Research Article

Statistical Mathematical Analysis of COVID-19 at World Level

Marín-Machuca Olegario*, Carlos Enrique Chinchay-Barragán, Moro-Pisco José Francisco, Vargas-Ayala Jessica Blanca, Machuca-Mines José Ambrosio, María del Pilar Rojas-Rueda and Zambrano-Cabanillas Abel Walter

Published: 05 April, 2024 | Volume 7 - Issue 1 | Pages: 040-047

Worldwide, statistical data of people infected by COVID-19 has been taken until March 29, 2023, which, when correlated, showed a predictive logistic  model. The purpose was to determine the predictive model, which was acceptable, in such a way that the proportionality constant and the correlation and determination coefficients are of great importance to estimating epidemiological and pandemic data; coinciding with what was reported by other authors. Bearing in mind that a mathematical model is a mathematical description through a function or equation of a phenomenon in the real world; whose purpose is to understand infections and make predictions for the future. The stages were: to model the number of people infected as a function of time, formulate, and choose the logistic model, determine the model and obtain mathematical conclusions, and make predictions (estimates) about the number of people infected by COVID-19 worldwide. The logistic model was derived to predict the speed of people infected by COVID-19 and the critical time (tc = 733 days) for which the speed was maximum (1694,7209 infected/day). The Pearson correlation coefficient for the time elapsed (t) and the number of people infected (N) worldwide, based on 32 cases, was r = -0.88; the relationship between time and those infected is real, there is a “very strong correlation” between the time elapsed (t) and the number of people infected (N) and 77.03% of the variance in N is explained by t. 

Read Full Article HTML DOI: 10.29328/journal.ijpra.1001082 Cite this Article Read Full Article PDF


