47205 353358 21265627 13 144532 381885 22804592 42 384344 455316 26885507 63 489619 513003 30138103 84 576857 579608 33704504 126 825733 736847 41807951 161 1 021 306 895560 49537251 187 1 174 969 1031651 55804718 229 1 528 933 1287155 66673381 243 1 707 231 1382588 70432309 278 2 124 707 1644209 79898472 299 2 431 542 1816909 85473904 342 2 852 496 2205560 96062636 376 3 260 857 2542599 103049617 387 3 400 028 2656377 104947857 429 3 862 475 3106807 110181355 457 4 087 826 3416052 111665588 485 4 345 952 3727041 111426693 527 4 745 551 4186331 107898074 561 4 948 224 4542667 102551500 575 5 048 856 4683559 99808583 631 5 436 623 5203942 86588782 659 5 665 031 5434774 79168104 687 5 946 761 5644665 71590271 715 6 115 681 5833522 64095831 728 6 168 449 5914179 60699954 770 6 262 426 6145646 50306053 798 6 302 937 6276799 43989803 842 6 382 570 6449526 35200170 873 6 454 522 6549629 29861033 889 6 488 025 6595138 27374256 921 6 534 601 6674983 22921397 947 6 563 777 6730098 19780904 987 6 625 253 6800376 15697371 1023 6 761 565 6851028 12699150 1059 6 832 250 6891946 10243513 The estimated number of fatalities due to COVID-19 worldwide is determined by Equation (3) and represented in Figure 2. The estimated velocity of fatalities due to COVID-19 worldwide is determined by Equation (4) and represented in Figure 3. 7788 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 8, No. 6: 7782-7790, 2024 DOI: 10.55214/25768484.v8i6.3687 © 2024 by the authors; licensee Learning Gate Figure 2. Representation of the number of fatalities and the estimated number of fatalities as a function of elapsed time (days). Figure 2 represents the accumulated number of fatalities and the estimated number of fatalities due to COVID-19 worldwide as a function of elapsed time. Figure 3. Estimated velocity of fatalities (persons/day) due to COVID-19 worldwide as a function of elapsed time (days). In Figure 3, the estimated velocity of fatalities (persons/day) due to COVID-19 worldwide is plotted as a function of elapsed time. Fatalities Estimated fatalities 7789 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 8, No. 6: 7782-7790, 2024 DOI: 10.55214/25768484.v8i6.3687 © 2024 by the authors; licensee Learning Gate Significance test of 𝑟. The Pearson correlation coefficient “𝑟” between elapsed time t, (days) and the number of fatalities (𝑁), worldwide due to COVID-19, based on 36 cases, was 𝑟 = −0,9728; The standard error of 𝑟 was calculated using the following expression: 𝑡𝑐 = |𝑟| √1−𝑟2 × √𝑁 − 2… (1) 𝑡𝑐 = |−0,9728| √1−(−0,9728)2 × √36 − 2 = 24,4871 and 𝑡𝑡(34;0,95) = 1,6955 Interpretation: Since 𝑡𝑐𝑎𝑙 = 24,4871 is greater tan 𝑡𝑡𝑎𝑏 = 1,6955; it is concluded that the relationship between time, 𝑡(days) and the number of fatalities (𝑁) is real; Therefore, there is no significant difference, and the predictive model provides a high estimation of the correlated data. There is a "very strong correlation" between elapsed time (𝑡) and the number of fatalities (𝑁) with 94,67 % of the variance in 𝑁 explained by 𝑡; for the global number of fatalities due to COVID-19. 4. Discussion The mathematical model (Equation 3) to estimate the number of fatalities due to COVID-19 worldwide proved to be quite reliable, achieving a Pearson correlation coefficient of 𝒓 = −𝟎, 𝟗𝟕𝟐𝟖, consistent with what was reported by Florencio15. Using Equation 5, the critical time (𝑡𝑐) was estimated to be 465 days, corresponding to the maximum estimated velocity of infections worldwide due to COVID-19, which was 11 177,4525 𝑝𝑒𝑟𝑠𝑜𝑛𝑠/𝑑𝑎𝑦. According to the calendar, this occurred on July 24, 2021, aligning with the findings of Manrique et al17 and Marín et al16. The predictive mathematical model (Equation 3), the proportionality constant (𝑘 = −0,0063) and the correlation (𝑟 = −0,9728) and determination (𝑟2 × 100 = 94,67%) coefficients are of great importance for analyzing and estimating data related to epidemiological and pandemic phenomena, which coincides with the observations of Hernández et al19. It is concluded from the study that the theory of Bronshtein and Semendiaev20 can be applied without difficulty, provided that the timing (time) of processes or phenomena is carefully considered, particularly when they exhibit behavior that does not always ascend or descend continuously. Logistic (factual) models can generally be applied, with the utmost rigor, to pandemic and epidemiological phenomena, offering high resolution and a strong degree of estimation compared to real data. Statistical analysis determined that the correlation coefficient of Equation 3 indicates a "very strong negative correlation" between the number of fatalities and elapsed time, with 94.67% of the variance in 𝑁 explained by 𝑡; for the global number of fatalities due to COVID-19. It is recommended that the statistical data for the dependent variable (number of people infected with COVID-19) be analyzed as a function of more than one independent variable. Additionally, the data for the independent variable should be evenly spaced to enable the application and improvement of other calculation, analysis, and interpretation techniques. Copyright: © 2024 by the authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). References [1] Liu X.