Treatment of Polio Delayed Epidemic Model via Computer Simulations

We study an epidemic model with a nonlinear incidence rate which describes the psychological effect of certain serious diseases on the community when the ratio of the number of infectives to that of the susceptibles is getting larger. The model has set up a challenging issue regarding its dynamics near the origin since it is not well defined there. By carrying out a global analysis of the model and studying the stabilities of the disease-free equilibrium and the endemic equilibrium, it is shown that either the number of infective individuals tends to zero as time evolves or the disease persists. Computer simulations are presented to illustrate the results.

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ANALYSIS ON AN EPIDEMIC MODEL WITH A RATIO-DEPENDENT NONLINEAR INCIDENCE RATE

International Journal of Biomathematics ◽

10.1142/s1793524511001374 ◽

2011 ◽

Vol 04 (02) ◽

pp. 227-239 ◽

Cited By ~ 10

Author(s):

BO LI ◽

SANLING YUAN ◽

WEIGUO ZHANG

Keyword(s):

Qualitative Analysis ◽

Incidence Rate ◽

Computer Simulations ◽

Epidemic Model ◽

Mass Action ◽

Global Dynamics ◽

Nonlinear Incidence Rate ◽

Nonlinear Incidence ◽

Set Up ◽

Disease Free

In this paper, we study the global dynamics of an epidemic model with nonlinear incidence rate of saturated mass action which depends on the ratio of the number of infectives to that of the susceptibles. The model has set up a challenging issue regarding its dynamics at the R-axis since it is not well defined on it. By carrying out a global qualitative analysis of the model and studying the stabilities of the disease-free equilibrium and the endemic equilibrium, it is shown that either the number of infective individuals tends to zero as time evolves or the disease persists. Computer simulations are presented to illustrate the results.

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A High Resolution Study of G.P. Zones in Aluminum - 4.2 at % Silver

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100055904 ◽

1982 ◽

Vol 40 ◽

pp. 722-723 ◽

Cited By ~ 1

Author(s):

R. Gronsky

Keyword(s):

Electron Microscopy ◽

Transmission Electron Microscopy ◽

High Resolution ◽

Computer Simulations ◽

Structural Characteristics ◽

X Ray Diffraction ◽

X Ray ◽

Transmission Electron ◽

Resolution Study

The phenomenon of clustering in Al-Ag alloys has been extensively studied since the early work of Guinierl, wherein the pre-precipitation state was characterized as an assembly of spherical, ordered, silver-rich G.P. zones. Subsequent x-ray and TEM investigations yielded results in general agreement with this model. However, serious discrepancies were later revealed by the detailed x-ray diffraction - based computer simulations of Gragg and Cohen, i.e., the silver-rich clusters were instead octahedral in shape and fully disordered, atleast below 170°C. The object of the present investigation is to examine directly the structural characteristics of G.P. zones in Al-Ag by high resolution transmission electron microscopy.

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Multislice calculations for quasi-periodic and non-periodic objects

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100173820 ◽

1990 ◽

Vol 48 (4) ◽

pp. 138-139

Author(s):

R. Herrera ◽

A. Gómez

Keyword(s):

Electron Diffraction ◽

Computer Simulations ◽

Periodic Table ◽

Amorphous Materials ◽

Space Group ◽

Essential Step ◽

Shape Effects ◽

Atomic Scattering ◽

Diffraction Patterns ◽

Periodic Continuation

Computer simulations of electron diffraction patterns and images are an essential step in the process of structure and/or defect elucidation. So far most programs are designed to deal specifically with crystals, requiring frequently the space group as imput parameter. In such programs the deviations from perfect periodicity are dealt with by means of “periodic continuation”.However, for many applications involving amorphous materials, quasiperiodic materials or simply crystals with defects (including finite shape effects) it is convenient to have an algorithm capable of handling non-periodicity. Our program “HeGo” is an implementation of the well known multislice equations in which no periodicity assumption is made whatsoever. The salient features of our implementation are: 1) We made Gaussian fits to the atomic scattering factors for electrons covering the whole periodic table and the ranges [0-2]Å−1 and [2-6]Å−1.

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Computer simulations for the TEM bend contour technique

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100163137 ◽

1996 ◽

Vol 54 ◽

pp. 134-135

Author(s):

Vladimir Yu. Kolosov ◽

Anders R. Thölén

Keyword(s):

Computer Simulations ◽

Real Space ◽

Advantages And Disadvantages ◽

Short Overview ◽

Diffraction Contrast ◽

Beam Method ◽

Convergent Beam ◽

Contour Technique

In this paper we give a short overview of two TEM applications utilizing the extinction bend contour technique (BC) giving the advantages and disadvantages; especially we consider two areas in which the BC technique remains unique. Special attention is given to an approach including computer simulations of TEM micrographs.BC patterns are often observed in TEM studies but are rarely exploited in a serious way. However, this type of diffraction contrast was one of the first to be used for analysis of imperfections in crystalline foils, but since then only some groups have utilized the BC technique. The most extensive studies were performed by Steeds, Eades and colleagues. They were the first to demonstrate the unique possibilities of the BC method and named it real space crystallography, which developed later into the somewhat similar but more powerful convergent beam method. Maybe, due to the difficulties in analysis, BCs have seldom been used in TEM, and then mainly to visualize different imperfections and transformations.

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