A Comparative Analysis between a SIRD Compartmental Model and the Richards Growth Model

A. M. S. Macêdo, A. A. Brum, G. C. Duarte-Filho, F. A. G. Almeida, R. Ospina, G. L. Vasconcelos


We propose a compartmental SIRD model with time-dependent parameters that can be used to give epidemiological interpretations to the phenomenological parameters of the Richards growth model. We illustrate the use of the map between these two models by fitting the fatality curves of the COVID-19 epidemic data in Italy, Germany, Sweden, Netherlands, Cuba, and Japan, up to July 30, 2020.


COVID-19; Fatality curve; SIRD model; Richards growth model; Intervention strategies

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WHO, “World Health Organization (WHO). Director-General’s opening

remarks at the media briefing on COVID-19 - 30 July 2020.” https:


remarks-at-the-media-briefing-on-covid-19---30-july-2020, 2020. Accessed: 2020-07-30.

WHO, “World Health Organization (WHO). Director-General’s ope-

ning remarks at the media briefing on COVID-19 - 30 March 2020.”


opening-remarks-at-the-media-briefing-on-covid-19-30-march-2020, 2020. Accessed: 2020-03-30.

W. O. Kermack and A. G. McKendrick, “A contribution to the mathematical theory of epidemics,” Proceedings of the royal society of london. Series A, Containing papers of a mathematical and physical character, vol. 115, no. 772, pp. 700–721, 1927.

D. Caccavo, “Chinese and Italian COVID-19 outbreaks can be correctly described by a modified SIRD model,” medRxiv medRxiv:2020.03.19.20039388, 2020.

M. Fukui and C. Furukawa, “Power laws in superspreading events: Evidence from coronavirus outbreaks and implications for SIR models,” medRxiv medRxiv:2020.06.11.20128058, 2020.

U. Tirnakli and C. Tsallis, “Epidemiological model with anomalous kineticsthe Covid-19 pandemics,” medRxiv medRxiv:2020.06.24.20139287, 2020.

A. Atkeson, “What will be the economic impact of covid-19 in the us? rough estimates of disease scenarios,” tech. rep., National Bureau of Economic Research, 2020.

E. B. Postnikov, “Estimation of COVID-19 dynamics “on a back-of-envelope”: Does the simplest SIR model provide quantitative parameters and predictions?,” Chaos, Solitons & Fractals, vol. 135, p. 109841, 2020.

Z. Yang, Z. Zeng, K. Wang, S.-S. Wong, W. Liang, M. Zanin, P. Liu, X. Cao, Z. Gao, Z. Mai, et al., “Modified SEIR and AI prediction of the epidemics trend of COVID-19 in China under public health interventions,” Journal of Thoracic Disease, vol. 12, no. 3, p. 165, 2020.

S. Zhao and H. Chen, “Modeling the epidemic dynamics and control of COVID- 19 outbreak in China,” Quantitative Biology, pp. 1–9, 2020.

I. Cooper, A. Mondal, and C. G. Antonopoulos, “A SIR model assumption for the spread of COVID-19 in different communities,” Chaos, Solitons & Fractals, p. 110057, 2020.

K. Wu, D. Darcet, Q. Wang, and D. Sornette, “Generalized logistic growth modeling of the COVID-19 outbreak in 29 provinces in China and in the rest of the world.” https://www.medrxiv.org/content/early/2020/03/16/

03.11.20034363.full.pdf, 2020.

G. L. Vasconcelos, A. M. Macêdo, R. Ospina, F. A. Almeida, G. C. Duarte-Filho, A. A. Brum, and I. C. Souza, “Modelling fatality curves of COVID-19 and the effectiveness of intervention strategies,” PeerJ, vol. 8, p. e9421, June 2020.

M. Gillman and N. Crokidakis, “Dynamics and future of SARS-CoV-2 in the human host,” medRxiv medRxiv 2020.07.14.20153270, 2020.

G. L. Vasconcelos, A. M. Macêdo, G. C. Duarte-Filho, A. A. Araújo, R. Ospina, and F. A. Almeida, “Complexity signatures in the COVID-19 epidemic: power law behaviour in the saturation regime of fatality curves,” medRxiv medRxiv 2020.07.12.20152140, 2020.

X.-S. Wang, J. Wu, and Y. Yang, “Richards model revisited: Validation by and application to infection dynamics,” Journal of Theoretical Biology, vol. 313, pp. 12–19, 2012.

R. Veiga, R. Murta, and R. Vicente, “Age-structured estimation of COVID-19 ICU demand from low quality data,” arXiv preprint arXiv:2006.06530, 2020.

M. F. do Prado, B. Brandão, S. L. Bastos, I. T. Peres, A. d. A. B. da Silva, L. F. Dantas, F. Araújo, and F. A. Bozza, “Analysis of covid-19 under-reporting in brazil,” Revista Brasileira de terapia intensiva, vol. 32, no. 2, pp. 224–228, 2020.

JHU, “Coronavirus COVID-19 Global Cases by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University (JHU) .” https://coronavirus.jhu.edu/map.html, 2020. Accessed: 2020-07-30.

F. Richards, “A flexible growth function for empirical use,” Journal of experimental Botany, vol. 10, no. 2, pp. 290–301, 1959.

X.-S. Wang, J. Wu, and Y. Yang, “Richards model revisited: Validation by and application to infection dynamics,” Journal of Theoretical Biology, vol. 313, pp. 12–19, 2012.

Y.-H. Hsieh, “Richards model: a simple procedure for real-time prediction of outbreak severity,” in Modeling and dynamics of infectious diseases, pp. 216–236, World Scientific, 2009.

O. Diekmann, J. A. P. Heesterbeek, and J. A. Metz, “On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations,” Journal of mathematical biology, vol. 28, no. 4, pp. 365–382, 1990.

O. Diekmann, J. Heesterbeek, and M. G. Roberts, “The construction of next- generation matrices for compartmental epidemic models,” Journal of the Royal Society Interface, vol. 7, no. 47, pp. 873–885, 2010.

J. J. Moré, “The Levenberg-Marquardt algorithm: implementation and theory,” in Numerical analysis, pp. 105–116, Springer, 1978.

M. Newville, T. Stensitzki, D. Allen, and A. Ingargiola, “Non-linear least-

squares minimization and curve-fitting for Python,” Chicago, IL, 2015.

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