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.

Asymptotic Behavior of the Fractional Order three Species Prey–Predator Model

2018 ◽  
Vol 19 (7-8) ◽  
pp. 721-733 ◽  
Author(s):  
M. Sambath ◽  
P. Ramesh ◽  
K. Balachandran
Keyword(s):  
Dynamical System ◽  
Asymptotic Behavior ◽  
Global Stability ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Numerical Results ◽  
Predator Prey ◽  
Local And Global Stability ◽  
Predator Prey Model ◽  
Predator Model

AbstractIn this work, we introduce fractional order predator–prey model with infected predator. First, we prove different mathematical results like existence, uniqueness, non-negativity and boundedness of the solutions of fractional order dynamical system. Further, we investigate the local and global stability of all feasible equilibrium points of the system. Numerical results are illustrated as several examples.

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 The The Dynamics of a Prey-Predator Model with Infectious Disease in Prey: Role of Media Coverage

2021 ◽  
pp. 4930-4952
Author(s):  
Wassan Hussein ◽  
Huda Abdul Satar
Keyword(s):  
Infectious Disease ◽  
Global Stability ◽  
Numerical Simulations ◽  
Functional Response ◽  
Media Coverage ◽  
Epidemiological Model ◽  
Local Bifurcation ◽  
Predator Model ◽  
Disease In Prey

In this paper, an eco-epidemiological model with media coverage effect is proposed and studied. A prey-predator model with modified Leslie-Gower and functional response is studied. An  -type of disease in prey is considered.  The existence, uniqueness and boundedness of the solution of the model are discussed. The local and global stability of this system are carried out. The conditions for the persistence of all species are established. The local bifurcation in the model is studied. Finally, numerical simulations are conducted to illustrate the analytical results.

Stability analysis in prey–predator system with mixed functional response

2016 ◽  
Vol 13 (4) ◽  
pp. 364-369
Author(s):  
V. Madhusudanan ◽  
S. Vijaya
Keyword(s):  
Global Stability ◽  
Numerical Simulations ◽  
Functional Response ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Type I ◽  
Content Type ◽  
Local And Global Stability ◽  
Interior Equilibrium ◽  
Predator System

Purpose This paper aims to propose and analyse a two-prey–one-predator system with mixed functional response. Design/methodology/approach The predator exhibits Holling type IV functional response to one prey and Holling type I response to other. The occurrence of various positive equilibrium points with feasibility conditions are determined. The local and global stability of interior equilibrium points are examined. The boundedness of system is analysed. The sufficient conditions for persistence of the system is obtained by using Bendixson–Dulac criteria. Numerical simulations are carried out to illustrate the analytical findings. Findings The authors have derived the local and global stability condition of interior equilibrium of the system. Originality/value The authors observe that the critical values of some system parameter undergo Hopf bifurcation around some selective equilibrium. Hence, numerical simulations reveal the condition for the system to be stable and oscillatory.

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 Mathematical Analysis of a Fractional COVID-19 Model Applied to Wuhan, Spain and Portugal

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 135
Author(s):  
Faïçal Ndaïrou ◽  
Delfim F. M. Torres
Keyword(s):  
Qualitative Analysis ◽  
Global Stability ◽  
Numerical Simulations ◽  
Equilibrium Point ◽  
Fractional Order ◽  
Mathematical Analysis ◽  
Stability And Convergence ◽  
Well Posed ◽  
Disease Free

We propose a qualitative analysis of a recent fractional-order COVID-19 model. We start by showing that the model is mathematically and biologically well posed. Then, we give a proof on the global stability of the disease free equilibrium point. Finally, some numerical simulations are performed to ensure stability and convergence of the disease free equilibrium point.

scholarly journals Dynamic Properties of the Fractional-Order Logistic Equation of Complex Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
A. M. A. El-Sayed ◽  
E. Ahmed ◽  
H. A. A. El-Saka
Keyword(s):  
Dynamical System ◽  
Global Stability ◽  
Fractional Order ◽  
Existence And Uniqueness ◽  
Dynamic Properties ◽  
Equilibrium Points ◽  
Stable Solution ◽  
Complex Variables ◽  
Logistic Equation ◽  
Local And Global Stability

We study the dynamic properties (equilibrium points, local and global stability, chaos and bifurcation) of the continuous dynamical system of the logistic equation of complex variables. The existence and uniqueness of uniformly Lyapunov stable solution will be proved.

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.

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