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 examined. The equilibrium points’ asymptotic stability is analyzed using linear stability. Then, global stability and persistence are investigated using the Lyapunov strategy. The occurrence of bifurcations of the model, such as of trans-critical or Hopf type, is also explored. Numerical simulations are used to verify the theoretical analysis. The Runge–Kutta method of fourth order is used in the simulation of the model. The analytical study and simulation findings show that the immune system is boosted by regular vitamin consumption, inhibiting the growth of tumor cells. Further, the chemotherapy drug contributes to the control of tumor cell progression. Vitamin intake and chemotherapy are treated both individually and in combination, and in all situations, the minimal level required to eliminate the cancer is determined.
This study evaluated the structural changes of enamel treated by the Regenerate system and carbon dioxide (CO2) laser against acid challenge. Thirty human enamel slabs were prepared and assigned into three groups: Group I: untreated (control); Group II: treated with the Regenerate system; and Group III exposed to CO2 laser. All specimens were subjected to an acid challenge (pH 4.5–7.0) for 14 days. Specimens were evaluated and compared at 120 points using five Raman microspectroscopic peaks; the phosphate vibrations ν1, ν2, ν3, and ν4 at 960, 433, 1029, and 579 cm−1, respectively, and the carbonate at 1070 cm−1, followed by Vickers microhardness test. The ratio of carbonate to phosphate was correlated to the equivalent mic
... Show MoreValues are penetrating or interfering in the lives of individuals and groups and are connected to them in the sense of life itself, because they are closely linked to the motives of behavior, hopes and goals, and can be said that values are everything. The concept of values is one of the concepts that have received the attention of researchers from different disciplines. This has resulted in a kind of confusion and variation in use from one specialization to the other, and uses multiple uses within one specialization. Therefore, there is no uniform definition of values because they relate to individuals. Individuals differ in many things, such as perception,
... Show MoreIn this paper, we investigate the impact of fear on a food chain mathematical model with prey refuge and harvesting. The prey species reproduces by to the law of logistic growth. The model is adapted from version of the Holling type-II prey-first predator and Lotka-Volterra for first predator-second predator model. The conditions, have been examined that assurance the existence of equilibrium points. Uniqueness and boundedness of the solution of the system have been achieve. The local and global dynamical behaviors are discussed and analyzed. In the end, numerical simulations are confirmed the theoretical results that obtained and to display the effectiveness of varying each parameter
Through an experimental program of eighteen specimens presented in this paper, the bond strength between reinforcing bar and rubberized concrete was produced by adding waste tire rubber instead of natural aggregate. The fine and coarse aggregate was replaced in 0%, 25%, and 50% with the small pieces of a waste tire. Natural aggregate replacement ratio, rebar size, embedded rebar length, the rebar yield stress of rebar, cover, and concrete compressive strength were studied in this investigation. Ultimate bond stress, bond stress-slip response, and failure modes were presented. The experimental results reported that a reduction of 19% in bond strength was noticed in 50% replaced rubberized concrete compared with convention
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The researcher shed light on a diet in Iraq before 2003 became in this period. And how the ration card has a variety of vocabulary and cover the need of the population of commodities and have a key role in saving Iraq from a real crisis in the period of economic siege, especially in light of the State's direction to support the agricultural sector, which in that period able to fill half of the market needs of food the basic. As well as providing strategic storage at the Ministry of Commerce enough for six months But after the events of 2003 and the crises that hit the country and the unstable security situation began to rise voices calling for reform of the ration card system as a system that is a burden on the
... Show MoreThe aim of this work is to study the effect of mud compositions on it’s rheological behavior under high temperature conditions. Seventeen samples of five types of water base mud in which (fresh water bentonite mud. Lignosulphonate mud, gypsum mud, polymer mud, and salt saturated mud) were tested with different temperatures using the fann viscometer model 50-c. All the tested samples, except the fresh water bentonite mud, have the same trend reduction in both plastic viscosity and yield point with increasing temperature. Six rheological models has been adapted: Bingham plastic, power law, Casson model represent the laboratory data accurately
Shade in house gardens is one of the problems that hinder the growth of lawn and its distribution in the soil, where the types of lawns differ in their durability and adaptation to shade. The research aims to know the resistance of some species of lawn plants to shade and to know the appropriate fertilization procedures that can be followed to reduce the negative effects. The study was conducted in the Amiriya district of Baghdad in a house garden. Three varieties of lawn plants Bermuda, Gazon, and Trifoglio were planted. Five fertilization treatments (contained N and P elements) and the control were used. The sunlight density with the temperature of the study field locations were estimated using the AMT-300 and the vegetation coverage perc
... Show MoreIn this research a theoretical study has been carried out on the behavior and strength of simply supported composite beams strengthened by steel cover plate taking into consideration partial interaction of shear connectors and nonlinear behavior of the materials and shear connectors. Following the procedure that already has been adopted by Johnson (1975), the basic differential equations of equilibrium and compatibility were reduced to single differential equation in terms of interface slip between concrete slab and steel beam. Furthermore, in order to consider the nonlinear behavior of steel, concrete and shear connectors, the basic equation was rearranged so that all terms related to materials are isol
... Show MoreIt is recognized that organisms live and interact in groups, exposing them to various elements like disease, fear, hunting cooperation, and others. As a result, in this paper, we adopted the construction of a mathematical model that describes the interaction of the prey with the predator when there is an infectious disease, as well as the predator community's characteristic of cooperation in hunting, which generates great fear in the prey community. Furthermore, the presence of an incubation period for the disease provides a delay in disease transmission from diseased predators to healthy predators. This research aims to examine the proposed mathematical model's solution behavior to better understand these elements' impact on an eco-epidemi
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