Table 1.
Parameters used in synthetic data generation.
Fig 1.
Comparison of errors in estimated parameters.
The percentage error in the estimated parameters using EnKF (ensemble size, n = 200) with different damping factors.
Fig 2.
Comparison of RMAE with different damping factors.
Relative Mean Absolute Error of the simulated model states (infected, recovered and death cases) as a function of damping factor.
Fig 3.
Comparison of RMAE with ensemble size.
RMAE of the number of the infected, recovered, death cases as a function of ensemble size.
Fig 4.
Evolution of the parameter estimates for the first test case (synthetic data).
Estimated parameters using augmented EnKF (α = 1 and ensemble size n = 200). In each plot, the blue line represents the target value of the model parameters, and the solid black line represents the EnKF mean value. The uncertainties (standard deviation curves) around the mean values are filled in grey.
Table 2.
Parameter estimates for the first test case (synthetic data).
EnKF estimated parameters with their associated uncertainties.
Fig 5.
Comparison of time varying parameters.
Best fit parameters of the time-varying infection, recovery and death rates.
Fig 6.
Profiles obtained using the SIRD model with true and estimated parameters.
The plots show the accuracy of the curve fitting between the synthetic observations and the simulated profiles obtained with the estimated parameters.
Table 3.
Performance of SIRD model with estimated parameters.
RMAE and R2 values of the simulated states.
Fig 7.
Cumulative number of COVID-19 cases.
Cumulative number of COVID-19 cases in Hubei province, China. Blue dots represents the reported data and black dots represents the modified (reconstructed) time-series data from January 22, 2020 (t = 0) to April 13, 2020 (t = 82).
Table 4.
Initial parameter values for case_orig and case_mod.
Initial ensemble for parameter values randomly drawn from a uniform distribution with an initial range of values as presented below.
Fig 8.
Evolution of the parameter estimates for case_orig.
In each plot, the solid black line represents the EnKF mean value. The uncertainties (standard deviation curves) around the mean values are filled in grey.
Fig 9.
Evolution of the parameter estimates for case_mod.
In each plot, the solid black line represents the EnKF mean value. The uncertainties (standard deviation curves) around the mean values are filled in grey.
Table 5.
Parameter estimates for the second test case (real data).
EnKF estimated parameters with their associated uncertainties for case_orig and case_mod.
Fig 10.
Comparison of time varying parameters with real data.
The best-fit parameters of the estimated time-varying infection, recovery and death rates of case_orig and case_mod.
Fig 11.
The simulated profiles considering the estimated parameters for case_orig (in solid red lines) and case_mod (in solid black lines). The plots show the accuracy of the curve fitting between the simulated and observed data (blue dots for reported data and black dots for modified active cases).
Table 6.
Comparison of the estimated model using real data.
R2 values of the simulated states for case_orig and case_mod.
Table 7.
Comparison of transmission (infection) rate.
Comparison of estimated β(0) from case_orig with some recent work. The values are directly taken from the reported results of five different methods (SFS, MOSFS, DE, EAKF and data fitting) presented in the reference literature [2, 11, 18, 54].