scholarly journals DYNAMICAL ANALYSIS OF A NOVEL DISCRETE FRACTIONAL SITRS MODEL FOR COVID-19

Fractals ◽  
2021 ◽  
pp. 2140035
Author(s):  
AMR ELSONBATY ◽  
ZULQURNAIN SABIR ◽  
RAJAGOPALAN RAMASWAMY ◽  
WALEED ADEL
Keyword(s):  
Experimental Data ◽  
Numerical Simulation ◽  
Stability Analysis ◽  
Continuous Time ◽  
Present Model ◽  
Equilibrium Points ◽  
Disease Spread ◽  
Dynamical Analysis ◽  
Infection Rates ◽  
Proposed Model

In this paper, a discrete fractional Susceptible-Infected-Treatment-Recovered-Susceptible (SITRS) model for simulating the coronavirus (COVID-19) pandemic is presented. The model is a modification to a recent continuous-time SITR model by taking into account the possibility that people who have been infected before can lose their temporary immunity and get reinfected. Moreover, a modification is suggested in the present model to correct the improper assumption that the infection rates of both normal susceptible and old aged/seriously diseased people are equal. This modification complies with experimental data. The equilibrium points for the proposed model are found and results of thorough stability analysis are discussed. A full numerical simulation is carried out and gives a better analysis of the disease spread, influences of model’s parameters, and how to control the virus. Comparisons with clinical data are also provided.

scholarly journals “Stability Analysis of Three Species Ammensalism Model with Time Delay”

2019 ◽  
Vol 8 (2S11) ◽  
pp. 3664-3670
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Time Delay ◽  
Global Stability ◽  
Analytical Study ◽  
Present Model ◽  
Ecological Model ◽  
Equilibrium Points

The present model is devoted to an analytical study of a three species syn-ecological model which the 1 st species ( ) N1 ammensal on the 2 nd species ( ) N2 and 2 nd species ( ) N2 ammensal on the 3 rd species ( ) N3 . Here 1 st species and 2 nd species are neutral to each other. A time delay is established between 1 st species and 2 nd species and 2 nd species and 3rd species. All attainable equilibrium points of the model are known and native stability for each case is mentioned and also the global stability of co-existing state is discussed by constructing appropriate Lyapunov operate. Further, precise solutions of perturbed equations are derived. The steadiness analysis is supported by numerical simulation victimization MatLab.

scholarly journals Stability and Bifurcation of a Prey-Predator-Scavenger Model in the Existence of Toxicant and Harvesting

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Huda Abdul Satar ◽  
Raid Kamel Naji
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Food Web ◽  
Equilibrium Points ◽  
Local Bifurcation ◽  
Persistence Conditions ◽  
Stability And Bifurcation ◽  
Periodic Dynamics ◽  
The Stability ◽  
Food Web Model

In this paper a prey-predator-scavenger food web model is proposed and studied. It is assumed that the model considered the effect of harvesting and all the species are infected by some toxicants released by some other species. The stability analysis of all possible equilibrium points is discussed. The persistence conditions of the system are established. The occurrence of local bifurcation around the equilibrium points is investigated. Numerical simulation is used and the obtained solution curves are drawn to illustrate the results of the model. Finally, the nonexistence of periodic dynamics is discussed analytically as well as numerically.

scholarly journals DYNAMICS OF ENVIRONMENTAL POLLUTIONTHROUGH VEHICLES

2020 ◽  
Vol 5 (4) ◽  
pp. 38-47
Author(s):  
Nita Shah ◽  
Shreya Patel ◽  
Moksha Satia ◽  
Foram Thakkar
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Air Pollution ◽  
Stability Analysis ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
System Stability ◽  
System Stability Analysis ◽  
Almost All ◽  
Day By Day

In today’s time as air pollution is increasing day by day the use of non-polluted has to be increased in almost all nooks and corner of the countries. In this paper a mathematical model is developed to analyse environmental pollution through polluted and non-polluted vehicles. Basic reproduction number has been calculated which will the decide the behavior of the system. Stability analysis has been carried out at equilibrium points. Numerical simulation is done to analyse the result for various compartments.

scholarly journals Stability analysis of an ecoepidemiological model consisting of a prey and tow competing predators with Si-disease in prey and toxicant

2020 ◽  
Vol 99 (3) ◽  
pp. 55-61
Author(s):  
Evren Hincal ◽  
◽  
Shorsh Mohammed ◽  
Bilgen Kaymakamzade ◽  
◽  
...  
Keyword(s):  
Stability Analysis ◽  
Functional Response ◽  
Linear Functional ◽  
Prey Species ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Epidemiological Models ◽  
Proposed Model ◽  
Infected Prey ◽  
Disease In Prey

In the present paper, we study two eco-epidemiological models. The first one consists of a prey and two competing predators with SI-disease in prey species spreading by contacts between susceptible prey and infected prey. This model assumes linear functional response. The second model is the modification of the first one when the effect of toxicant is taken into account. In this paper, we examine the dynamical behavior of non-survival and free equilibrium points of our proposed model.

