Forecasting COVID-19 Epidemic in Spain and Italy Using A Generalized Richards Model with Quantified Uncertainty

Authors

  • Isnani Darti Biomathematics Research Group, Department of Mathematics, University of Brawijaya, Malang 65145
  • Agus Suryanto Biomathematics Research Group, Department of Mathematics, University of Brawijaya, Malang 65145
  • Hasan S. Panigoro 1) Biomathematics Research Group, Department of Mathematics, University of Brawijaya, Malang 65145 2) Department of Mathematics, State University of Gorontalo, Bone Bolango 96119
  • Hadi Susanto 1) Department of Mathematics, Khalifa University, Abu Dhabi Campus, PO Box 127788, Abu Dhabi, United Arab Emirates 2) Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester, CO4 3SQ

DOI:

https://doi.org/10.5614/cbms.2020.3.2.1

Keywords:

Generalized Richards Models, Uncertainty, Boostraap, COVID-19

Abstract

The Richards model and its generalized version are deterministic models that are often implemented to fit and forecast the cumulative number of infective cases in an epidemic outbreak. In this paper we employ a generalized Richards model to predict the cumulative number of COVID-19 cases in Spain and Italy, based on available epidemiological data. To quantify uncertainty in the parameter estimation, we use a parametric bootstrapping approach to construct a 95% confidence interval estimation for the parameter model. Here we assume that the time series data follow a Poisson distribution. It is found that the 95% confidence interval of each parameter becomes narrow with the increasing number of data. All in all, the model predicts daily new cases of COVID-19 reasonably well during calibration periods. However, the model fails to produce good forecasts when the amount of data used for parameter estimations is not sufficient. Based on our parameter estimates, it is found that the early stages of COVID-19 epidemic, both in Spain and in Italy, followed an almost exponentially growth. The epidemic peak in Spain and Italy is respectively on 2 April 2020 and 28 March 2020. The final sizes of cumulative number of COVID-19 cases in Spain and Italy are forecasted to be at 293220 and 237010, respectively.

References

Chen, Z-L., Zhang, Q., Lu, Y., Guo, Z-M., Zhang, X., Zhang, W-J., Guo, C., Liao, C-H., Li, Q-L., Han, X-H. and Lu, J-H., Distribution of the COVID-19 epidemic and correlation with population emigration from Wuhan, China, Chinese medical journal, 133(9):1044–1050, 2020.

Zhao, S., Musa, S.S., Lin, Q., Ran, J., Yang, G., Wang, W., Lou, Y., Yang, L., Gao, D., He, D. and Wang, M.H., Estimating the Unreported Number of Novel Coronavirus (2019-nCoV) Cases in China in the First Half of January 2020: A Data-Driven Modelling Analysis of the Early Outbreak, Journal of Clinical Medicine, 9(2):388, 2020.

Wu, P., Hao, X., Lau, E.H.Y., Wong, J.Y., Leung, K.S.M., Wu, J.T., Cowling, B.J. and Leung, G.M., Real-time tentative assessment of the epidemiological characteristics of novel coronavirus infections in Wuhan, China, as at 22 January 2020, Euro surveillance: bulletin Europeen sur les maladies transmissibles = European communicable disease bulletin, 25(3):1–6, 2020.

Zhu, N., Zhang, D., Wang, W., Li, X., Yang, B., Song, J., Zhao, X., Huang, B., Shi, W., Lu, R., Niu, P., Zhan, F., Ma, X., Wang, D., Xu, W., Wu, G., Gao, G.F. and Tan, W., A novel coronavirus from patients with pneumonia in China, 2019, New England Journal of Medicine, 382(8):727–733, 2020.

Cui, J., Li, F. and Shi, Z.L., Origin and evolution of pathogenic coronaviruses, Nature Reviews Microbiology, 17(3):181–192, 2019.

