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Analysis of bias in an Ebola epidemic model by extended Kalman filter approach

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  • Ndanguza, Denis
  • Mbalawata, Isambi S.
  • Haario, Heikki
  • Tchuenche, Jean M.

Abstract

Ebola is a highly infectious disease generally characterized by sporadic outbreaks. A deterministic Ebola model is formulated and converted into Itô stochastic differential equations by adding noise on each compartment. In order to estimate the model parameter values, we use the extended Kalman filter technique as the filtering method and sum of square of errors to compute an approximation of the likelihood. From the obtained likelihood function, the maximum likelihood and MCMC methods for parameters estimation are then used. These parameter estimates provide useful information on quantities of epidemiological interest. Two cases are analyzed: (1) the model error covariance is set to be zero and (2) the bias is fully incorporated into the model. A comparison between these two cases is carried out to assess whether the bias is having a measure effect on parameters and states estimation. Finally, we investigate whether an estimate obtained from a biased study differs systematically from the true source population of the study. Our results indicate that the more the increase of bias, the more the noise in states simulation and parameters estimation compared to the deterministic model.

Suggested Citation

  • Ndanguza, Denis & Mbalawata, Isambi S. & Haario, Heikki & Tchuenche, Jean M., 2017. "Analysis of bias in an Ebola epidemic model by extended Kalman filter approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 142(C), pages 113-129.
    • Handle: RePEc:eee:matcom:v:142:y:2017:i:c:p:113-129
    DOI: 10.1016/j.matcom.2017.05.005
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    References listed on IDEAS

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    1. Li, Guihua & Jin, Zhen, 2005. "Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1177-1184.
    2. Isambi Mbalawata & Simo Särkkä & Heikki Haario, 2013. "Parameter estimation in stochastic differential equations with Markov chain Monte Carlo and non-linear Kalman filtering," Computational Statistics, Springer, vol. 28(3), pages 1195-1223, June.
    3. Phenyo E. Lekone & Bärbel F. Finkenstädt, 2006. "Statistical Inference in a Stochastic Epidemic SEIR Model with Control Intervention: Ebola as a Case Study," Biometrics, The International Biometric Society, vol. 62(4), pages 1170-1177, December.
    4. Sherry Towers & Shehzad Afzal & Gilbert Bernal & Nadya Bliss & Shala Brown & Baltazar Espinoza & Jasmine Jackson & Julia Judson-Garcia & Maryam Khan & Michael Lin & Robert Mamada & Victor M Moreno & F, 2015. "Mass Media and the Contagion of Fear: The Case of Ebola in America," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-13, June.
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    Cited by:

    1. Song, Jialu & Xie, Hujin & Gao, Bingbing & Zhong, Yongmin & Gu, Chengfan & Choi, Kup-Sze, 2021. "Maximum likelihood-based extended Kalman filter for COVID-19 prediction," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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