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 supported our theoretical findings
Abstract
The hydrometallurgical method was used to platinum and palladium leaching with aqua regia solution (3HCl: HNO3). The leaching experiments were designed to obtain the optimum conditions by using Taguchi method with 16 experiments at three different factors (time, temperature and solid to liquid ratio), and each factor has four different levels. In this study, leaching the powder sample of catalytic converter that contains platinum and palladium was conducted on the basis of the formation of chloro complexes platinum and palladium (PtCl62-, PdCl42-) with different concentrations in the acidic solution. The optimum condi
... Show MoreIn this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R3 is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.
Mathematical Subject Classificat
... Show MoreThis paper deals with two preys and stage-structured predator model with anti-predator behavior. Sufficient conditions that ensure the appearance of local and Hopf bifurcation of the system have been achieved, and it’s observed that near the free predator, the free second prey and the free first prey equilibrium points there are transcritical or pitchfork and no saddle node. While near the coexistence equilibrium point there is transcritical, pitchfork and saddle node bifurcation. For the Hopf bifurcation near the coexistence equilibrium point have been studied. Further, numerical analysis has been used to validate the main results.
Background Birth defects are one of the causes of pediatric disability and mortality in all around the world. Data on birth defects from population-based studies originating from developing countries are lacking. Cleft lip (CL), cleft lip and palate (CLP), and isolated cleft palate (CP), collectively termed oral clefts, occur in all races, both sexes, and all socioeconomic groups and vary internationally (1). The main aim of this research is to establish the frequency of cleft lip and/or palate in the population of the Al-Ramadi City, and to characterize the demographic features of affected individuals and find possible risk factors. Materials and methods We conducted a survey of the Educational Maternal and Pediatric Hospital in Al-Ramadi
... Show MoreIn spite of economic importance of sugar cane and sugar beet as they described as industrial crops they still face decreasing rates of production and productivity in Iraq , and their production was not able to satisfy the local industrial demands for sugar . Thus this study aimed at studying and analyzing, production and productivity of sugar cane and sugar beet in Iraq and this has been done by using non serial data that can be obtained from official offices in Iraq . The area and production of sugar cane in Iraq recorded positive annual growth rates during 1970- 1978 which were 6% and 5% consequently , while the productivity of sugar cane recorded at the same duration of time negative annual growth rate which was 1% , while they recorded
... Show MoreThe Search stressed on the importance of the role of property tax as a tributaries of the state budget that depend on it to cover the side of public expenditures, along with the rest of the other types of taxes through a review of the tax framework and tax proceeds and stand on the research problem and its effects, according to the following logic questions : -
- What is the contribution of property tax in the overall tax revenue?
- Are there any certain problems in collection of property tax?
3. What are the factors that lead to a negative impact on the outcome of the property tax?
4. How do we strengthen the role of the property tax in the overall tax revenue?
This r
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