The objective of this paper is to study the stability of SIS epidemic model involving treatment. Two types of such eco-epidemiological models are introduced and analyzed. Boundedness of the system is established. The local and global dynamical behaviors are performed. The conditions of persistence of the models are derived.
In the present work, asphaltenes and resins separated from emulsion samples collected from two Iraqi oil wells, Nafut Kana (Nk) and Basrah were used to study the emulsion stability. The effect of oil resins to asphaltene (R/A) ratio, pH of the aqueous phase, addition of paraffinic solvent (n-heptane), aromatic solvent (toluene), and blend of both (heptol) in various proportions on the stability of emulsions had been investigated. The conditions of experiments were specified as an agitation speed of 1000 rpm for 30 minutes, heating at 50 °C, and water content of 30%. The results showed that as the R/A ratio increases, the emulsion will be unstable and the amount of water separated from emulsion increases. It was noticed that the em
... Show MoreA three species food web model involving a stage structure and cannibalism in the top predator species is proposed and studied. It is assumed that the prey species growth logistically in the absence of predator and the predation process occurred according to theLotka-Volterra functional response. The existence, uniqueness and bounded-ness of the solution of the model are investigated. The local and global stability conditions of all possible equilibrium points are established.The persistence conditions of the model are also determined. The local bifurcation near each of the equilibrium points is analyzed. The global dynamics of the model is investigated numerically and compared with the obtained analytical results. It is observed that the p
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The most famous thing a person does is talk. He loves and hates, and continues with it confirming relationships, and with it, too, comes out of disbelief into faith. Marry a word and separate with a word. He reaches the top of the heavens with a kind word, with which he will gain the pleasure of God, and the Lord of a word that the servant speaks to which God writes with our pleasure or throws him on his face in the fire. Emotions are inflamed, the United Nations is intensified with a word, and relations between states and war continue with a word.
What comes out of a person’s mouth is a translator that expresses the repository of his conscience and reveals the place of his bed, for it is evidence of
... Show MoreBackground: The insertion torque (IT) values and implant stability quotient (ISQ) values are the measurements most used to assess primary implant stability. This study aimed to assess the relationship between ISQ values and IT. Materials and methods: This study included 24 patients with a mean (SD) age of 47.9 (13.64) years (range 25-75 years). The patients received 42 dental implants (DI), 33 in the mandible and 9 in the maxilla. The DI were installed using the motorized method with 35 Ncm torque, When DI could not be inserted to the requisite depth by the motorized method, a hand ratchet was used and the IT was recorded as ˃ 35 Ncm. Implant stability was measured utilizing Osstell® ISQ. The secondary stability was measured after 16
... Show Morehis analysis aims to establish Riemann-Liouville derivation andintegral operators regarding the recently suggested seven-parameter Mittag-Leffler function then investigates the corresponding special cases. In addition,certain notable results associated with those new operators have been dis-cussed
An expression for the transition charge density is investigated where the deformation in nuclear collective modes is taken into consideration besides the shell model transition density. The inelastic longitudinal form factors C2 calculated using this transition charge density with excitation of the levels for Cr54,52,50 nuclei. In this work, the core polarization transition density is evaluated by adopting the shape of Tassie model together with the derived form of the ground state two-body charge density distributions (2BCDD's). It is noticed that the core polarization effects which represent the collective modes are essential in obtaining a remarkable agreement between the calculated inelastic longitudinal F(q)'s and those of experimen
... Show MoreDyspepsia is a significant public health issue that affects the entire world population. In this work, we formulate and analyze a deterministic model for the population dynamics of Gut bacteria in the presence of antibiotics and Probiotic supplements. All the possible equilibria and their local stability are obtained. The global stability around the positive equilibrium point is established. Numerical simulations back up our analytical findings and show the temporal dynamics of gut microorganisms.
 
        