Keywords
ecuaciones diferenciales de primer orden
previsión de enfermedades a corto plazo
método Bootstrap
ecuaciones
tiempo
medición
parámetros
contagio
pandemia discrete phenomenological models
first-order difference equations
short-term disease forecasting
bootstrap method
equations
time
measurement
parameters
infection
pandemics
How to Cite
Abstract
The COVID-19 pandemic has motivated a resurgence in the use of phenomenological growth models for predicting the early dynamics of infectious diseases. These models assume that time is a continuous variable, whereas in the present contribution the discrete versions of Gompertz and Generalized Logistic models are used for early monitoring and short-term forecasting of the spread of an epidemic in a region. The time-continuous models are represented mathematically by first-order differential equations, while their discrete versions are represented by first-order difference equations that involve parameters that should be estimated prior to forecasting. The methodology for estimating such parameters is described in detail. Real data of COVID-19 infection in Cuba is used to illustrate this methodology. The proposed methodology was implemented for the first thirty-five days and was used to predict accurately the data reported for the following twenty days.
References
Brauer F., Castillo-Chavez C. and Feng Z. (2019). Mathematical Models in Epidemiology, Texts in Applied Mathematics. Springer, New York, NY.
Bürger R., Chowell G., and Lara-Díaz L. Y. (2021). Measuring differences between phenomenological growth models applied to epidemiology. Mathematical Biosciences, 334, 108558. https://doi.org/10.1016/j.mbs.2021.108558
Dinh L., Chowell G., Mizumoto K. and Nishiura H. (2016). Estimating the subcritical transmissibility of the Zika outbreak in the State of Florida, USA, 2016. Theoretical Biology and Medical Modelling, 13, 20. https://doi.org/10.1186/s12976-016-0046-1
Efron B. and Tibshirani R. J. (1994). An Introduction to the Bootstrap. Chapman & Hall/CRC Monographs on Statistics & Applied Probability. Taylor & Francis.
Kingsland S. (1982). The Refractory Model: The logistic curve and the history of population ecology. The Quarterly Review of Biology, 57(1), 29-52. http://dx.doi.org/10.1086/412574
León-Mecías A. and Mesejo-Chiong J. A. (2020). Modelos fenomenológicos aplicados al estudio de la COVID-19 en Cuba. Ciencias Matemáticas, 34, 19-32. http://www.revinfodir.sld.cu/index.php/infodir/article/view/1032
López M., Peinado A. and Ortiz A. (2021). Characterizing two outbreak waves of COVID-19 in Spain using phenomenological epidemic modelling. PLoS ONE, 16(6): e0253004. http://dx.doi.org/10.1371/journal.pone.0253004
Malavika B., Marimuthu S., Joy M., Nadaraj A., Asirvatham E. S. and Jeyaseelan L. (2021). Forecasting COVID-19 epidemic in India and high incidence states using SIR and logistic growth models. Clinical Epidemiology and Global Health, 9, 26-33. http://dx.doi.org/10.1016/j.cegh.2020.06.006
May R. M. (1976). Simple mathematical models with very complicated dynamics. Nature, 261, 459-467. http://dx.doi.org/10.1038/261459a0
Pell B., Kuang Y., Viboud C. and Chowell G. (2018). Using phenomenological models for forecasting the 2015 Ebola challenge. Epidemics, 22, 62-70. http://dx.doi.org/10.1016/j.epidem.2016.11.002
Pincheira-Brown P. and Bentancor A. (2021). Forecasting COVID-19 infections with the semi-unrestricted generalized growth model. Epidemics, 37:100486. http://dx.doi.org/10.1016/j.epidem.2021.100486
Roosa K., Lee Y., Luo R., Kirpich A., Rothenberg R., Hyman J. M., Yan P. and Chowell G. (2020). Short-term forecasts of the COVID-19 epidemic in Guangdong and Zhejiang, China: February 13–23, 2020. Journal of Clinical Medicine, 9(2), 596. http://dx.doi.org/10.3390/jcm9020596
Roosa K., Lee Y., Luo R., Kirpich A., Rothenberg R., Hyman J. M., Yan P. and Chowell G. (2020). Real-time forecasts of the COVID-19 epidemic in China from February 5th to February 24th, 2020. Infectious Disease Modelling, 5, 256-263. http://dx.doi.org/10.1016/j.idm.2020.02.002
Shanafelt D. W., Jones G., Lima M., Perrings Ch. And Chowell G. (2018). Forecasting the 2001 Foot-and-Mouth Disease Epidemic in the UK. EcoHealth, 15(2), 338-347. http://dx.doi.org/10.1007/s10393-017-1293-2
Shen C. Y. (2020). Logistic growth modelling of COVID-19 proliferation in China and its international implications. International Journal of Infectious Diseases, 96, 582-589. http://dx.doi.org/10.1016/j.ijid.2020.04.085
Tsoularis A. and Wallace J. (2002). Analysis of logistic growth models. Mathematical Biosciences, 179(1), 21-55. http://dx.doi.org/10.1016/S0025-5564(02)00096-2
Vasconcelos G. L., Macêdo A. M. S., Ospina R., Almeida F. A. G., Duarte-Filho G. C., Brum A. A. and Souza I. C. L. (2020). Modelling fatality curves of COVID-19 and the effectiveness of intervention strategies. PeerJ, 23, 8, e9421. https://doi.org/10.7717/peerj.9421
Viboud C., Simonsen L. and Chowell G. (2016). A generalized-growth model to characterize the early ascending phase of infectious disease outbreaks. Epidemics, 15, 27-37. http://dx.doi.org/https://doi.org/10.1016/j.epidem.2016.01.002
Wu K., Darcet D., Wang Q. and Sornette D. (2020). Generalized logistic growth modeling of the COVID-19 outbreak in 29 provinces in China and in the rest of the world. Nonlinear Dynamics, 101, 1561–1581. https://doi.org/10.1007/s11071-020-05862-6
Wu Y., Zhang L., Cao W., Liu X. and Feng X. (2021). The generalized-growth modeling of COVID-19. Frontiers in Physics, 8, 603001. https://doi.org/10.3389/fphy.2020.603001
Zhao S., Musa S. S., Fu H., He D. and Qin J. (2019). Simple framework for real-time forecast in a data-limited situation: The Zika virus (ZIKV) outbreaks in Brazil from 2015 to 2016 as an example. Parasites and Vectors, 12, 344. https://doi.org/10.1186/s13071-019-3602-9
Zhou G. and Yan G. (2003). Severe Acute Respiratory Syndrome Epidemic in Asia. Emerging Infectious Diseases, 9(12), 1608-1610. https://doi.org/10.3201/eid0912.030382
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