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


  • 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



Generalized Richards Models, Uncertainty, Boostraap, COVID-19


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.


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