Dynamical analysis of fractional-order differentiated Cournot triopoly game

2020 ◽  
Vol 26 (15-16) ◽  
pp. 1367-1380
Author(s):  
Abdulrahman Al-khedhairi
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Dynamical Analysis ◽  
Periodic Forcing ◽  
Nash Equilibrium Point ◽  
Dynamical Behaviors ◽  
Theoretical Results

The objective of the article is to study the dynamics of the proposed fractional-order Cournot triopoly game. Sufficient conditions for the existence and uniqueness of the triopoly game solution are obtained. Stability analysis of equilibrium points of the fractional-order game is also discussed. The conditions for the presence of Nash equilibrium point along with its global stability analysis are studied. The interesting dynamical behaviors of the arbitrary-order Cournot triopoly game are discussed. Moreover, the effects of seasonal periodic forcing on the game’s behaviors are examined. The 0–1 test is used to distinguish between regular and irregular dynamics of system behaviors. Numerical analysis is used to verify the theoretical results that are obtained, and revealed that the nonautonomous fractional-order model induces more complicated dynamics in the Cournot triopoly game behavior and the seasonally forced game exhibits more complex dynamics than the unforced one.

scholarly journals The Dynamical Analysis of a Prey-Predator Model with a Refuge-Stage Structure Prey Population

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Raid Kamel Naji ◽  
Salam Jasim Majeed
Keyword(s):  
Mathematical Model ◽  
Equilibrium Points ◽  
Stage Structure ◽  
Dynamical Analysis ◽  
Local Bifurcation ◽  
Structure Population ◽  
Global Stability Analysis ◽  
Proposed Model ◽  
Predator Model ◽  
Predator System

We proposed and analyzed a mathematical model dealing with two species of prey-predator system. It is assumed that the prey is a stage structure population consisting of two compartments known as immature prey and mature prey. It has a refuge capability as a defensive property against the predation. The existence, uniqueness, and boundedness of the solution of the proposed model are discussed. All the feasible equilibrium points are determined. The local and global stability analysis of them are investigated. The occurrence of local bifurcation (such as saddle node, transcritical, and pitchfork) near each of the equilibrium points is studied. Finally, numerical simulations are given to support the analytic results.

scholarly journals Dynamical Analysis of a Continuous Stirred-Tank Reactor with the Formation of Biofilms for Wastewater Treatment

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Karen López Buriticá ◽  
Simeón Casanova Trujillo ◽  
Carlos D. Acosta ◽  
Héctor A. Granada Diaz
Keyword(s):  
Growth Rate ◽  
Wastewater Treatment ◽  
Stability Analysis ◽  
Equilibrium Points ◽  
Stirred Tank ◽  
Dynamical Analysis ◽  
Continuous Stirred Tank Reactor ◽  
Stirred Tank Reactor ◽  
Tank Reactor ◽  
Continuous Stirred Tank

This paper analyzes the dynamics of a system that models the formation of biofilms in a continuous stirred-tank reactor (CSTR) when it is utilized for wastewater treatment. The growth rate of the microorganisms is modeled using two different kinetics, Monod and Haldane kinetics, with the goal of studying the influence of each in the system. The equilibrium points are identified through a stability analysis, and the bifurcations found are characterized.

scholarly journals A STOCHASTIC MODEL FOR GERMINATION

2020 ◽  
Vol 27 (2) ◽  
pp. 375-385
Author(s):  
JOSÉ VILLA-MORALES
Keyword(s):  
Experimental Data ◽  
Markov Chain ◽  
Stochastic Model ◽  
Continuous Time ◽  
Continuous Time Markov Chain ◽  
Germination Time ◽  
Germination Process ◽  
Proposed Model

Assuming that the germination process of a seed passes through several stages (or states), including a state of non-germination, we model this phenomenon by means of a continuous-time Markov chain. The distribution of the germination time and the average of the first germination is obtained. In particular, when the duration of the process at each stage is on average the same we see that the proposed model adjusts rather well some experimental data.

scholarly journals Stability Analysis of Model tuberculosis Spread in Diabetes Mellitus Patients with Treatment Factors

2020 ◽  
Vol 17 (1) ◽  
pp. 50-60
Author(s):  
Nursamsi Nursamsi
Keyword(s):  
Diabetes Mellitus ◽  
Numerical Simulation ◽  
Stability Analysis ◽  
Equilibrium Point ◽  
Immune Function ◽  
Blood Sugar ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Sugar Levels ◽  
The Stability

Diabetes mellitus (Dm) is a disease associated with impaired immune function so it is more susceptible to get infections including Tuberculosis (Tb). Tb disease can also worsen blood sugar levels which can cause Dm disease. This study aims to analyze and determine the stability of the equilibrium point of the spread of Tb disease in patients with Dm with consideration nine compartments, which are susceptible Tb without Dm, susceptible Tb without Dm complication, susceptible Tb with Dm complication, expose Tb without Dm, expose Tb with Dm, infected Tb without Dm, infected Tb with Dm, recovered Tb without Dm, and recovered Tb with Dm with treatment factors. The result obtained from the analysis of the model is two equilibrium points, which are the non endemic and endemic equilibrium points. The endemic equilibrium point does not exist if , endemic will appear if . Analytical and numerical simulation show that the spread of disease can be reduced and stopped if treatment is given to the infected compartment.

DYNAMICAL ANALYSIS OF FRACTIONAL ORDER ZIKV MODEL

2021 ◽  
Vol 10 (5) ◽  
pp. 2469-2481
Author(s):  
N.A. Hidayati ◽  
A. Suryanto ◽  
W.M. Kusumawinahyu
Keyword(s):  
Numerical Simulation ◽  
Equilibrium Point ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Dynamical Analysis ◽  
Stability Conditions ◽  
Order Model ◽  
Fractional Order Model ◽  
The Stability ◽  
S Model

The ZIKV model presented in this article is developed by modifying \cite{Bonyah2016}’s model. The classical order is changed into fractional order model. The equilibrium points of the model are determined and the stability conditions of each equilibrium point have been done using Routh-Hurwitz conditions. Numerical simulation is presented to verify the result of stability analysis result. Numerical simulation is also used to shows the effect of the order $\alpha$ to the stability of the model’s equilibrium point.

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