Selected article for: "cumulative number and exponential curve"
Author: Peter X Song; Lili Wang; Yiwang Zhou; Jie He; Bin Zhu; Fei Wang; Lu Tang; Marisa Eisenberg
Title: An epidemiological forecast model and software assessing interventions on COVID-19 epidemic in China
  • Document date: 2020_3_3
    • ID: m9icky9z_38
    Snippet: We assume an exponential growth curve for the cumulative number of infected cases in Hubei before Feb 12 of the form yptq " ae λt`b , where parameters λ, a, b are to be estimated. Under the boundary conditions ypt " Jan 12q " 0 and ypt " Feb 12q " a expp31λq`b, we would like to minimize the one-step ahead extrapolation error on Feb 13. The constrained optimal solution can be obtained by the means of Lagrange Multipliers; the estimates areλ " .....
    Document: We assume an exponential growth curve for the cumulative number of infected cases in Hubei before Feb 12 of the form yptq " ae λt`b , where parameters λ, a, b are to be estimated. Under the boundary conditions ypt " Jan 12q " 0 and ypt " Feb 12q " a expp31λq`b, we would like to minimize the one-step ahead extrapolation error on Feb 13. The constrained optimal solution can be obtained by the means of Lagrange Multipliers; the estimates areλ " 0.06605,â " 7142.80,b " 7142.80. The resulting calibration curves for the cumulative and daily added number of infected cases are shown as the solid red curves in Figure 8 . For example, on Jan 31, the reported cumulative number of infected cases is 7,153, but the calibrated number of infected cases is 17,911, with an increment of 10,758 cases. As shown later, this data quality control (QC) step helps improve the performance of MCMC.

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