The novel coronavirus disease, coined as COVID-19, is a murderous and infectious disease initiated from Wuhan, China. This killer disease has taken a large number of lives around the world and its dynamics could not be controlled so far. In this article, the spatio-temporal compartmental epidemic model of the novel disease with advection and diffusion process is projected and analyzed. To counteract these types of diseases or restrict their spread, mankind depends upon mathematical modeling and medicine to reduce, alleviate, and anticipate the behavior of disease dynamics. The existence and uniqueness of the solution for the proposed system are investigated. Also, the solution to the considered system is made possible in a well-known functions space. For this purpose, a Banach space of function is chosen and the solutions are optimized in the closed and convex subset of the space. The essential explicit estimates for the solutions are investigated for the associated auxiliary data. The numerical solution and its analysis are the crux of this study. Moreover, the consistency, stability, and positivity are the indispensable and core properties of the compartmental models that a numerical design must possess. To this end, a nonstandard finite difference numerical scheme is developed to find the numerical solutions which preserve the structural properties of the continuous system. The M-matrix theory is applied to prove the positivity of the design. The results for the consistency and stability of the design are also presented in this study. The plausibility of the projected scheme is indicated by an appropriate example. Computer simulations are also exhibited to conclude the results. 相似文献
Recently, the world is facing the terror of the novel corona-virus, termed as COVID-19. Various health institutes and researchers are continuously striving to control this pandemic. In this article, the SEIAR (susceptible, exposed, infected, symptomatically infected, asymptomatically infected and recovered) infection model of COVID-19 with a constant rate of advection is studied for the disease propagation. A simple model of the disease is extended to an advection model by accommodating the advection process and some appropriate parameters in the system. The continuous model is transposed into a discrete numerical model by discretizing the domains, finitely. To analyze the disease dynamics, a structure preserving non-standard finite difference scheme is designed. Two steady states of the continuous system are described i.e., virus free steady state and virus existing steady state. Graphical results show that both the steady states of the numerical design coincide with the fixed points of the continuous SEIAR model. Positivity of the state variables is ensured by applying the M-matrix theory. A result for the positivity property is established. For the proposed numerical design, two different types of the stability are investigated. Nonlinear stability and linear stability for the projected scheme is examined by applying some standard results. Von Neuman stability test is applied to ensure linear stability. The reproductive number is described and its pivotal role in stability analysis is also discussed. Consistency and convergence of the numerical model is also studied. Numerical graphs are presented via computer simulations to prove the worth and efficiency of the quarantine factor is explored graphically, which is helpful in controlling the disease dynamics. In the end, the conclusion of the study is also rendered. 相似文献
In this research article, we interrogate two new modifications in inverse Weierstrass iterative method for estimating all roots of non-linear equation simultaneously. These modifications enables us to accelerate the convergence order of inverse Weierstrass method from 2 to 3. Convergence analysis proves that the orders of convergence of the two newly constructed inverse methods are 3. Using computer algebra system Mathematica, we find the lower bound of the convergence order and verify it theoretically. Dynamical planes of the inverse simultaneous methods and classical iterative methods are generated using MATLAB (R2011b), to present the global convergence properties of inverse simultaneous iterative methods as compared to classical methods. Some non-linear models are taken from Physics, Chemistry and engineering to demonstrate the performance and efficiency of the newly constructed methods. Computational CPU time, and residual graphs of the methods are provided to present the dominance behavior of our newly constructed methods as compared to existing inverse and classical simultaneous iterative methods in the literature. 相似文献
