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Browsing Faculty of Military Sciences by Author "Berhe, Hailay Weldegiorgis"
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 asa 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 (𝛽). It is also demonstrated that control of the effective transmission rate is essential to stop the spreading of the disease.