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Prediction of influenza peaks in Russian cities: Comparing the accuracy of two SEIR models

  • * Corresponding author: vnleonenko@yandex.ru

    * Corresponding author: vnleonenko@yandex.ru 
Abstract Full Text(HTML) Figure(10) / Table(3) Related Papers Cited by
  • This paper is dedicated to the application of two types of SEIR models to the influenza outbreak peak prediction in Russian cities. The first one is a continuous SEIR model described by a system of ordinary differential equations. The second one is a discrete model formulated as a set of difference equations, which was used in the Baroyan-Rvachev modeling framework for the influenza outbreak prediction in the Soviet Union. The outbreak peak day and height predictions were performed by calibrating both models to varied-size samples of long-term data on ARI incidence in Moscow, Saint Petersburg, and Novosibirsk. The accuracy of the modeling predictions on incomplete data was compared with a number of other peak forecasting methods tested on the same dataset. The drawbacks of the described prediction approach and possible ways to overcome them are discussed.

    Mathematics Subject Classification: 37N25, 65C20, 92C60.


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  • Figure 1.  An example of the epidemic curve extraction from the interpolated ARI incidence

    Figure 2.  ARI incidence curve showing the discrepancy between different curve allocation algorithms

    Figure 3.  The fitting quality of the algorithms in the case of complete outbreak data

    Figure 4.  An example of epidemic peak prediction by Baroyan-Rvachev model

    Figure 5.  An example of estimating forecast accuracies. The height of the green bars corresponds to the duration of the outbreak before reaching the peak, the markers indicate the day when the accuracy criterion was reached by the particular model. The absent bars correspond to the years without an epidemic outbreak

    Figure 6.  The dependence of the percentage of accurate predictions from the number of days before the peak, in overall for the three cities

    Figure 7.  The dependence of the percentage of accurate predictions from the number of days before the peak, horizontal stripe

    Figure 8.  The dependence of the percentage of accurate predictions from the number of days before the peak, vertical stripe

    Figure 9.  The dependence of the percentage of accurate predictions from the number of days before the peak, square

    Figure 10.  The comparison of the statistical and modeling forecasting methods

    Table 1.  Parameters of the fitting algorithm for the continuous SEIR model

    Epidemiological parameters
    $\alpha$Initial ratio of susceptible individuals in the populationEstimated-
    $\beta$Intensity of infectionEstimated1/(person$\cdot$day)
    $\gamma$Intensity of transition to infective form of the disease0.391/day
    $\delta$Intensity of recovery0.1331/day
    $I_{0}$Initial ratio of the infected0.0001-
    Curve positioning parameters
    $k_{inc}$Relative vertical bias of the modeled incidence curve positionEstimated-
    $\Delta_s$Absolute horizontal bias of the modeled incidence curve epidemic start position compared to the dataEstimatedday
     | Show Table
    DownLoad: CSV

    Table 2.  Parameters of the fitting algorithm for Baroyan-Rvachev model

    Model parameters
    $\alpha$Initial ratio of susceptible individuals in the populationEstimated-
    $\beta$Intensity of infectionEstimated-
    $I_{0}$Initial ratio of infected in the populationEstimated-
    $T$Duration of infectionFixedday
    $g_\tau$A fraction of infectious individuals among those who were infected $\tau$ days before the current momentFixed-
    $\rho$Population sizeFixedpersons
    Curve positioning parameters
    $\Delta_p$Absolute horizontal bias of the modeled incidence curve peak position compared to the dataEstimatedday
     | Show Table
    DownLoad: CSV

    Table 3.  Varied model parameters

    DefinitionDescriptionValueVariation type
    Continuous SEIR model
    $\alpha$Initial ratio of susceptible individuals in the population$[10^{-2}; 1.0]$BFGS optimization
    $\beta$Intensity of infection$[10^{-7}; 50.0]$BFGS optimization
    $k_{inc}$Relative vertical bias of the modeled incidence curve position$[0.8; 1.0]$BFGS optimization
    $\Delta_s$Absolute horizontal bias of the modeled incidence curve epidemic start position compared to the data$5, \dots, 54$Iteration
    Baroyan-Rvachev model
    $k$The service parameter defining the product of $\alpha$ and $\beta$$[1.02; 1.6]$BFGS optimization
    $I_{0}$Initial ratio of infected in the population$[10^{-1}; 50.0]$BFGS optimization
    $\Delta_p$*Absolute horizontal bias of the modeled incidence curve peak position compared to the data$-3, \dots, 3$Iteration
    $\theta^{(dat)}_{peak}$**Prospected incidence curve peak day$17, \dots, 83$Iteration
      * For complete incidence data ** For incomplete incidence data
     | Show Table
    DownLoad: CSV
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