In this research, dynamical study of an SIR epidemical model with nonlinear direct incidence rate (Beddington-De Angelis ) type, and regress of treatment investigated .An  analytical study  to the model shows that there are two equilibrium points appear, the discussed successfully with sufficient condition, the existence of local bifurcation and Hopf bifurcation was analyzed, finally numerical simulations are done to explain the analytic studies.

In this paper, we studied the effect of magnetic hydrodynamic (MHD) on accelerated flows of a viscoelastic fluid with the fractional Burgers’ model. The velocity field of the flow is described by a fractional partial differential equation of fractional order by using Fourier sine transform and Laplace transform, an exact solutions for the velocity distribution are obtained for the following two problems: flow induced by constantly accelerating plate, and flow induced by variable accelerated plate. These solutions, presented under integral and series forms in terms of the generalized Mittag-Leffler function, are presented as the sum of two terms. The first term, represent the velocity field corresponding to a Newtonian fluid, and the se

Gypseous soil, which covers vast area in west, middle, east and south west regions of Iraq exhibit acceptable strength properties when dry, but it is weak and collapsible when it comes in touch with moisture from rain or other sources. When such weak soil is adopted for earth reinforced embankment construction, it may exhibit hazardous situation. Gypseous soil was investigated for the optimum liquid asphalt requirements of both cutback and emulsion using the one-dimensional unconfined compression strength test. The optimum fluid content was 13% (7% of cutback with 6% water content), and 17% (9% of emulsion with 8% water content). A laboratory model box of 50x50x25 cm was used as a representative of embankment; soil or asphalt stabilize

Optimization is essentially the art, science and mathematics of choosing the best among a given set of finite or infinite alternatives. Though currently optimization is an interdisciplinary subject cutting through the boundaries of mathematics, economics, engineering, natural sciences, and many other fields of human Endeavour it had its root in antiquity. In modern day language the problem mathematically is as follows - Among all closed curves of a given length find the one that closes maximum area. This is called the Isoperimetric problem. This problem is now mentioned in a regular fashion in any course in the Calculus of Variations. However, most problems of antiquity came from geometry and since there were no general methods to solve suc

     This paper is concerned with a Holling-II stage-structured predator-prey system in which predators are divided into an immature and mature predators. The aim is to explore the impact of the prey's fear caused by the dread of mature predators in a prey-predator model including intraspecific competitions and prey shelters. The theoretical study includes the local and global stability analysis for the three equilibrium points of the system and shows the prey's fear may lead to improving the stability at the positive equilibrium point. A numerical analysis is given to ensure the accuracy of the theoretical outcomes and to testify the conditions of stability of the system near the non-trivial equilibrium points.

 The objective of this study is to select a suitable observing region at Baghdad location (44^o 22^' 48^", 33^o 16^' 30^") with low interference that may affect frequency of 1.42 GHz. Baghdad University Radio Telescope (BURT) is used in this study to determine a convenient region for observation in Baghdad sky. Different azimuths and elevations were chosen at different observations time. The results of this study showed that the best observations regions were located at azimuth (120^o-160^o) and (210^o-260^o). These regions included less sky temperature and estimated to be (42.8 to 163) K. The sky temperature model could be represente

In this study, we set up and analyze a cancer growth model that integrates a chemotherapy drug with the impact of vitamins in boosting and strengthening the immune system. The aim of this study is to determine the minimal amount of treatment required to eliminate cancer, which will help to reduce harm to patients. It is assumed that vitamins come from organic foods and beverages. The chemotherapy drug is added to delay and eliminate tumor cell growth and division. To that end, we suggest the tumor-immune model, composed of the interaction of tumor and immune cells, which is composed of two ordinary differential equations. The model’s fundamental mathematical properties, such as positivity, boundedness, and equilibrium existence, are exami

This article examines and proposes a dietary chain model with a prey shelter and alternative food sources. It is anticipated that mid-predators' availability is positively correlated with the number of refuges. The solution's existence and exclusivity are examined. It is established that the solution is bounded. It is explored whether all potential equilibrium points exist and are locally stable. The Lyapunov approach is used to investigate the equilibrium points' worldwide stability. Utilizing a Sotomayor theorem application, local bifurcation is studied. Numerical simulation is used to better comprehend the dynamics of the model and define the control set of parameters.