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.

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

The present study is an academic attempt to show how the threeUmayyad poets ; Jarir ,
Al-Farazdaq and Al-Akhtal have skillfully employed old conventions and traditions in their
poetry to serve a dual purpose of making their ideas striking , memorable and compelling and
of reaching eminence as poets.
The primary aim of the poets has been to amuse , convince and influence the readers or
listeners of their poetry . as it were, a mirror image of the social , religious and historical
beliefs , values and customs which prevailed throughout the ages before the emergence.

The wide use of pesticides in recent years leads to rapid distribution of these pollutants in the environment (air, water and soil).They were transported by means of air or water to biological ecosystems. They become more toxic through the processes of biological magnification while some of them persist for along period.The aim of this work is to show the negative effect that chemical pesticides causes, and in the same to show their side effect on the environment and health in Iraq. We could conclude that the bad use of these chemicals could cause an urgent impact now or in the future. Governmental offices dealing with these materials should take the right measures to minimize the danger and the misuse of these chemicals by seeking alternat