We investigate mathematical models of the Hepatitis B and C viruses in the study, considering vaccination effects into account. By utilising fractional and ordinary differential equations, we prove the existence of equilibrium and the well-posedness of the solution. We prove worldwide stability with respect to the fundamental reproduction number. Our numerical techniques highlight the biological relevance and highlight the effect of fractional derivatives on temporal behaviour. We illustrate the relationships among susceptible, immunised, and infected populations in our epidemiological model. Using comprehensive numerical simulations, we analyse the effects of fractional derivatives and highlight solution behaviours. Subsequent investigatio
... Show MoreIn This paper, we have been approximated Grűnwald-Letnikov Derivative of a function having m continuous derivatives by Bernstein Chlodowsky polynomials with proving its best approximation. As well as we have been solved Bagley-Torvik equation and Fokker–Planck equation where the derivative is in Grűnwald-Letnikov sense.
The Caputo definition of fractional derivatives introduces solution to the difficulties appears in the numerical treatment of differential equations due its consistency in differentiating constant functions. In the same time the memory and hereditary behaviors of the time fractional order derivatives (TFODE) still common in all definitions of fractional derivatives. The use of properties of companion matrices appears in reformulating multilevel schemes as generalized two level schemes is employed with the Gerschgorin disc theorems to prove stability condition. Caputo fractional derivatives with finite difference representations is considered. Moreover the effect of using the inverse operator which tr
Thin films of (CdO)x (CuO)1-x (where x = 0.0, 0.2, 0.3, 0.4 and 0.5) were prepared by the pulsed laser deposition. The CuO addition caused an increase in diffraction peaks intensity at (111) and a decrease in diffraction peaks intensity at (200). As CuO content increases, the band gap increases to a maximum of 3.51 eV, maximum resistivity of 8.251x 104 Ω.cm with mobility of 199.5 cm2 / V.s, when x= 0.5. The results show that the conductivity is ntype when x value was changed in the range (0 to 0.4) but further addition of CuO converted the samples to p-type.
Background: The development of orthodontic biomaterials that attract less biofilm has been a goal for decades. Adhesion and colonization of cariogenic streptococci are considered to play key roles in the development of enamel demineralization related to orthodontic materials. The aim of this study was to quantitatively evaluate the Mutans streptococci adhesion to coated orthodontic archwires (Epoxy and Teflon) and uncoated archwires (stainless steel and nickel-titanium) with respect to incubation time in the presence and absence of saliva. Material and Method: Six types of archwires stainless steel and nickel titanium with two type of coating (Epoxy, Teflon) were used in this study. Twelve specimens of each archwire were incubated in steri
... Show MoreIn this research we study the effect of UV radiation on pure PC samples and doped samples with plasticizer (DOP) for different exposure times (6, 12, 18, 24h). The study have been made on the change in the IR spectra causes by the UV radiation on both kinds of samples, besides the morphology changes were also studied by the optical microscope. From the results we conclude that the increasing of exposure causes the elaboration of CO2 and C2 gases.
Background: Gotu Kola (Centella asiatica) has been used as a traditional medicine for many years to cure different kinds of diseases. Studies have been reported that Gotu Kola extracts might be used as a cure for oral diseases such as periodontal disease. In the present study, Gotu Kola leaves extracted with water will be used to evaluate its effect on some microorganisms living in the human saliva using minimum inhibitory concentration (MIC) method. Material and Method:Gotu Kola fresh leaves extract have been used with water as a solvent, a rotary evaporator was used to separate the solvent from the extract. The following microorganisms: Streptococci, Lactobacilli, and Staphylococcus aureus have been isolated fromthe Saliva of ten voluntee
... Show MoreFemale infection with HPV (human papilla virus) has been established as an essential cause of CIN (cervical intraepithelial neoplasia). The danger of transformation from CIN to frank malignancy should be considered. Objective: The goal of this study is to evaluate the effectiveness of CO2 laser vaporization of ectocervical lesion high grade squamous intraepithelial lesion (HGSIL). Patients and Methods: Four Female out of 150 affected with HGSIL lesions were submitted to CO2 laser vaporization and followed up in 4 months later, and 10 women with HGSIL lesion submitted to electrocautery diathermy for the comparison. Results: Among women treated by CO2 laser vaporization, 3 women had negative results (clear cervix), at 4 months follow up; o
... Show MoreIn this paper, double Sumudu and double Elzaki transforms methods are used to compute the numerical solutions for some types of fractional order partial differential equations with constant coefficients and explaining the efficiently of the method by illustrating some numerical examples that are computed by using Mathcad 15.and graphic in Matlab R2015a.