scholarly journals Global Dynamics of a Mathematical Model on Smoking

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Zainab Alkhudhari ◽  
Sarah Al-Sheikh ◽  
Salma Al-Tuwairqi
Keyword(s):  
Mathematical Model ◽  
Global Stability ◽  
Numerical Simulations ◽  
The Other ◽  
Global Dynamics ◽  
Local And Global Stability ◽  
Two Equilibria

We derive and analyze a mathematical model of smoking in which the population is divided into four classes: potential smokers, smokers, temporary quitters, and permanent quitters. In this model we study the effect of smokers on temporary quitters. Two equilibria of the model are found: one of them is the smoking-free equilibrium and the other corresponds to the presence of smoking. We examine the local and global stability of both equilibria and we support our results by using numerical simulations.

scholarly journals Analysis of the Dynamics of SI-SI-SEIR Avian Influenza A(H7N9) Epidemic Model with Re-infection

2020 ◽  
pp. 43-73
Author(s):  
Oluwafemi I. Bada ◽  
Abayomi S. Oke ◽  
Winfred N. Mutuku ◽  
Patrick O. Aye
Keyword(s):  
Mathematical Model ◽  
Avian Influenza ◽  
Global Stability ◽  
Numerical Simulations ◽  
Epidemic Model ◽  
Influenza A ◽  
Equilibrium Points ◽  
Local And Global Stability ◽  
Continuous Contact ◽  
Non Linear

The spread of Avian influenza in Asia, Europe and Africa ever since its emergence in 2003, has been endemic in many countries. In this study, a non-linear SI-SI-SEIR Mathematical model with re-infection as a result of continuous contact with both infected poultry from farm and market is proposed. Local and global stability of the three equilibrium points are established and numerical simulations are used to validate the results.

scholarly journals Volterra–Lyapunov Stability Analysis of the Solutions of Babesiosis Disease Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1272
Author(s):  
Fengsheng Chien ◽  
Stanford Shateyi
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Global Stability ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Disease Model ◽  
Transmission Dynamics ◽  
Global Stability Analysis ◽  
Lyapunov Stability Analysis ◽  
Disease Free

This paper studies the global stability analysis of a mathematical model on Babesiosis transmission dynamics on bovines and ticks populations as proposed by Dang et al. First, the global stability analysis of disease-free equilibrium (DFE) is presented. Furthermore, using the properties of Volterra–Lyapunov matrices, we show that it is possible to prove the global stability of the endemic equilibrium. The property of symmetry in the structure of Volterra–Lyapunov matrices plays an important role in achieving this goal. Furthermore, numerical simulations are used to verify the result presented.

scholarly journals Fractional order prey-predator model with infected predators in the presence of competition and toxicity

2020 ◽  
Vol 15 ◽  
pp. 38
Author(s):  
M. R. Lemnaouar ◽  
M. Khalfaoui ◽  
Y. Louartassi ◽  
I. Tolaimate
Keyword(s):  
Global Stability ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Local And Global Stability ◽  
Predator Model ◽  
Reserved Area

In this paper, we propose a fractional-order prey-predator model with reserved area in the presence of the toxicity and competition. We prove different mathematical results like existence, uniqueness, non negativity and boundedness of the solution for our model. Further, we discuss the local and global stability of these equilibria. Finally, we perform numerical simulations to prove our results.

Global dynamics of hepatitis C viral infection with logistic proliferation

2016 ◽  
Vol 09 (04) ◽  
pp. 1650056
Author(s):  
Sandip Banerjee ◽  
Ram Keval ◽  
Sunita Gakkhar
Keyword(s):  
Mathematical Model ◽  
Hepatitis C Virus ◽  
Stability Analysis ◽  
Hepatitis C ◽  
Viral Infection ◽  
Global Stability ◽  
Geometric Approach ◽  
Global Dynamics ◽  
Viral Dynamics ◽  
Global Stability Analysis

A modified mathematical model of hepatitis C viral dynamics has been presented in this paper, which is described by four coupled ordinary differential equations. The aim of this paper is to perform global stability analysis using geometric approach to stability, based on the higher-order generalization of Bendixson’s criterion. The result is also supported numerically. An important epidemiological issue of eradicating hepatitis C virus has been addressed through the global stability analysis.

scholarly journals Mathematical Model for Impact of Media on Cleanliness Drive in India

2018 ◽  
Vol 7 (1) ◽  
pp. 29-36
Author(s):  
N H Shah ◽  
J S Patel ◽  
F A Thakkar ◽  
M H Satia
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Lyapunov Function ◽  
Global Stability ◽  
Transfer Rate ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Local And Global Stability