Han, Q., Lin, Q., Jin, S. and You, L., Coronavirus 2019-nCoV: A brief perspective from the front line, Journal of Infection, 80(4):373–377, 2020.

Li, J-H., You, Z., Wang, Q., Zhou, Z-J., Qiu, Y., Luo, R. and Ge, X-Y., The epidemic of 2019-novel-coronavirus (2019-nCoV) pneumonia and insights for emerging infectious diseases in the future, Microbes and Infection, 22(2):80–85, 2020.

Sartor, G., Riccio, M.D., Poz, I.D., Bonanni, P. and Bonaccorsi, G., COVID-19 in Italy: considerations on official data, International journal of infectious diseases, 98:188–190, 2020.

Worldometer, Coronavirus Cases Data, https://www.worldometers.info/coronavirus/#countries, 2020. Accessed on June 21, 2020.

Vergori, A.S. and Arima, S., Cultural and non-cultural tourism: Evidence from Italian experience, Tourism Management, 78:104058, 2020.

Fern´andez, X.L., Coto-Mill´an, P. and D´ıaz-Medina, B., The impact of tourism on airport efficiency: The Spanish case, Utilities Policy, 55:52–58, 2018.

AS English, Coronavirus: How long has Spain been on lockdown and when will it end?, https://en.as.com/en/2020/04/09/otherfgsports/1586460059fg015568.html, 2020. Accessed on July 14, 2020.

Florence, Italy, the first country in Europe to enter lockdown, starts to emerge, https://www.economist.com/europe/2020/05/09/italy-the-first-country-in-europe-to-enter-lockdown-starts-to-emerge, 2020. Accessed on July 14, 2020.

S¸ ahin, U. and S¸ ahin, T., Forecasting the cumulative number of confirmed cases of COVID-19 in Italy, UK and USA using fractional nonlinear grey Bernoulli model, Chaos, Solitons and Fractals, 138: 109948, 2020.

Fanelli, D. and Piazza, F., Analysis and forecast of COVID-19 spreading in China, Italy and France, Chaos, Solitons and Fractals, 134:109761, 2020.

Chintalapudi, N., Battineni, G. and Amenta, F., COVID-19 virus outbreak forecasting of registered and recovered cases after sixty day lockdown in Italy: A data driven model approach, Journal of Microbiology, Immunology and Infection, 53(3):396–403, 2020.

Ahmar, A.S. and del Val, E.B., SutteARIMA: Short-term forecasting method, a case: Covid-19 and stock market in Spain, Science of the Total Environment, 729:138883, 2020.

Zhuang, Z., Zhao, S., Lin, Q., Cao, P., Lou, Y., Yang, L., Yang, S., He, D. and Xiao, L., Preliminary estimates of the reproduction number of the coronavirus disease (COVID-19) outbreak in Republic of Korea and Italy by 5 March 2020, International Journal of Infectious Diseases, 95:308–310, 2020.

Chintalapudi, N., Battineni, G., Sagaro, G.G. and Amenta, F., COVID-19 outbreak reproduction number estimations and forecasting in Marche, Italy, International Journal of Infectious Diseases, 96:327–333, 2020.

D’Arienzo, M. and Coniglio, A., Assessment of the SARS-CoV-2 basic reproduction number, R0, based on the early phase of COVID-19 outbreak in Italy, Biosafety and Health, 2(2):57–59, 2020.

Hyafil, A. and Mori˜na, D., (in press), Analysis of the impact of lockdown on the reproduction number of the SARS-Cov-2 in Spain, Gaceta Sanitaria, 2020.

Susanto, H., Tjahjono, V.R., Hasan, A., Kasim, M.F., Nuraini, N., Putri, E.R.M., Kusdiantara, R. and Kurniawan, H., How many can you infect? simple (and naive) methods of estimating the reproduction number, Communication in Biomathematical Sciences, 3(1):28–36, 2020.

