A Segmented SIR-D Mathematical Model for Coronavirus Propagation Dynamics (COVID-19) in Peru
DOI:
https://doi.org/10.17268/sel.mat.2020.01.15Keywords:
Coronavirus (Covid-19), Epidemiology, Ordinary Differential Equations, Computational Simulation, Regression MethodsAbstract
The present study proposes the use of a segmented SIR-D mathematical model to predict the evolution of epidemiological populations of interest in the COVID-19 pandemic (Susceptible [S], Infected [I], Recovered [R] and dead [D]), information that is often key to guiding decision-making in the fight against epidemics. In order to obtain a better model calibration and a lower prediction error in the short term, we performed the model segmentation in 6 stages of periods of 14 days each. At each stage, the epidemiological that define the system of equations are empirically estimated by linear regression of the epidemiological surveillance data that the Peruvian Ministry of Health collects and reports daily. This strategy showed better model calibration compared to an unsegmented SIR-D model.
References
Acuña-Zegarra M A, Santana-Cibrian M, Velasco-Hernandez J. Modeling behavioral change and COVID-19 containment in Mexico: A trade-off between lockdown and compliance. Mathematical Biosciences, 2020; 325(108370). Disponible en https://www.sciencedirect.com/science/article/pii/S0025556420300596?via%3Dihub
Amat Rodrigo J. Métodos de regresión no lineal: Regresión Polinómica, Regression Splines, Smooth Splines y GAMs.[Internet]: Ciencia de Datos, Estadística, Programación y Machine Learning; 2017 (citado 18 mayo 2020). Disponible en https://www.cienciadedatos.net/documentos/32_metodos_de_regresion_no_lineal_polinomica_splines_gams
Aguilar J, Faust J, Westafer L, Gutierrez J. Investigating the Impact of Asymptomatic Carriers on COVID-19 Transmission. medRxiv (The Preprint Server for Health Sciences). 2020. Disponible en https://www.medrxiv.org/content/10.1101/2020.03.18.20037994v3
Chatterjee K, Chatterjee K, Kumar A, & Shankar S. Healthcare impact of COVID-19 epidemic in India: A stochastic mathematical model. Medical journal, Armed Forces India. 2020. Disponible en https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7126697/
Centro Nacional de Epidemiología, Prevención y Control de Enfermedades. Sala Situacional del Covid-19 Perú. Miniseterio de Salud, Perú. 2020 (citado 15 mayo 2020). Disponible en https://www.dge.gob.pe/portal/index.php?
option=com_content&view=article&id=678
Dai L, Vorselen D, Korolev KS, Gore J. Generic indicators for loss of resilience before a tipping point leading to population collapse. Science. 2012;336(6085):1175-1177. Recuperado de doi:10.1126/science.1219805
De Pereda D. Modelización matemática de la difusión de una epidemia de peste porcina entre granjas. Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid. 2010. Disponible en http://www.mat.ucm.es/˜ivorra/papers/Diego-Epidemiologia.pdf
Doungmo EF, Maritz R, Munganga J. Some properties of the Kermack-McKendrick epidemic model with fractional derivative and nonlinear incidence. Advances in Difference Equations, 278. 2014. Recuperado de https://doi.org/10.1186/1687-1847-2014-278
Fang Y, Nie Y, Penny M. Transmission dynamics of the COVID-19 outbreak and effectiveness of government interventions: A data-driven analysis. Journal of Medical Virology, 2020; 92:645-659. Disponible en https://doi.org/10.1002/jmv.25750
Fernández-Villaverde J, Jones Ch. Estimating and Simulating a SIRD Model of COVID-19 for Many Countries, States, and Cities. Stanford University. 2020. Disponible en https://web.stanford.edu/˜chadj/sird-paper.pdf
Gonzáles M. Modelización y simulación en epidemiología. Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid. 2017. Recuperado de http://www.mat.ucm.es/˜ivorra/papers/tfg-maria.pdf
Instituto Nacional de Estadística e Informática (2020). Nota de Prensa No.006, 485 Aniversario de Lima (17 de enero de 2020). Disponible en http://m.inei.gob.pe/prensa/noticias/
