In this paper, a Cholera epidemic model is proposed and studied analytically as well as numerically. It is assumed that the disease is transmitted by contact with Vibrio cholerae and infected person according to dose-response function. However, the saturated treatment function is used to describe the recovery process. Moreover, the vaccine against the disease is assumed to be utterly ineffective. The existence, uniqueness and boundedness of the solution of the proposed model are discussed. All possible equilibrium points and the basic reproduction number are determined. The local stability and persistence conditions are established. Lyapunov method and the second additive compound matrix are used to study the global stability of the system. The conditions that guarantee the occurrence of local bifurcation and backward bifurcation are determined. Finally, numerical simulation is used to investigate the global dynamical behavior of the Cholera epidemic model and understand the effects of parameters on evolution of the disease in the environment. It is observed that the solution of the model is very sensitive to varying in parameters values and different types of bifurcations are obtained including backward bifurcation.
This paper contains an equivalent statements of a pre- space, where are considered subsets of with the product topology. An equivalence relation between the preclosed set and a pre- space, and a relation between a pre- space and the preclosed set with some conditions on a function are found. In addition, we have proved that the graph of is preclosed in if is a pre- space, where the equivalence relation on is open.
On the other hand, we introduce the definition of a pre-stable ( pre-stable) set by depending on the concept of a pre-neighborhood, where we get that every stable set is pre-stable. Moreover, we obtain that
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In this paper, a shallow foundation (strip footing), 1 m in width is assumed to be constructed on fully saturated and partially saturated Iraqi soils, and analyzed by finite element method. A procedure is proposed to define the H – modulus function from the soil water characteristic curve which is measured by the filter paper method. Fitting methods are applied through the program (SoilVision). Then, the soil water characteristic curve is converted to relation correlating the void ratio and matric suction. The slope of the latter relation can be used to define the H – modulus function. The finite element programs SIGMA/W and SEEP/W are then used in the analysis. Eight nodded isoparametric quadrilateral elements are used for modeling
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Quantum channels enable the achievement of communication tasks inaccessible to their
classical counterparts. The most famous example is the distribution of secret keys. Unfortunately, the rate
of generation of the secret key by direct transmission is fundamentally limited by the distance. This limit
can be overcome by the implementation of a quantum repeater. In order to boost the performance of the
repeater, a quantum repeater based on cut-off with two different types of quantum memories is suggestd,
which reduces the effect of decoherence during the storage of a quantum state.
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In this study, polymeric composites were prepared from unsaturated polyester as a base material with glass powder (fluorescent) in different weight ratios (4, 6, 8, 10,and 11%) as a support material and after comparison before and after reinforcement of the prepared composites, an increase was found. In the values of mechanical properties (hardness, compressive strength), the shock resistance values decreased, but an increase in temperature leads to an increase in the values of shock resistance, as well as the values of compressive strength And it reduces the hardness value.
Coronavirus disease 2019 (COVID-19) is a flu-like infection caused by a novel virus known as Severe Acute Respiratory Syndrome coronavirus 2 (SARS-CoV-2). After the widespread around the world, it was announced by the World Health Organization (WHO) as a global pandemic. The symptoms of COVID-19 may arise within 2 weeks and the severity ranged from mild with signs of respiratory infection to severe cases of organ failure and even death. Management of COVID-19 patients includes supportive treatment and pharmacological medications expected to be effective with no definitive cure of the disease. The aims of this study are highlighting the management protocol and supportive therapy especially vitamin D and manifesting the clinical symptoms b
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