-X Y, Li G, Qin Y, Zhu, Li., Zhang K, Zhao M, Hu X.-L, Wang X-L. and Zheng X. Effects of air pollutants on occurrences of influenza-like illness and laboratory-confirmed influenza in Hefei, China. International Journal of Biometeorology .2019.63(1), 51-60. [2] Van Doremalen, N, Bushmaker T, Morris D H, Holbrook M G, Gamble A, Williamson B. N, Tamin A, Harcourt J L, Thornburg N J, Gerber S I, Lloyd-Smith J O, de Wit E & Munster V J . Aerosol and Surface Stability of SARS- CoV-2 as compared with SARS-CoV-1. The New England journal of medicine, 2020.382(16), 1564–1567. Disponible en: https://doi.org/10.1056/NEJMc2004973. [3] Lowen, A and Palese P. Transmission of influenza virus in temperate zones is predominantly by aerosol, in the tropics by contact: a hypothesis.2009. Disponible en: https://doi.org/10.1371/currents.rrn1002 https://creativecommons.org/licenses/by/4.0/ https://doi.org/10.1056/NEJMc2004973 https://doi.org/10.1371/currents.rrn1002 7790 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 8, No. 6: 7782-7790, 2024 DOI: 10.55214/25768484.v8i6.3687 © 2024 by the authors; licensee Learning Gate [4] Chen G, W Zhang S, Li Y, Zhang G, Williams R, Huxley H, Ren W, Cao & Guo Y. The impact of ambient fine particles on influenza transmission and the modification effects of temperature in China: A multi-city study. Environmental International,2017. 98, 82-88. [5] Tellier RY, Li BJ, Cowling BJ & Tang JW. Recognition of aerosol transmission of infectious agents: a commentary. BMC Infectious Diseases.2019. [6] Zhou P, Yang XL, Wang XG, Hu B, Zhang L & Zhang W. A pneumonia outbreak associated with a new coronavirus of probable bat origin. Nature. 2020. 579, 270 – 273. [7] Mizumoto Kand Chowell G. Estimating. Risk for Death from 2019 Novel Coronavirus Disease, China.2020. [8] Levison E. Early transmission dynamics in Wuhan, China. Medicina de la Facultad de Medicina de Drexler University.2020. [9] Bravo A, y Valera M. SARS-CoV-2 y pandemia de síndrome respiratorio agudo (COVID -19). Ars Pharmaceutica (Internet),2020. 61(2), 63-79. Disponible en: https://dx.doi.org/10.30827/ars.v61i2.15177 [10] Wang LF and Cowled C. Bats and viruses: a new frontier of emerging infectious diseases. 1st ed. Hoboken: Wiley- Blackwell.2015. [11] Organización Mundial de la Salud. COVID-19: Cronología de la actuación de la OMS.2019. Disponible en: https://www.who.int/es/news/item/27-04-2020-who-timeline---covid-19 [12] Guo YR, Cao Q, Hong Z, Tan Y, Chen S, Jin H, Tan K, Wan D, & Yan Y. The origin, transmission, and clinical therapies on coronavirus disease 2019 (COVID-19).2020. [13] Guan W, Ni Z, Hu Y, Liang W, Ou C, He J, Liu L, Shan H, Lei C, Hui C, Li L, Zeng G, Yuen K, Chen R, Tang C, Chen P, Xiang J, Jin S, Wan, J, Liang Z, Peng Y, Wei L, Liu Y, Hu, Y, Pen, P, Wang J, Liu Z, Chen G, Zheng Q, Luo J, Zhu S, & Zhong N. (2020). Clinical Characteristics of coronavirus Disease 2019 in China. The New England Journal of Medicine.2020. 282, 1708-1720. Disponible en: https://www.nejm.org/doi/pdf/10.1056/nejmoa2002032 [14] Yang X, Yu Y, Xu J, Shu H, Xia J, Liu H, Wu Y, Zhang L, Yu Z, Fang M, Yu T, Wang Y, Pan S, Zou X, Yuan S & Shang Y. (2020). Clinical course and outcomes of critically ill patients with SARS-CoV-2 pneumonia in Wuhan, China: a single-centered, retrospective, observational study. The Lancet. Respiratory medicine.2020. 8(5), 475–481. Didponible en: https://doi.org/10.1016/S2213-2600(20)30079-5 [15] Florencio C F. Cálculos estadísticos sobre un modelo cerrado SIR extrapolando datos del actual brote de Coronavirus a un escenario de población mexicana, Alcaldía Magdalena Contreras. Servicios de Salud Pública CDMX. México. 2020. [16] Marín, O., Zambrano A W, García E G, Ortiz JI, Rivas D E & Marín O. Modelamiento matemático del comportamiento epidemiológico de la pandemia COVID-19 en China. The Biologist,2020. 18(1). Disponible en: https://doi.org/10.24039/rtb2020181473 [17] Manrique C A, Agudelo V M, González O, Gutiérrez C F, Téllez C F y Herrera G. Modelo SIR de la Pandemia de COVID-19 en Colombia. Rev. Salud Pública. 2020. Vol. 22 N°.1 Bogotá. Disponible en: https://doi.org/10.15446/rsap.v22n2.85977Organización Panamericana de la Salud. Informe de situación COVID - 19 a nivel mundial.2022. [18] Hernández R, Fernández C & Baptista M P. Metodología de la investigación. Editorial McGraw-Hill Interamericana Editores, S.A. de C.V. C.P. 01376, México D.F.2014. [19] Bronshtein, I and Semendiaev K. Manual de matemáticas para Ingenieros y Estudiantes. 4ª Edición. Editorial Mir. Moscú. URSS.2018. https://dx.doi.org/10.30827/ars.v61i2.15177 https://www.who.int/es/news/item/27-04-2020-who-timeline---covid-19 https://www.nejm.org/doi/pdf/10.1056/nejmoa2002032 https://doi.org/10.1016/S2213-2600(20)30079-5 https://doi.org/10.24039/rtb2020181473 https://doi.org/10.15446/rsap.v22n2.85977