scholarly journals Asymptotic stability of the stationary solution for a new mathematical model of charge transport in semiconductors

2012 ◽  
Vol 70 (2) ◽  
pp. 357-382
Author(s):  
A. M. Blokhin ◽  
D. L. Tkachev
Keyword(s):  
Mathematical Model ◽  
Asymptotic Stability ◽  
Charge Transport ◽  
Stationary Solution

A mathematical analysis of a tuberculosis epidemic model with two treatments and exogenous re-infection

2020 ◽  
pp. 2050082
Author(s):  
Mehdi Lotfi ◽  
Azizeh Jabbari ◽  
Hossein Kheiri
Keyword(s):  
Mathematical Model ◽  
Asymptotic Stability ◽  
Stable Disease ◽  
Reproduction Number ◽  
Geometric Approach ◽  
Backward Bifurcation ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Bifurcation Phenomenon ◽  
Disease Free

In this paper, we propose a mathematical model of tuberculosis with two treatments and exogenous re-infection, in which the treatment is effective for a number of infectious individuals and it fails for some other infectious individuals who are being treated. We show that the model exhibits the phenomenon of backward bifurcation, where a stable disease-free equilibrium coexists with a stable endemic equilibria when the related basic reproduction number is less than unity. Also, it is shown that under certain conditions the model cannot exhibit backward bifurcation. Furthermore, it is shown in the absence of re-infection, the backward bifurcation phenomenon does not exist, in which the disease-free equilibrium of the model is globally asymptotically stable when the associated reproduction number is less than unity. The global asymptotic stability of the endemic equilibrium, when the associated reproduction number is greater than unity, is established using the geometric approach. Numerical simulations are presented to illustrate our main results.

scholarly journals On the global attractors in one mathematical model of antiviral immunity

2020 ◽  
Author(s):  
Alexei Tsygvintsev
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Immune System ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Antiviral Immunity ◽  
Global Attractors ◽  
Viral Pathogens ◽  
Basic Reproductive Ratio ◽  
The Mathematical Model

AbstractWe consider the mathematical model introduced by Batholdy et al. [1] describing the interaction between viral pathogens and immune system. We prove the global asymptotic stability of the infection steady-state if the basic reproductive ratio R0 is greater than unity. That solves the conjecture announced in [7].

scholarly journals Stability Analysis of a Nonlinear System with Different Growth Functions

2018 ◽  
Vol 37 ◽  
pp. 111-119
Author(s):  
Md Kamrujjaman ◽  
Ashrafi Meher Niger
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Nonlinear System ◽  
Asymptotic Stability ◽  
Carrying Capacity ◽  
Competitive Exclusion ◽  
Logistic Growth ◽  
Limited Growth ◽  
Growth Functions

A competitive mathematical model for the growth of two species is considered in this study. The main goal of the present study is to investigate the roles of two different growth functions: the logistic growth and the food limited growth. We established the main results that determine the asymptotic stability of semi-trivial as well as the coexistence solutions. If higher carrying capacity is embodied for the population following logistic growth then competitive exclusion of a food limited population is imminent and vice versa.GANIT J. Bangladesh Math. Soc.Vol. 37 (2017) 111-119

scholarly journals A Mathematical Model of Cancer Treatment by Radiotherapy

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Zijian Liu ◽  
Chenxue Yang
Keyword(s):  
Mathematical Model ◽  
Periodic Solution ◽  
Asymptotic Stability ◽  
Cancer Treatment ◽  
Cancer Cells ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Numerical Examples ◽  
Globally Asymptotic Stability

A periodic mathematical model of cancer treatment by radiotherapy is presented and studied in this paper. Conditions on the coexistence of the healthy and cancer cells are obtained. Furthermore, sufficient conditions on the existence and globally asymptotic stability of the positive periodic solution, the cancer eradication periodic solution, and the cancer win periodic solution are established. Some numerical examples are shown to verify the validity of the results. A discussion is presented for further study.

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