Parameter Estimation and Sensitivity Analysis of Dysentery Diarrhea Epidemic Model

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 $R_{\mathrm{0}}>\mathrm{1}$. 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 $R_{\mathrm{0}}=\mathrm{1.1208}$. 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 (${\beta }_h$). It is also demonstrated that control of the effective transmission rate is essential to stop the spreading of the disease.