A mathematical model on cleanliness drive in India is analysed for active cleaners and passive cleaners. Cleanliness and endemic equilibrium points are found. Local and global stability of these equilibrium points are discussed using Routh-Hurwitz criteria and Lyapunov function respectively. Impact of media (as a control) is studied on passive cleaners to become active. Numerical simulation of the model is carried out which indicates that with the help of media transfer rate to active cleaners from passive cleaners is higher.

scholarly journals A Mathematical Model of Universal Basic Income and Its Numerical Simulations

Algorithms ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 331
Author(s):  
Maria Letizia Bertotti
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Numerical Simulations ◽  
Real World ◽  
Poverty Alleviation ◽  
The Other ◽  
Nonlinear Ordinary Differential Equations ◽  
Basic Income ◽  
Market Society ◽  
Number Of Individuals

In this paper, an elementary mathematical model describing the introduction of a universal basic income in a closed market society is constructed. The model is formulated in terms of a system of nonlinear ordinary differential equations, each of which gives account of how the number of individuals in a certain income class changes in time. Societies ruled by different fiscal systems (with no taxes, with taxation and redistribution, with a welfare system) are considered and the effect of the presence of a basic income in the various cases is analysed by means of numerical simulations. The main findings are that basic income effectively acts as a tool of poverty alleviation: indeed, in its presence the portion of individuals in the poorest classes and economic inequality diminish. Of course, the issue of a universal basic income in the real world is more complex and involves a variety of aspects. The goal here is simply to show how mathematical models can help in forecasting scenarios resulting from one or the other policy.

Controlling Asthma Due to Air Pollution

2020 ◽  
pp. 1-22
Author(s):  
Ankush H. Suthar ◽  
Purvi M. Pandya
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Air Pollution ◽  
Control Theory ◽  
Global Stability ◽  
Optimal Control Theory ◽  
Positive Impact ◽  
Equilibrium Points ◽  
Local And Global Stability ◽  
Number Of Individuals

The health of our respiratory systems is directly affected by the atmosphere. Nowadays, eruption of respiratory disease and malfunctioning of lung due to the presence of harmful particles in the air is one of the most sever challenge. In this chapter, association between air pollution-related respiratory diseases, namely dyspnea, cough, and asthma, is analysed by constructing a mathematical model. Local and global stability of the equilibrium points is proved. Optimal control theory is applied in the model to optimize stability of the model. Applied optimal control theory contains four control variables, among which first control helps to reduce number of individuals who are exposed to air pollutants and the remaining three controls help to reduce the spread and exacerbation of asthma. The positive impact of controls on the model and intensity of asthma under the influence of dyspnea and cough is observed graphically by simulating the model.

scholarly journals Mathematical Modeling of the Impact of Rehabilitation Centers on Illicit Drug Usage

2021 ◽  
Author(s):  
Isa Baba ◽  
Saudatu Baba Sambo
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Global Stability ◽  
Numerical Simulations ◽  
Drug Users ◽  
Illicit Drug ◽  
Endemic Equilibrium ◽  
Drug Usage ◽  
Rehabilitation Centers ◽  
The Impact

Abstract This paper presents a mathematical model that studies the importance of treatment at rehabilitation centers intending to show the impact of the rehabilitation centers in minimizing illicit drug usage. We consider the global stability of endemic equilibrium using the properties of Volterra-Lyapunov matrices. Numerical simulations were carried out to show the impact of rehabilitation centers on illicit drug users.

Mathematical Model to Analyze Effect of Demonetization

2020 ◽  
pp. 270-286
Author(s):  
Nita H. Shah ◽  
Bijal M. Yeolekar ◽  
Zalak Ashvinkumar Patel
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Differential Equations ◽  
Global Stability ◽  
Banking Sector ◽  
Nonlinear Differential Equations ◽  
National Currency ◽  
Limited Time ◽  
Local And Global Stability ◽  
The Government

Demonetization is a fundamental regulatory act of stripping in which a currency unit's status as an exchange is professed worthless. Generally, it is done whenever there is a change of national currency, often to be replaced of the old notes or coins with a new one. Sometimes, a country totally replaces the old currency with new currency. For example, in India recently the government demonetized RS. 500 and 1000 notes. So, one has to deposit their cash within limited time in the banks. The demonetization affects individuals mildly or potentially, which in turn affects banking sector. So, SMPB-model is proposed and analyzed for demonetization. The SMP-model is formulated with the system of nonlinear differential equations. The effect of demonetization is studied by calculating threshold using next generation matrix. The local and global stability for demonetization free equilibrium and demonetization equilibrium is worked out. The existence of the equilibrium is investigated. The model is validated with numerical simulation.

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