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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 . 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 . 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 ( ). 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, Hindawi, vol. 2019, pages 1-13, February.
    • Handle: RePEc:hin:jnljam:8465747
    DOI: 10.1155/2019/8465747
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    Cited by:

    1. Berhe, Hailay Weldegiorgis, 2020. "Optimal Control Strategies and Cost-effectiveness Analysis Applied to Real Data of Cholera Outbreak in Ethiopia’s Oromia Region," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Berhe, Hailay Weldegiorgis & Qureshi, Sania & Shaikh, Asif Ali, 2020. "Deterministic modeling of dysentery diarrhea epidemic under fractional Caputo differential operator via real statistical analysis," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    3. Munir, Mohammad & Kausar, Nasreen & Shakil, Mohammad, 2021. "Parameter identification for multiperiodic functions," Technological Forecasting and Social Change, Elsevier, vol. 173(C).
    4. Yudie Hu & Hongyan Wang & Shaoping Jiang, 2024. "Analysis and Optimal Control of a Two-Strain SEIR Epidemic Model with Saturated Treatment Rate," Mathematics, MDPI, vol. 12(19), pages 1-17, September.
    5. Chih-Wen Chang & Zohaib Ali Qureshi & Sania Qureshi & Asif Ali Shaikh & Muhammad Yaqoob Shahani, 2024. "Real-Data-Based Study on Divorce Dynamics and Elimination Strategies Using Nonlinear Differential Equations," Mathematics, MDPI, vol. 12(16), pages 1-23, August.

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