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.
The estimation of the regular regression model requires several assumptions to be satisfied such as "linearity". One problem occurs by partitioning the regression curve into two (or more) parts and then joining them by threshold point(s). This situation is regarded as a linearity violation of regression. Therefore, the multiphase regression model is received increasing attention as an alternative approach which describes the changing of the behavior of the phenomenon through threshold point estimation. Maximum likelihood estimator "MLE" has been used in both model and threshold point estimations. However, MLE is not resistant against violations such as outliers' existence or in case of the heavy-tailed error distribution. The main goal of t
... Show MoreIn the current paper, the effect of fear in three species Beddington–DeAngelis food chain model is investigated. A three species food chain model incorporating Beddington-DeAngelis functional response is proposed, where the growth rate in the first and second level decreases due to existence of predator in the upper level. The existence, uniqueness and boundedness of the solution of the model are studied. All the possible equilibrium points are determined. The local as well as global stability of the system are investigated. The persistence conditions of the system are established. The local bifurcation analysis of the system is carried out. Finally, numerical simulations are used t
A field trial was conducted in Experimental Station of The Field Crops Department – College Of Agriculture In Abu Ghraib, University of Baghdad to assess the effect of sulphur applications and the time after application on pH and EC of soil sample solutions ,and on the growth and yield of rape seed (Brassica napus L.)A split plot design was used with four replications , The main plot included four sulphur applications levels (0,2000,3000,4000Kg S/ha) the sub plot were the time after application (0,1,2,and 3 moths) .Sulphur application significantly decreased soil pH value ,although that decrease reached minimum parameter after two months from application date .Rather increment of sulphur application level significantly raised soil EC val
... Show MorePre-breakdown phenomenon was investigated within the two, non-mixed dielectric liquids; transformation oil and cresol. Finite element technique was used to follow the initiation and growth of plasma channels (streamer discharge) within pin-plane configuration. That was done for different spacing between the pin-electrode and the liquid-liquid interface. Streamer growth model assumed that, the streamer initiation occurs at the region of the highest value of electric field. Our study shows that the streamer initiates at the tip of the pin and growths toward the other electrode. The study shows, too, that the streamer path controlled by the difference of permittivity of the two liquids and spacing distance of the liquid-liquid interface fro
... Show MoreAn experiment during the two seasons 2019, 2020. The experiment conducted according to Split Plot Design by two factors; the first was addition Nano NPK with five levels (control, addition 7.5 g.plant-1, addition 15 g.plant-1, spray 1 g.L-1, spray 2 g.L-1). The second factor was four levels of Mineral NPK which were (control, 50 g.plant-1, 100 g.plant-1, 50 g.plant-1+1.5 g.L-1) respectively. N3 (spray 1 g.L-1 ) increased plant height, stem diameter first season, branch number se
This research is concerned with studying (the concept of freedom in the texts of Yaşar Kamal the play), as the Turkish playwright (Kamal Yasar) is one of the contemporary playwrights who have been interested in and criticize society, and perhaps the concept of freedom in his texts took a different form, through his ability to renew and present his attempts to create A theatrical form different from his earlier writers in dealing with the life of the peasants and the oppression that went through them, as the researcher identified the problem of his research with the following question: What is the concept of freedom in the texts of Yashar Kamal? The research aims to define the concept of freedom in the texts of Yashar Kamal of the play,
... Show MoreIt is no secret to everyone that the Arab individual suffers from poor self-awareness and political awareness, which made the state and the importance of its existence and preserving its institutions not among his interests, which made researchers wonder about the possibility of strengthening it and the extent of its impact on the future of building the contemporary Arab state. So, the study attempts to addressing the issue of community awareness and its impact on building the state through a clear intellectual vision that blended what is social and political to define the concept of community awareness and highlight its importance and role as a basic pillar in shaping and building modern Arab countries in the Arab world and ways to enha
... Show MoreThis research was conducted under Lath house canopy of a nursery circumstances, Baghdad University for season 2013 in order to study the effect of soak lemon seeds sour orange with different levels of licorice concentrations extract (0, 0.5, 2.5 and 4.5 g/l) for 24 hours in the percentage of germination and some recipes vegetative growth of seedlings .the results outweigh the bitter orange seedlings and focus soak for licorice extract 4.5 g / l significant superiority in most of the traits plant height, leaf number, root length, stem diameter, amounting to 31.077 cm, 14.46 paper / plant, 25.35 cm, 0.52 mm respectively, which showed significant differences for the treatment of comparison which gave lower values. Clear that the licorice ext
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