Shen, C.Y., Logistic growth modelling of COVID-19 proliferation in China and its international implications, International Journal of Infectious Diseases, 96:582–589, 2020.

Malavika, B., Marimuthu, S., Joy, M., Nadaraj, A., Asirvatham, E.S. and Jeyaseelan, L., (in press), Forecasting COVID-19 epidemic in India and high incidence states using SIR and logistic growth models, Clinical Epidemiology and Global Health, 2020.

Wang, P., Zheng, X., Li, J. and Zhu, B., Prediction of Epidemic Trends in COVID-19 with Logistic Model and Machine Learning Technics, Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, 139:110058, 2020.

Li, J. and Lou, Y., Characteristics of an epidemic outbreak with a large initial infection size, Journal of Biological Dynamics, 10(1):366–378, 2016.

Hsieh, Y-H., Richards model: A simple procedure for real-time prediction of outbreak severity, In Ma, Z., Zhou, Y. and Wu, J., editors, Modeling and Dynamics of Infectious Diseases. World Scientific, Singapore, pp. 216–236, 2009.

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

Hsieh, Y-H., Pandemic influenza A (H1N1) during winter influenza season in the southern hemisphere, Influenza Other Respir Viruses, 4:187–197, 2010.

Dinh, L., Chowell, G., Mizumoto, K. and Nishiura, H., Estimating the subcritical transmissibility of the Zika outbreak in the State of Florida, USA, 2016, Theoretical Biology and Medical Modelling, 13: 20, 2016.

Nuraini, N., Khairudin, K. and Apri, M., Modeling Simulation of COVID-19 in Indonesia based on Early Endemic Data, Communication in Biomathematical Sciences, 3:1–8, 2020.

Roosa, K., Lee, Y., Luo, R., Kirpich, A., Rothenberg, R., Hyman, J.M., Yan, P. and Chowell, G., Real-time forecasts of the COVID-19 epidemic in China from February 5th to February 24th, 2020, Infectious Disease Modelling, 5:256–263, 2020.

Roosa, K., Lee, Y., Luo, R., Kirpich, A., Rothenberg, R., Hyman, J.M., Yan, P. and Chowell, G., Short-term Forecasts of the COVID-19 Epidemic in Guangdong and Zhejiang, China: February 13–23, 2020, Journal of Clinical Medicine, 9:596, 2020.

Viboud, C., Simonsen, L. and Chowell, G., A generalized-growth model to characterize the early ascending phase of infectious disease outbreaks, Epidemics, 15:27–37, 2016.

Chowell, G. and Viboud, C., Is it growing exponentially fast? – Impact of assuming exponential growth for characterizing and forecasting epidemics with initial near-exponential growth dynamics, Infectious Disease Modelling, 1:71–78, 2016.

Chowell, G., Hincapie-Palacio, D., Ospina, J., Pell, B., Tariq, A., Dahal, S., Moghadas, S., Smirnova, A., Simonsen, L. and Viboud, C., Using Phenomenological Models to Characterize Transmissibility and Forecast Patterns and Final Burden of Zika Epidemics, Plos Currents, 8:27366586, 2016.

Chowell, G., Sattenspiel, L., Bansal, S. and Viboud, C., Mathematical models to characterize early epidemic growth: A review, Physics of Life Reviews, 18:66–97, 2016.

Shanafelt, D.W., Jones, G., Lima, M., Perrings, C. and Chowell, G., Forecasting the 2001 Foot-and-Mouth Disease Epidemic in the UK, EcoHealth, 15:338–347, 2018.

Wu, K., Darcet, D., Wang, Q. and Sornette, D., 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, 2020.

Chowell, G., Fitting dynamic models to epidemic outbreaks with quantified uncertainty: A primer for parameter uncertainty, identifiability, and forecasts, Infectious Disease Modelling, 2(3):379–398, 2017.

Downloads

Published

2021-05-10

Issue

Section

Articles