Mathematical modeling and forecasting of COVID-19: experience in Santiago de Cuba province

E. E. Ramirez-Torres, A. R. Selva Castañeda, Y. Rodríguez-Aldana, S. Sánchez Domínguez, L. E. Valdés García, A. Palú-Orozco, E.R. Oliveros-Domínguez, L. Zamora-Matamoros, R. Labrada-Claro, M. Cobas-Batista, D. Sedal-Yanes, O. Soler-Nariño, P. A. Valdés-Sosa, J. I. Montijano, L. E. Bergues Cabrales


In the province of Santiago de Cuba, Cuba, the COVID-19 epidemic has a limited progression that shows an early small-number peak of infections. Most published mathematical models fit data with high numbers of confirmed cases. In contrast, small numbers of cases make it difficult to predict the course of the epidemic. We present two known models adapted to capture the noisy dynamics of COVID-19 in the Santiago de Cuba province. Parameters of both models were estimated using the approximate-Bayesian-computation framework with dedicated error laws. One parameter of each model was updated on key dates of travel restrictions. Both models approximately predicted the infection peak and the end of the COVID-19 epidemic in Santiago de Cuba. The first model predicted 57 reported cases and 16 unreported cases. Additionally, it estimated six initially exposed persons. The second model forecasted 51 confirmed cases at the end of the epidemic. In conclusion, an opportune epidemiological investigation, along with the low number of initially exposed individuals, might partly explain the favorable evolution of the COVID-19 epidemic in Santiago de Cuba. With the available data, the simplest model predicted the epidemic evolution with greater precision, and the more complex model helped to explain the epidemic phenomenology.


COVID-19 epidemic, mathematical modelling, approximate Bayesian computation, Poisson noise

Full Text:



D. He, J. Dushoff, T. Day, J. Ma, and D. J. Earn, P. Roy. Soc.

B-Biol. Sci. 280, 20131345 (2013).

C. Anastassopoulou, L. Russo, A. Tsakris, and C. Siettos, PloS One 15, e0230405 (2020).

K. Jagodnik, F. Ray, F. M. Giorgi, and A. Lachmann, Preprint

medRvix 14 (2020).

G. C. Calafiore, C. Novara, and C. Possieri, arXiv preprint

arXiv:2003.14391 (2020).

B. Ivorra, M. R. Ferrández, M. Vela-Pérez, and A. Ramos,

Commun. Nonlinear Sci. , 105303 (2020).

C. Reno, J. Lenzi, A. Navarra, E. Barelli, D. Gori, A. Lanza,

R. Valentini, B. Tang, and M. P. Fantini, J. Clin. Med. 9, 1492


M. D’Arienzo and A. Coniglio, Biosafety and Health (2020).

D. Fanelli and F. Piazza, Chaos Solitons Fract. 134, 109761


E. B. Postnikov, Chaos Solitons Fract. 135, 109841 (2020).

J. Wangping, H. Ke, S. Yang, C. Wenzhe, W. Shengshu,

Y. Shanshan, W. Jianwei, K. Fuyin, T. Penggang, Li. Jing,

L. Miao, and H. Yao, Front. Med. 7, 169 (2020).

A. L. Lloyd, P. Roy. Soc. B-Biol. Sci. 268, 985 (2001).

S. Zhao and H. Chen, Quant. Biol., 1 (2020).

R. F. Reis, B. de Melo Quintela, J. de Oliveira Campos, J.

M. Gomes, B. M. Rocha, M. Lobosco, and R. W. dos Santos,

Chaos Solitons Fract., 109888 (2020).

C. S. M. Currie, J. W. Fowler, K. Kotiadis, T. Monks, B. S.

Onggo, D. A. Robertson, and A. A. Tako, J. Simulat. , 1 (2020).

S. Zhao, S. S. Musa, Q. Lin, J. Ran, G. Yang,W.Wang, Y. Lou, L. Yang, D. Gao, D. He, and M. H. Wang, J. Clin. Med. 9, 388 (2020).

G. Giordano , F. Blanchini, R. Bruno, P. Colaneri, A. Di Filippo, A. Di Matteo, and M. Colaneri, Nat. Med., 1 (2020).

R. M. Anderson, H. Heesterbeek, D. Klinkenberg, and T. D.

Hollingsworth, The Lancet 395, 931 (2020).

A. Minter and R. Retkute, Epidemics 29, 100368 (2019).

S. Galea, M. Riddle, and G. A. Kaplan, Int. J. Epidemiol. 39,


H. H. Weiss, Materials matematics, 0001 (2013).

G. V. Rossum, The Python Library Reference: Release 3.6.4, 12th Media Services, 2018.

L. Ferretti, C. Wymant, M. Kendall, L. Zhao, A. Nurtay, L.

Abeler-Dorner, M. Parker, D. Bonsall, and C. Fraser, Science


P. E. McKnight and J. Najab, The Corsini encyclopedia of psychology, 1 (2010).

A. R. Tuite and D. N. Fisman, Ann. Intern. Med. (2020).

R. Li, S. Pei, B. Chen, Y. Song, T. Zhang, W. Yang, and J.

Shaman, Science 368, 489 (2020).