The present study was carried out to investigate the growth characteristics of different ryegrass (Lolium perenne L.) cultivars and their ability to remediate eutrophic water using floating plant-bed technology. Greenhouse and lake experiments were conducted to evaluate the grass genotypes for water remediation. Twelve cultivars of ryegrass including Grazer, Secale Cerale, Energa, Rustmaster, AngusI, Abundant, AngusII, Jivet, Gulf, Surrey, Major and Barwoltra were grown in the floating plant-bed system. The plant biomass, plant NP (nitrogen and phosphorus) accumulations and the water purification capacity of selected grasses were significantly different (P < 0.05). Abundant, AngusII and Major showed most efficient purification capacity of eutrophic water. In a greenhouse, after 26 days of growth, the eutrophic water was purified to various extents by the different ryegrass cultivars. Nitrogen removal efficiency varied from 52.20% to 73.82% and phosphorus removal efficiency ranged from 75.12% to 84.77%. In a lake experiment at Huajiachi pond, after 162 days of growth, the plant shoot biomass increased from 321.5 to 922.8 g/m(2) dry weight basis, shoot NP accumulation ranged from 61.5 to 168.2 mg m(-2) d(-1) and 11.9 to 47.2 mg m(-2) d(-1) respectively. NP accumulation rate by the various cultivars of ryegrass was highly positively correlated to their biomass production and water purification capacity. Thus, plant biomass could be used as an indicator for assessing purification capacity of a ryegrass cultivar. 相似文献
Multimedia Tools and Applications - Corneal reflection extracted from an eye image identifies the relationship between the subject of the image and the scene in front of the subject. The... 相似文献
Berseem seed oil was fractionated into non-polar and polar components. Tentative identification was made of hydrocarbons, sterol esters, triglycerides, free fatty acids and partial glycerides in the non-polar fraction and of lysophosphatidyl choline, phosphatidyl inositol, lysophosphatidyl ethanolamine, phosphatidyl choline, phosphatidyl glycerol, phosphatidyl ethanolamine, digalactosyl diglycerides, sterol glycosides, phosphatidic acid, monogalactosyl diglycerides, cerebrosides and esterified sterol glycosides in the polar fraction. The fatty acid constituents of the major polar and of all the non-polar lipid components are also reported. 相似文献
GEANT4 – based Monte Carlo simulations have been carried out for the determination of photo-peak efficiency of heavily shielded small high purity germanium detector (HPGe) used for monitoring radiation levels in nuclear power plants. The GEANT4 simulated values of HPGe detector efficiency for point as well as for disk sources, for two different values of collimator diameter, have been found in good agreement with the corresponding published results obtained by using the MCNP code. The work has been extended to study the effect of radial displacement of a source relative to a detector on photo-peak efficiency for both point and disk source, and at various values of γ-ray energies. Also the effect of disk source radius on photo-peak efficiency has been studied. Besides the results of different available physics models in GEANT4 have also been compared. The computed values of efficiency for point as well as for disk sources using the Penelope and Livermore physics models have been found correspondingly consistent for various values of γ-ray energies while some differences (e.g., Penelope model yields 6.3% higher values of photo-peak efficiency for Eγ = 1.332 MeV, 10 mm collimator diameter) have been observed in the corresponding valued obtained by using the Standard physics model. 相似文献
In contrast to the conventional direct current railway electrification system (DC-RES), the medium voltage direct current (MVDC)-RES is considered promising for long-distance high-speed corridors. In the MVDC-RES, traction substations (TSSs) are placed much farther and train loads are much heavier than in the conventional DC-RES. Hence, the MVDC-RES brings a drastic change in catenary voltage, TSS spacing, and train loading, which affects rail potential and stray current. In this connection, this work performs some significant quantitative analysis of rail potential and stray current in the MVDC-RES environment. An MVDC simulation model is proposed and different grounding schemes are analyzed for a single-train and two TSSs scenario as well as for a multi-train multi-TSS scenario. According to the simulation and analysis, the maximum values of rail potential and stray current at MVDC-RES distances and the maximum safe distance between adjacent TSSs are determined.
The study investigated the use of maleated high density polyethylene (mHDPE) as a compatibilizer in high density polyethylene/hydroxyapatite (HDPE/HA) composites for biomedical applications. The addition of HA increased the strength and stiffness of HDPE/HA composites while the use of mHDPE in HDPE/HA composites improved its elongation at break values. The SEM images revealed that the addition of mHDPE has induced the formation of HDPE fibrils in mHDPE/HA composites. The size of apatite layer increased with simulated body fluid (SBF) immersion time and the formation of apatite layers on the surface of composites indicates excellent biocompatibility properties. 相似文献