la-poblacion-de-lima-supera-los-nueve-millones-y-medio-de-habitantes-12031/
Ivorra B, Ferrández MR, Vela-P´erez M, Ramos AM. Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China. Communications in nonlinear science & numerical simulation, 105303. Advance online publication. 2020. Disponible en https://doi.org/10.1016/j.cnsns.2020.105303
Liang K. Mathematical model of infection kinetics and its analysis for COVID-19,SARS and MERS. Infection. Genetics and Evolution, 2020; 82(104306). Recuperado de https://www.sciencedirect.com/science/article/pii/
S1567134820301374?via%3Dihub
Lin F, Muthuraman K, Lawley M. An optimal control theory approach to non-pharmaceutical interventions. BMC Infect Dis 2020; 10(32). Disponible en https://doi.org/10.1186/1471-2334-10-32
Ministerio de Salud. Sala Situacional del Covid-19 Perú. Ministerio de Salud, Perú. 2020 (citado 16 mayo 2020). Disponible en https://covid19.minsa.gob.pe/sala_situacional.asp
Munayco C, Tariq A, Rothenberg R, Soto-Cabezas G, Reyes M, Valle A, Rojas-Mezarina L, Cabezas C, Loayza M, Chowell G. Early transmission dynamics of COVID-19 in a southern hemisphere setting: Lima-Peru, February 29th-March 30th, 2020. medRxiv (The Preprint Server for Health Sciences). 2020. Disponible en https://www.medrxiv.org/content/10.1101/2020.04.30.20077594v2.full.pdf
Natekin A, Knoll A. Gradient boosting machines, a tutorial. Frontiers in neurorobotics, 2013; 7(21). Disponible en https://doi.org/10.3389/fnbot.2013.00021
Organización Mundial de la Salud. Brote de enfermedad por coronavirus (COVID-19). 2020 (citado 18 mayo 2020). Disponible en https://www.who.int/es/emergencies/diseases/novel-coronavirus-2019
Organización Mundial de la Salud. Novel Coronavirus (2019-nCoV), Situation Report-1. 2020 (citado 15 mayo 2020). Disponible en https://www.who.int/docs/default-source/coronaviruse/situation-reports/20200121-sitrep-1-2019-ncov.pdf?sfvrsn=20a99c10_4
Organización Mundial de la Salud. Coronavirus disease (COVID-2019) situation reports. 2020 (citado 14 mayo 2020). Disponible en https://www.who.int/emergencies/diseases/novel-coronavirus-2019/situation-reports/
Tárnok A. Machine Learning, COVID-19 (2019-nCoV), and multi-OMICS. Cytometry A, 2020; 97(3):215–216. Disponible en https://pubmed.ncbi.nlm.nih.gov/32142596/
Vinay R, Zhang L. Time series forecasting of COVID-19 transmission in Canada using LSTM networks. Chaos, Solitons & Fractals, 2020; 135(109864). Disponible en https://www.sciencedirect.com/science/article/abs/pii/S0960077920302642
Yan SJ, Chughtai AA, Macintyre CR. Utility and potential of rapid epidemic intelligence from internet-basedsources. International Journal of Infectious Diseases, 2017; 63:77-87. Disponible en https://www.sciencedirect.com/science/article/abs/pii/S0960077920302642
Published
How to Cite
Issue
Section
License
The authors who publish in this journal accept the following conditions:
1. The authors retain the copyright and assign to the journal the right of the first publication, with the work registered with the Creative Commons Attribution License,Atribución 4.0 Internacional (CC BY 4.0) which allows third parties to use what is published whenever they mention the authorship of the work And to the first publication in this magazine.
2. Authors may make other independent and additional contractual arrangements for non-exclusive distribution of the version of the article published in this journal (eg, include it in an institutional repository or publish it in a book) provided they clearly state that The paper was first published in this journal.
3. Authors are encouraged to publish their work on the Internet (for example, on institutional or personal pages) before and during the review and publication process, as it can lead to productive exchanges and to a greater and more rapid dissemination Of the published work.