W. C. Roda, M. B. Varughese, D. Han, and M. Y. Li, Infect.

Dis. Model. (2020).

G. Guzzetta, P. Poletti, M. Ajelli, F. Trentini, V. Marziano,

D. Cereda, M. Tirani, G. Diurno, A. Bodina, A. Barone, L.

Crottogini, M. Gramegna, A. Melegaro, and S. Merler, Euro

Surveill. 25, 2000293 (2020).

E. L. Piccolomini and F. Zama, arXiv preprint

arXiv:2003.09909 (2020).

Z. Liu, P. Magal, O. Seydi, and G. Webb, Biology 9, 50 (2020).

A. J. Kucharski, T. W. Russell, C. Diamond, Y. Liu, J. Edmunds, S. Funk, and R. M. Eggo, Lancet. Infect. Dis. (2020).

V. Amrhein, T. Roth, and F. Korner-Nievergelt, F1000 Research 2, 278 (2015).

M. A. Beaumont, Annu. Rev. Ecol. Evol. Syst. 41, 379 (2010).

M. A. Beaumont, J. M. Cornuet, J. M. Marin, and C. P. Robert, Biometrika 96, 983 (2009).

A. C. Cameron and F. A. Windmeijer, J. Econom. 77, 329


G. W. Corder and D. I. Foreman, Nonparametric statistics for non-statisticians, 2011.

C. C. Drovandi and A. N. Pettitt, Biometrics 67, 225 (2011).

A. Gelman, Stat. Sci. 24, 176 (2009).

J. Kruschke, Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan, Academic Press, 2014.

M. Lenormand, F. Jabot, and G. Deffuant, Comput. Stat. 28,


R. Libeskind-Hadas and E. Bush, Computing for Biologists:

Python Programming and Principles, Cambridge University

Press, 2014.

Q. Lin et al., Int. J. Infect. Dis. 93, 211 (2020).

J. Lintusaari, M. U. Gutmann, R. Dutta, S. Kaski, and J. Corander, Syst. Biol. 66, e66 (2017).

J. M. Marin, P. Pudlo, C. P. Robert, and R. J. Ryder, Stat. Comput. 22, 1167 (2012).

P. Marjoram, J. Molitor, V. Plagnol, and S. Tavaré, Proc. Natl. Acad. Sci. USA 100, 15324 (2003).

P. Del Moral, A. Doucet, and A. Jasra, Stat. Comput. 22, 1009 (2012).

H. Motulsky and A. Christopoulos, Fitting Models to Biological Data Using Linear and Nonlinear Regression: A Practical Guide to Curve Fitting, Oxford University Press, 2004.

G. W. Peters, Y. Fan, and S. A. Sisson, Stat. Comput. 22, 1209 (2012).

J. K. Pritchard, M. T. Seielstad, A. Perez-Lezaun, and M. W.

Feldman, Mol. Biol. Evol. 16, 1791 (1999).

N. M. Razali and Y. B. Wah, Journal of statistical modeling

and analytics 2, 21 (2011).

V. K. Rohatgi and A. M. E. Saleh, An Introduction to Probability and Statistics, John Wiley & Sons, 2015.

S. Sanche, Y. T. Lin, C. Xu, E. Romero-Severson, N. W. Hengartner, and R. Ke, arXiv preprint arXiv:2002.03268 (2020).

D. F. Slezak, C. Suárez, G. A. Cecchi, G. Marshall, and

G. Stolovitzky, PloS One 5 (2010).

A. Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation, volume 89, Society for Industrial and Applied Mathematics, 2005.

T. Toni, D. Welch, N. Strelkowa, A. Ipsen, and M. P. Stumpf,

J. R. Soc. Interface 6, 187 (2009).

R. D. Wilkinson, Stat. Appl. Genet. Mol. Biol. 12, 129 (2013).

S. A. Sisson, Y. Fan, and M. Beaumont, Handbook of Approximate Bayesian Computation, Chapman and Hall/CRC, 2018.



  • There are currently no refbacks.

REVISTA MEXICANA DE FÍSICA, year 67, issue 2, March-April 2021. Bimonthly Journal published by Sociedad Mexicana de Física, A. C. Departamento de Física, 2º Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Apartado Postal 70-348. Tel. (+52)55-5622-4946,, e-mail: Chief Editor: José Alejandro Ayala Mercado. INDAUTOR Certificate of Reserve: 04-2019-080216404400-203, ISSN: 2683-2224 (on line), 0035-001X (print), both granted by Instituto Nacional del Derecho de Autor. Responsible for the last update of this issue, Technical Staff of Sociedad Mexicana de Física, A. C., Fís. Efraín Garrido Román, 2º. Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Date of last modification, March 1st., 2021.

The responsibility of the materials published in Revista Mexicana de Física rests solely with their authors and their content does not necessarily reflect the criteria of the Editorial Committee or the Sociedad Mexicana de Física. The total or partial reproduction of the texts hereby published is authorized as long as the complete source and the electronic address of the publications are cited.

There is no fee for article processing, submission or publication.

Revista Mexicana de Física by Sociedad Mexicana de Física, A. C. is distributed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License