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Parameter Estimation and Sensitivity Analysis of Dysentery Diarrhea Epidemic Model

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  • Hailay Weldegiorgis Berhe
  • Oluwole Daniel Makinde
  • David Mwangi Theuri

Abstract

In this paper, dysentery diarrhea deterministic compartmental model is proposed. The local and global stability of the disease‐free equilibrium is obtained using the stability theory of differential equations. Numerical simulation of the system shows that the backward bifurcation of the endemic equilibrium exists for R0 > 1. The system is formulated as a standard nonlinear least squares problem to estimate the parameters. The estimated reproduction number, based on the dysentery diarrhea disease data for Ethiopia in 2017, is R0 = 1.1208. This suggests that elimination of the dysentery disease from Ethiopia is not practical. A graphical method is used to validate the model. Sensitivity analysis is carried out to determine the importance of model parameters in the disease dynamics. It is found out that the reproduction number is the most sensitive to the effective transmission rate of dysentery diarrhea (βh). It is also demonstrated that control of the effective transmission rate is essential to stop the spreading of the disease.

Suggested Citation

  • Hailay Weldegiorgis Berhe & Oluwole Daniel Makinde & David Mwangi Theuri, 2019. "Parameter Estimation and Sensitivity Analysis of Dysentery Diarrhea Epidemic Model," Journal of Applied Mathematics, John Wiley & Sons, vol. 2019(1).
    • Handle: RePEc:wly:jnljam:v:2019:y:2019:i:1:n:8465747
    DOI: 10.1155/2019/8465747
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    References listed on IDEAS

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    1. Oluwatobi Blessing Ojo & Siaka Lougue & Woldegebriel Assefa Woldegerima, 2017. "Bayesian generalized linear mixed modeling of Tuberculosis using informative priors," PLOS ONE, Public Library of Science, vol. 12(3), pages 1-14, March.
    2. Misra, A.K. & Gupta, Alok & Venturino, Ezio, 2016. "Cholera dynamics with Bacteriophage infection: A mathematical study," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 610-621.
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    Cited by:

    1. Assefa Denekew Zewdie & Sunita Gakkhar, 2020. "A Mathematical Model for Nipah Virus Infection," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).

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