In this paper, a mathematical model is proposed and studied to describe the spread of shigellosis disease in the population community. We consider it divided into four classes namely: the 1^st class consists of  unaware susceptible individuals, 2^nd class of infected individuals, 3^rd class of aware susceptible individuals and 4^th class are people carrying bacteria. The solution existence, uniqueness as well as bounded-ness are discussed for the shigellosis model proposed. Also, the stability analysis has been conducted for all possible equilibrium points. Finally the proposed model is studied numerically to prove the analytic results and discussing the effects of the external sources for dis

A harvested prey-predator model with infectious disease in preyis investigated. It is assumed that the predator feeds on the infected prey only according to Holling type-II functional response. The existence, uniqueness and boundedness of the solution of the model are investigated. The local stability analysis of the harvested prey-predator model is carried out. The necessary and sufficient conditions for the persistence of the model are also obtained. Finally, the global dynamics of this model is investigated analytically as well as numerically. It is observed that, the model have different types of dynamical behaviors including chaos.

  In this paper, we introduce and discuss an algorithm for the numerical solution of two- dimensional fractional dispersion equation.  The algorithm for the numerical solution of this equation is based on explicit finite difference approximation. Consistency, conditional stability, and convergence of this numerical method are described. Finally, numerical example is presented to show the dispersion behavior according to the order of the fractional derivative and we demonstrate that our explicit finite difference approximation is a computationally efficient method for solving two-dimensional fractional dispersion equation

The paper presents a highly accurate power flow solution, reducing the possibility of ending at local minima, by using Real-Coded Genetic Algorithm (RCGA) with system reduction and restoration. The proposed method (RCGA) is modified to reduce the total computing time by reducing the system in size to that of the generator buses, which, for any realistic system, will be smaller in number, and the load buses are eliminated. Then solving the power flow problem for the generator buses only by real-coded GA to calculate the voltage phase angles, whereas the voltage magnitudes are specified resulted in reduced computation time for the solution. Then the system is restored by calculating the voltages of the load buses in terms

     In this paper, the class of meromorphic multivalent functions of the form by using fractional differ-integral operators is introduced. We get Coefficients estimates, radii of convexity and star likeness. Also closure theorems and distortion theorem for the class ,  is calculaed.

The present work investigates the effect of magneto – hydrodynamic (MHD) laminar natural convection flow on a vertical cylinder in presence of heat generation and radiation. The governing equations which used are Continuity, Momentum and Energy equations. These equations are transformed to dimensionless equations using Vorticity-Stream Function method and the resulting nonlinear system
of partial differential equations are then solved numerically using finite difference approximation. A thermal boundary condition of a constant wall temperature is considered. A computer program (Fortran 90) was built to calculate the rate of heat transfer in terms of local Nusselt number, total mean Nusselt number, velocity distribution as well as te

Numerical study is adapted to combine between piezoelectric fan as a turbulent air flow generator and perforated finned heat sinks. A single piezoelectric fan with different tip amplitudes placed eccentrically at the duct entrance. The problem of solid and perforated finned heat sinks is solved and analyzed numerically by using Ansys 17.2 fluent, and solving three dimensional energy and Navier–Stokes equations that set with RNG based k−ε scalable wall function turbulent model. Finite volume algorithm is used to solve both phases of solid and fluid. Calculations are done for three values of piezoelectric fan amplitudes 25 mm, 30 mm, and 40 mm, respectively. Results of this numerical study are compared with previous b

This paper shews how to estimate the parameter of generalized exponential Rayleigh (GER) distribution by three estimation methods. The first one is maximum likelihood estimator method the second one is moment employing estimation method (MEM), the third one is rank set sampling estimator method (RSSEM)The simulation technique is used for all these estimation methods to find the parameters for generalized exponential Rayleigh distribution. Finally using the mean squares error criterion to compare between these estimation methods to find which of these methods are best to the others

In this study, He's parallel numerical algorithm by neural network is applied to type of integration of fractional equations is Abel’s integral equations of the 1^st and 2^nd kinds. Using a Levenberge – Marquaradt training algorithm as a tool to train the network. To show the efficiency of the method, some type of Abel’s integral equations is solved as numerical examples. Numerical results show that the new method is very efficient problems with high accuracy.

A (b,t)-blocking set B in PG(2,q) is set of b points such that every line of PG(2,q) intersects B in at least t points and there is a line intersecting B in exactly t points. In this paper we construct a minimal (b,t)-blocking sets, t = 1,2,3,4,5 in PG(2,5) by using conics to obtain complete arcs and projective codes related with them.