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.
In this paper, an ecoepidemiological deterministic model for the transmission dynamics of maize streak virus (MSV) disease in maize plant is proposed and analysed qualitatively using the stability theory of differential equations.The basic reproduction number with respect to the MSV free equilibrium is obtained using next generation matrix approach. The conditions for local and global asymptotic stability of MSV free and endemic equilibria are established. The model exhibits forward bifurcation and the sensitivity indices of various embedded parameters with respect to the MSV eradication or spreading are determined. Numerical simulation is performed and dispalyed graphically to justify the analytical results.
The thermodynamic first and second law analyses of a temperature dependent viscosity hydromagnetic generalized unsteady Couette flow with permeable walls is investigated. The transient model problem for momentum and energy balance is tackled numerically using a semi-discretization method while the steady state boundary value problem is solved by shooting method together with Runge-Kutta-Fehlberg integration scheme. The velocity and the temperature profiles are obtained and are utilized to compute the skin friction coefficient, Nusselt number, entropy generation rate and the Bejan number. Pertinent results are presented graphically and discussed quantitatively.
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