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2019 Parameter Estimation and Sensitivity Analysis of Dysentery Diarrhea Epidemic Model
Hailay Weldegiorgis Berhe, Oluwole Daniel Makinde, David Mwangi Theuri
J. Appl. Math. 2019: 1-13 (2019). DOI: 10.1155/2019/8465747

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 R 0 > 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 R 0 = 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 ( β h ). It is also demonstrated that control of the effective transmission rate is essential to stop the spreading of the disease.

Citation

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Hailay Weldegiorgis Berhe. Oluwole Daniel Makinde. David Mwangi Theuri. "Parameter Estimation and Sensitivity Analysis of Dysentery Diarrhea Epidemic Model." J. Appl. Math. 2019 1 - 13, 2019. https://doi.org/10.1155/2019/8465747

Information

Received: 3 August 2018; Accepted: 23 December 2018; Published: 2019
First available in Project Euclid: 15 March 2019

zbMATH: 07051376
MathSciNet: MR3916581
Digital Object Identifier: 10.1155/2019/8465747

Rights: Copyright © 2019 Hindawi

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