Estimation; Logistic model; Global pandemic COVID-19; Validation


  1. Chen G, Zhang W, Li S, Zhang Y, Williams G, Huxley R, Ren H, Cao W, Guo Y. The impact of ambient fine particles on influenza transmission and the modification effects of temperature in China: A multi-city study. Environ Int. 2017 Jan;98:82-88. doi: 10.1016/j.envint.2016.10.004. Epub 2016 Oct 11. PMID: 27745688; PMCID: PMC7112570.
  2. Tellier R, Li Y, Cowling BJ, Tang JW. Recognition of aerosol transmission of infectious agents: a commentary. BMC Infect Dis. 2019 Jan 31;19(1):101. doi: 10.1186/s12879-019-3707-y. PMID: 30704406; PMCID: PMC6357359.
  3. Liu XX, Li Y, Qin G, Zhu Y, Li X, Zhang J, Zhao K, Hu M, Wang XL, Zheng X. Effects of air pollutants on occurrences of influenza-like illness and laboratory-confirmed influenza in Hefei, China. Int J Biometeorol. 2019 Jan;63(1):51-60. doi: 10.1007/s00484-018-1633-0. Epub 2018 Oct 31. PMID: 30382350.
  4. Shereen MA, Khan S, Kazmi A, Bashir N, Siddique R. COVID-19 infection: Origin, transmission, and characteristics of human coronaviruses. J Adv Res. 2020 Mar 16;24:91-98. doi: 10.1016/j.jare.2020.03.005. PMID: 32257431; PMCID: PMC7113610.
  5. Revollé A. Coronavirus in Peru: This is how the pandemic evolves in the country. The Republic newspaper. 2020.
  6. Levison E. Early transmission dynamics in Wuhan, China. Medicine from Drexel University School of Medicine. 2020.
  7. Zhou P, Yang XL, Wang XG, Hu B, Zhang L, Zhang W, Si HR, Zhu Y, Li B, Huang CL, Chen HD, Chen J, Luo Y, Guo H, Jiang RD, Liu MQ, Chen Y, Shen XR, Wang X, Zheng XS, Zhao K, Chen QJ, Deng F, Liu LL, Yan B, Zhan FX, Wang YY, Xiao GF, Shi ZL. A pneumonia outbreak associated with a new coronavirus of probable bat origin. Nature. 2020 Mar;579(7798):270-273. doi: 10.1038/s41586-020-2012-7. Epub 2020 Feb 3. Erratum in: Nature. 2020 Dec;588(7836):E6. PMID: 32015507; PMCID: PMC7095418.
  8. Mizumoto K, Chowell G. Estimating Risk for Death from Coronavirus Disease, China, January-February 2020. Emerg Infect Dis. 2020 Jun;26(6):1251-1256. doi: 10.3201/eid2606.200233. Epub 2020 Jun 17. PMID: 32168464; PMCID: PMC7258458.
  9. Bravo A, Valera M. SARS-CoV-2 and Pandemic acute respiratory syndrome (COVID-19). Ars Pharmaceutica. 2020; 61(2): 63-79.
  10. Ahmed SF, Quadeer AA, McKay MR. Preliminary Identification of Potential Vaccine Targets for the COVID-19 Coronavirus (SARS-CoV-2) Based on SARS-CoV Immunological Studies. Viruses. 2020 Feb 25;12(3):254. doi: 10.3390/v12030254. PMID: 32106567; PMCID: PMC7150947.
  11. Guo YR, Cao QD, Hong ZS, Tan YY, Chen SD, Jin HJ, Tan KS, Wang DY, Yan Y. The origin, transmission and clinical therapies on coronavirus disease 2019 (COVID-19) outbreak - an update on the status. Mil Med Res. 2020 Mar 13;7(1):11. doi: 10.1186/s40779-020-00240-0. PMID: 32169119; PMCID: PMC7068984.
  12. Coronaviridae Study Group of the International Committee on Taxonomy of Viruses. The species Severe acute respiratory syndrome-related coronavirus: classifying 2019-nCoV and naming it SARS-CoV-2. Nat Microbiol. 2020 Apr;5(4):536-544. doi: 10.1038/s41564-020-0695-z. Epub 2020 Mar 2. PMID: 32123347; PMCID: PMC7095448.
  13. Van Doremalen N, Bushmaker T, Morris DH, Holbrook MG, Gamble A, Williamson BN, Tamin A, Harcourt JL, Thornburg NJ, Gerber SI, Lloyd-Smith JO, de Wit E, Munster VJ. Aerosol and Surface Stability of SARS-CoV-2 as Compared with SARS-CoV-1. N Engl J Med. 2020 Apr 16;382(16):1564-1567. doi: 10.1056/NEJMc2004973. Epub 2020 Mar 17. PMID: 32182409; PMCID: PMC7121658.
  14. Wang LF, Cowled C. Bats and viruses: a new frontier of emerging infectious diseases. 1st Hoboken: Wiley-Blackwell. 2015.
  15. Guan WJ, Ni ZY, Hu Y, Liang WH, Ou CQ, He JX, Liu L, Shan H, Lei CL, Hui DSC, Du B, Li LJ, Zeng G, Yuen KY, Chen RC, Tang CL, Wang T, Chen PY, Xiang J, Li SY, Wang JL, Liang ZJ, Peng YX, Wei L, Liu Y, Hu YH, Peng P, Wang JM, Liu JY, Chen Z, Li G, Zheng ZJ, Qiu SQ, Luo J, Ye CJ, Zhu SY, Zhong NS; China Medical Treatment Expert Group for Covid-19. Clinical Characteristics of Coronavirus Disease 2019 in China. N Engl J Med. 2020 Apr 30;382(18):1708-1720. doi: 10.1056/NEJMoa2002032. Epub 2020 Feb 28. PMID: 32109013; PMCID: PMC7092819.
  16. 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. 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. https://doi.org/10.1016/S2213-2600(20)30079-5
  17. World Health Organization. Report of the WHO-China Joint Mission on Coronavirus Disease 2019 (COVID-19). 2020.
  18. Zhang W, Liu S, Osgood N, Zhu H, Qian Y, Jia P. Using simulation modelling and systems science to help contain COVID-19: A systematic review. Syst Res Behav Sci. 2022 Aug 19:10.1002/sres.2897. doi: 10.1002/sres.2897. Epub ahead of print. PMID: 36245570; PMCID: PMC9538520.
