In this paper, we established a mathematical model of an SI1I2R epidemic disease with saturated incidence and general recovery functions of the first disease I1. Considering the basic reproduction number, we obtained conditions for both disease-free and co-existing cases. The equilibrium points local stability is verified by using the Routh-Hurwitz criterion, while for the global stability, we used a suitable Lyapunov function to analyze the endemic spread of the positive equilibrium point. Moreover, we carried out the local bifurcation around both equilibrium points (disease-free and co-existing), where we obtained that the disease-free equilibrium point undergoes a transcritical bifurcation. We conduct numerical simulations that suppo

Development of a precise and delicate reaction has been acquired for the determination of vancomycin hydrochloride using batch and cloud point extraction (CPE) methods. The first method is based on the formation of azo dye as a result of diazotized dapsone coupled with vancomycin HCl (VAN) in a basic medium. The sensitivity of this reaction was enhanced by utilizing a nonionic surfactant (Triton X-114) and the cloud point extraction technique (second method). The azo dye formed was extracted into the surfactant-rich phase, dissolved in ethanol and detected at λ_max 440 nm spectrophotometrically. The reaction was investigated using both batch and CPE methods (with and without extraction), and a simple comparison between the two

A total of 13 samples of domestic cat Felis cattus (Linnaeus, 1758 ) and 9 samples of wild cat Felis chaus furax (de Winton, 1898) of the Felidae Family were trapped and examined to detect the hard ticks. The areas of the collection were: Baghdad, Al-Rashidiya, Tharthar, Nahrawan, AL-Mahmoudiya (middle of Iraq) and AL-Haretha (south of Iraq), Mosul (north of Iraq). The results of the current study revealed that four species belong to two genera of hard ticks: Haemaphysalis sp. (Koch, 1844), Rhipicephalus turanicus (Morel, 1969), Rhipicephalus sanguineus (Neumann, 1904) and Rhipicephalus appendiculatus (Santos, 1955). The rates and the density of infestation were discussed. The current study aimed to clarify the infestation differe

Proverbs are considered as a major source of ancient events and happenings. Similar to other past events related to life, proverbs have many important and famous values in people's life. This study will shed lights on the use of proverbs as short sentences based on long experiences. The aim of the study is to explicate the roles, and the importance of proverbs in our life and how they are used to convey thoughts to people throughout simple words with denotation. Thus, proverbs explicate the truth and experience of our grandfathers when directed for criticism. Few proverbs were used by writers to criticize, mimic and reprint their personalities. Hence, proverbs will achieve portions of the unique roles of understanding. The model to

In this article we study the variance estimator for the normal distribution when the mean is un known depend of the cumulative function between unbiased estimator and Bays estimator for the variance of normal distribution which is used include Double Stage Shrunken estimator to obtain higher efficiency for the variance estimator of normal distribution when the mean is unknown by using small volume equal volume of two sample .

In the present study, free convection heat and mass transfer of fluid in a square packed bed enclosure is numerically investigated. For the considered geometrical shape, the left vertical wall of enclosure was assumed to be kept at high temperature and concentration while the opposite wall was kept at low temperature and concentration with insulating both the top and bottom walls of enclosure. The Brinkman– Forchheimer extended Darcy model was used to solve the momentum equations, while the energy equations for fluid and solid phases were solved by using the local thermal non-equilibrium (LTNE) model.Computations are performed for a range of the Darcy number from 10-5 to 10-1, the porosity from 0.5 to 0.9, and buoyancy ratio from -15 t