scholarly journals Mathematical analysis of a two-patch model of tuberculosis disease with staged progression

2012 ◽  
Vol 36 (12) ◽  
pp. 5792-5807 ◽  
Author(s):  
Jean Jules Tewa ◽  
Samuel Bowong ◽  
S.C. Oukouomi Noutchie
Keyword(s):  
Mathematical Analysis ◽  
Patch Model ◽  
Tuberculosis Disease

scholarly journals Stability and bifurcation in a two-patch model with additive Allee effect

2021 ◽  
Vol 7 (1) ◽  
pp. 536-551
Author(s):  
Lijuan Chen ◽  
◽  
Tingting Liu ◽  
Fengde Chen
Keyword(s):  
Numerical Simulation ◽  
Asymptotic Stability ◽  
Population Density ◽  
Mathematical Analysis ◽  
Allee Effect ◽  
Total Population ◽  
Population Abundance ◽  
Dispersal Rate ◽  
Saddle Node Bifurcation ◽  
Patch Model

<abstract><p>A two-patch model with additive Allee effect is proposed and studied in this paper. Our objective is to investigate how dispersal and additive Allee effect have an impact on the above model's dynamical behaviours. We discuss the local and global asymptotic stability of equilibria and the existence of the saddle-node bifurcation. Complete qualitative analysis on the model demonstrates that dispersal and Allee effect may lead to persistence or extinction in both patches. Also, combining mathematical analysis with numerical simulation, we verify that the total population abundance will increase when the Allee effect constant $ a $ increases or $ m $ decreases. And the total population density increases when the dispersal rate $ D_{1} $ increases or the dispersal rate $ D_{2} $ decreases.</p></abstract>

scholarly journals Mathematical analysis of two-patch model for the dynamical transmission of tuberculosis

2012 ◽  
Vol 36 (6) ◽  
pp. 2466-2485 ◽  
Author(s):  
Jean Jules Tewa ◽  
Samuel Bowong ◽  
Boulchard Mewoli
Keyword(s):  
Mathematical Analysis ◽  
Patch Model

scholarly journals Mathematical Analysis of a General Two-Patch Model of Tuberculosis Disease with Lost Sight Individuals

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Abdias Laohombé ◽  
Isabelle Ngningone Eya ◽  
Jean Jules Tewa ◽  
Alassane Bah ◽  
Samuel Bowong ◽  
...  
Keyword(s):  
Sub Saharan Africa ◽  
Asymptotically Stable ◽  
Basic Reproduction Ratio ◽  
Reproduction Ratio ◽  
Patch Model ◽  
Latently Infected ◽  
Sub Saharan ◽  
Tuberculosis Disease ◽  
Theoretical Results ◽  
Disease Free

A two-patch model,SEi1,…,EinIiLi,  i=1,2, is used to analyze the spread of tuberculosis, with an arbitrary numbernof latently infected compartments in each patch. A fraction of infectious individuals that begun their treatment will not return to the hospital for the examination of sputum. This fact usually occurs in sub-Saharan Africa, due to many reasons. The model incorporates migrations from one patch to another. The existence and uniqueness of the associated equilibria are discussed. A Lyapunov function is used to show that when the basic reproduction ratio is less than one, the disease-free equilibrium is globally and asymptotically stable. When it is greater than one, there exists at least one endemic equilibrium. The local stability of endemic equilibria can be illustrated using numerical simulations. Numerical simulation results are provided to illustrate the theoretical results and analyze the influence of lost sight individuals.

scholarly journals Mathematical analysis on SEIR-type model of the Tuberculosis disease spread with vaccination and treatment elements

2019 ◽  
Vol 1235 ◽  
pp. 012120
Author(s):  
Marwan Ramli ◽  
Syarifah Chaira Zulfa ◽  
Natasya Ayuningtia Chaniago ◽  
Vera Halfiani
Keyword(s):  
Mathematical Analysis ◽  
Disease Spread ◽  
Type Model ◽  
Tuberculosis Disease

Density waves in disk galaxies

1967 ◽  
Vol 31 ◽  
pp. 313-317 ◽  
Author(s):  
C. C. Lin ◽  
F. H. Shu
Keyword(s):  
Mathematical Analysis ◽  
Spiral Structure ◽  
Stellar System ◽  
Collective Modes ◽  
Disk Galaxies ◽  
Spiral Pattern ◽  
Density Waves ◽  
The Galaxy ◽  
Detailed Mathematical Analysis

Density waves in the nature of those proposed by B. Lindblad are described by detailed mathematical analysis of collective modes in a disk-like stellar system. The treatment is centered around a hypothesis of quasi-stationary spiral structure. We examine (a) the mechanism for the maintenance of this spiral pattern, and (b) its consequences on the observable features of the galaxy.

Computing cell tractions from particle displacements on silicone rubber substrata

1994 ◽  
Vol 52 ◽  
pp. 162-163
Author(s):  
Tim Oliver ◽  
Akira Ishihara ◽  
Ken Jacobsen ◽  
Micah Dembo
Keyword(s):  
Plane Stress ◽  
Linear Elasticity ◽  
Silicone Rubber ◽  
Mathematical Analysis ◽  
Elastic Recovery ◽  
Video Images ◽  
Cell Traction Forces ◽  
Latex Beads ◽  
Cell Traction ◽  
Better Than

In order to better understand the distribution of cell traction forces generated by rapidly locomoting cells, we have applied a mathematical analysis to our modified silicone rubber traction assay, based on the plane stress Green’s function of linear elasticity. To achieve this, we made crosslinked silicone rubber films into which we incorporated many more latex beads than previously possible (Figs. 1 and 6), using a modified airbrush. These films could be deformed by fish keratocytes, were virtually drift-free, and showed better than a 90% elastic recovery to micromanipulation (data not shown). Video images of cells locomoting on these films were recorded. From a pair of images representing the undisturbed and stressed states of the film, we recorded the cell’s outline and the associated displacements of bead centroids using Image-1 (Fig. 1). Next, using our own software, a mesh of quadrilaterals was plotted (Fig. 2) to represent the cell outline and to superimpose on the outline a traction density distribution. The net displacement of each bead in the film was calculated from centroid data and displayed with the mesh outline (Fig. 3).

Equilibrium Profile of Modern Belted Radial Ply Tires: Its Determination and Performance Benefits

2013 ◽  
Vol 41 (2) ◽  
pp. 127-151
Author(s):  
Rudolf F. Bauer
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Finite Element Methods ◽  
Mathematical Analysis ◽  
Internal Stresses ◽  
Stress Concentrations ◽  
Equilibrium Profiles ◽  
Equilibrium Profile ◽  
And Performance ◽  
Beneficial Property

ABSTRACT The benefits of a tire's equilibrium profile have been suggested by several authors in the published literature, and mathematical procedures were developed that represented well the behavior of bias ply tires. However, for modern belted radial ply tires, and particularly those with a lower aspect ratio, the tire constructions are much more complicated and pose new problems for a mathematical analysis. Solutions to these problems are presented in this paper, and for a modern radial touring tire the equilibrium profile was calculated together with the mold profile to produce such tires. Some construction modifications were then applied to these tires to render their profiles “nonequilibrium.” Finite element methods were used to analyze for stress concentrations and deformations within all tires that did or did not conform to equilibrium profiles. Finally, tires were built and tested to verify the predictions of these analyses. From the analysis of internal stresses and deformations on inflation and loading and from the actual tire tests, the superior durability of tires with an equilibrium profile was established, and hence it is concluded that an equilibrium profile is a beneficial property of modern belted radial ply tires.

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