A Bayesian mixture model to describe COVID-19 outbreaks in the state of Guerrero, Mexico
Keywords:
mixture of distributions, Markov Chain, Monte Carlo, Bayesian estimation, COVID-19 outbreaksAbstract
The COVID-19 pandemic has put the entire world on alert due to the large number of infections, hospitalizations, and deaths caused by this disease. Since its beginning, in December 2019, outbreaks of considerable increases in the number of infections and deaths, have been occurring. In this work, the daily behavior of infections, hospitalizations, and deaths from COVID-19 in the state of Guerrero is mathematically modeled using a Bayesian mixture model with Gaussian distributions from March 15, 2020 to February 27, 2022. The parameters of interest were estimated using the Bayesian method, the posterior distributions of each of them were obtained using Markov Chains via Monte Carlo and the estimates were validated with the corresponding convergence analyses. With the mixture model, five outbreaks were identified for infected cases, and four for both hospitalized and deaths cases. Finally, the implementation of the model was carried out with the help of the R statistical software and the JAGS package.
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Baleanu, D., Mohammadi, H., Rezapour, S. (2020). A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative. Advances in Difference Equations, 2020, 299. https://doi.org/10.1186/s13662-020-02762-2
Beira, M.J., Sebastião, P.J. (2021). A differential equations model-fitting analysis of COVID-19 epidemiological data to explain multi-wave dynamics. Scientific Reports, 11, 16312. https://doi.org/10.1038/s41598-021-95494-6
Calvetti1, D., Hoover, A., Rose, J., Somersalo, E. (2020). Bayesian dynamical estimation of the parameters of an SE(A)IR COVID-19 spread model.
[2005.04365] Bayesian dynamical estimation of the parameters of an SE(A)IR COVID-19 spread model (arxiv.org)
Gelman, A., Chew, G.L., Shnaidman, M. (2004). Bayesian Analysis of Serial Dilution Assays. Biometrics, 60, 407-417. https://doi.org/10.1111/j.0006-341x.2004.00185.x
Green, P.H. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82, 711-732. https://doi.org/10.1093/biomet/82.4.711
Ghojogh, B., Ghojogh, A., Crowley, M., Karray,
F. (2019). Fitting A Mixture Distribution to Data: Tutorial. arXiv (Cornell University). http://export.arxiv.org/pdf/1901.06708
Kaciroti, N.A., Lumeng, C., Parekh, V., Boulton,
M.L. (2021). A Bayesian Mixture Model for Predicting the COVID-19 Related Mortality in
the United States. American Journal of Tropical Medicine and Hygiene, 104, 1484-1492. https://doi.org/10.4269/ajtmh.20-1147
Koufi, A.E., Koufi, N.E. (2021). Stochastic differential equation model of Covid-19: Case study of Pakistan. Results in physics, 34, 105218.
https://doi.org/10.1016/j.rinp.2022.105218 Manevski, D., Gorenjec, N.R., Kejžar, N., Blagus,
R. (2020). Modeling COVID-19 pandemic using Bayesian analysis with application to Slovene data. Mathematical biosciences, 329, 108466.
https://doi.org/10.1016/j.mbs.2020.108466 Robert, C.P., Casella, G. (2005). Monte Carlo
Statistical Methods (Springer Texts in Statistics). Springer-Verlag New York, Inc. eBooks. https://dl.acm.org/citation.cfm?id=1051451
R Core Team (2021). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.
PAHO (2020). Epidemic diseases – Cumulative suspected and confirmed COVID-19 cases reported by countries and territories in the Americas. Pan American Health Organization. covid19-cumulative cases-03.31.20.pdf (paho.org)
Plummer, M. (2019). rjags: Bayesian Graphical Models using MCMC. R package version 4-10. https://CRAN.R-project.org/package=rjags
Tejeira-Huacani, J.D. (2020). Análisis de un modelo matemático simple para la descripción de propagación de COVID-19. Revista Boliviana de Física, 37, 41-43.
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Copyright (c) 2026 Yaineris Ferrán, Francisco J. Ariza, Martín P. Árciga, Jorge Sánchez (Autor/a)
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