  19. Joshi H, Jha BK, Yavuz M. Modelling and analysis of fractional-order vaccination model for control of COVID-19 outbreak using real data. Math Biosci Eng. 2023 Jan;20(1):213-240. doi: 10.3934/mbe.2023010. Epub 2022 Sep 30. PMID: 36650763.
  20. Arora P, Kumar H, Panigrahi BK. Prediction and analysis of COVID-19 positive cases using deep learning models: A descriptive case study of India. Chaos Solitons Fractals. 2020 Oct;139:110017. doi: 10.1016/j.chaos.2020.110017. Epub 2020 Jun 17. PMID: 32572310; PMCID: PMC7298499.
  21. Chanchí G, Gómez A, Hernández-Londoño Cl. IoT system for monitoring and analysis of saturation level and heart rate in the early diagnosis of Covid-19. Ibérica Magazine of Information Systems and Technologies, E42. 2021; 272-285.
  22. Orosco J, Huamaní N. Forecasting the number of confirmed cases and deaths from COVID-19 using the logistic growth model in South American countries. Iberian Journal of Information Systems and Technologies, E40. 2021; 330-338.
  23. Mude W, Oguoma VM, Nyanhanda T, Mwanri L, Njue C. Racial disparities in COVID-19 pandemic cases, hospitalisations, and deaths: A systematic review and meta-analysis. J Glob Health. 2021 Jun 26;11:05015. doi: 10.7189/jogh.11.05015. PMID: 34221360; PMCID: PMC8248751.
  24. Msemburi W, Karlinsky A, Knutson V, Aleshin-Guendel S, Chatterji S, Wakefield J. The WHO estimates of excess mortality associated with the COVID-19 pandemic. Nature. 2023 Jan;613(7942):130-137. doi: 10.1038/s41586-022-05522-2. Epub 2022 Dec 14. PMID: 36517599; PMCID: PMC9812776.
  25. Wang P, Zheng X, Li J, Zhu B. Prediction of epidemic trends in COVID-19 with logistic model and machine learning technics. Chaos Solitons Fractals. 2020 Oct;139:110058. doi: 10.1016/j.chaos.2020.110058. Epub 2020 Jul 1. PMID: 32834611; PMCID: PMC7328553.
  26. Carvalho T. COVID-19 Research in Brief: 4 April to 10 April, 2020. Nat Med. 2020 Apr 10. doi: 10.1038/d41591-020-00009-x. Epub ahead of print. PMID: 32286558.
  27. Vargas C, Acosta R, Bernilla A. El nuevo coronavirus y la pandemia del COVID-19. Revista Médica Herediana. 2020; 31(2): 125-131. https://doi.org/10.20453/rmh.v31i2.3776
  28. CDC CpeCylPdE. Mpox. 2022. https://www.cdc.gov/poxvirus/monkeypox/index.html.
  29. Bunge EM, Hoet B, Chen L, Lienert F, Weidenthaler H, Baer LR, Steffen R. The changing epidemiology of human monkeypox-A potential threat? A systematic review. PLoS Negl Trop Dis. 2022 Feb 11;16(2):e0010141. doi: 10.1371/journal.pntd.0010141. PMID: 35148313; PMCID: PMC8870502.
  30. Fan Y, Zhao K, Shi ZL, Zhou P. Bat Coronaviruses in China. Viruses. 2019 Mar 2;11(3):210. doi: 10.3390/v11030210. PMID: 30832341; PMCID: PMC6466186.
  31. WHO OMdlS. Monkeypox. 2022. https://www.who.int/news-room/fact sheets/detail/monkeypox.
  32. Thanh Le T, Andreadakis Z, Kumar A, Gómez Román R, Tollefsen S, Saville M, Mayhew S. The COVID-19 vaccine development landscape. Nat Rev Drug Discov. 2020 May;19(5):305-306. doi: 10.1038/d41573-020-00073-5. PMID: 32273591.
  33. Florencio CF. Statistical calculations on a closed SIR model extrapolating data from the current Coronavirus outbreak to a scenario of the Mexican population, Mayor Magdalena Contreras. CDMX Public Health Services. Mexico. 2020.
  34. Marín-Machuca O, Zambrano-Cabanillas AW, García-Talledo EG, Ortiz-Guizado JI, Rivas-Ruiz DE, Marín-Sánchez O. Mathematical modeling of the epidemiological behavior of the COVID-19 pandemic in China. The Biologist. 2020; 18(1).
  35. Manrique-Abril FG, Agudelo-Calderon CA, González-Chordá VM, Gutiérrez-Lesmes O, Téllez-Piñerez CF, Herrera-Amaya G. Modelo SIR de la pandemia de COVID-19 en Colombia [SIR model of the COVID-19 pandemic in Colombia]. Rev Salud Publica (Bogota). 2020 Mar 1;22(2):123-131. Spanish. doi: 10.15446/rsap.V22n2.85977. PMID: 36753100.
  36. Marín-Machuca O, Chacón RD, Alvarez-Lovera N, Pesantes-Grados P, Pérez-Timaná L, Marín-Sánchez O. Mathematical Modeling of COVID-19 Cases and Deaths and the Impact of Vaccinations during Three Years of the Pandemic in Peru. Vaccines (Basel). 2023 Oct 27;11(11):1648. doi: 10.3390/vaccines11111648. PMID: 38005980; PMCID: PMC10674587.
  37. National Computer System of Deaths (SINADEF). Information on deceased persons from the National Death System in the Ministry of Health. 2022. https://www.minsa.gob.pe/defunciones/
  38. Bronshtein I, Semendiaev K. Mathematical Handbook for Engineers and Students. 4th Edition. Mir Publishing House. Moscow. USSR. 2018.
  39. Hernandez-Sampieri R, Fernandez-Collado C, Baptista-Lucio MP. Research methodology. McGraw-Hill Publishing Inter-American Publishers, S.A. of C.V. C.P. 01376, Mexico D.F. 2014.
  40. State of Health. COVID-19: Cumulative number of cases in the world 2020-2022. 2023. https://es.statista.com/estadisticas/1104227/numero-acumulado-de-casos-de coronavirus-covid-19-en-el-mundo-enero-marzo/


Similar Articles

Recently Viewed

Read More

Most Viewed

Read More

Help ?