scholarly journals Global Stability Analysis of a Five-Dimensional Unemployment Model with Distributed Delay

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3037
Author(s):  
Eva Kaslik ◽  
Mihaela Neamţu ◽  
Loredana Flavia Vesa
Keyword(s):  
Mathematical Model ◽  
Equilibrium Points ◽  
Distributed Delay ◽  
Rate Of Change ◽  
Positive Equilibrium ◽  
Full Time ◽  
Regular Employment ◽  
Distributed Time Delay ◽  
Full Time Employment ◽  
Theoretical Results

The present paper proposes a five-dimensional mathematical model for studying the labor market, focusing on unemployment, migration, fixed term contractors, full time employment and the number of available vacancies. The distributed time delay is considered in the rate of change of available vacancies that depends on the past regular employment levels. The non-dimensional mathematical model is introduced and the existence of the equilibrium points is analyzed. The positivity and boundedness of solutions are provided and global asymptotic stability findings are presented both for the employment free equilibrium and the positive equilibrium. The numerical simulations support the theoretical results.

Hopf Bifurcation Analysis of KdV–Burgers–Kuramoto Chaotic System with Distributed Delay Feedback

2019 ◽  
Vol 29 (01) ◽  
pp. 1950011 ◽  
Author(s):  
Jie Liu ◽  
Junbiao Guan ◽  
Zhaosheng Feng
Keyword(s):  
Hopf Bifurcation ◽  
Chaotic System ◽  
Equilibrium Points ◽  
Distributed Delay ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Form Theory ◽  
The Mean ◽  
Mean Time ◽  
Theoretical Results

In this paper, the KdV–Burgers–Kuramoto chaotic system with distributed delay feedback is studied. The local stability of equilibrium points of this system is analyzed and the conditions under which Hopf bifurcation occurs are obtained by choosing the mean time delay as a bifurcation parameter. The direction and stability of bifurcating periodic solutions are derived by means of the normal form theory and the center manifold theorem. Numerical simulations are also illustrated which are in agreement with our theoretical results.

scholarly journals A New Fractional Model for Cancer Therapy with M1 Oncolytic Virus

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Majda El Younoussi ◽  
Zakaria Hajhouji ◽  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Mathematical Model ◽  
Cancer Therapy ◽  
Fractional Differential Equations ◽  
Oncolytic Virus ◽  
Equilibrium Points ◽  
Well Posedness ◽  
Boundedness Of Solutions ◽  
Proposed Model ◽  
Fractional Differential ◽  
Theoretical Results

The aim of this work is to propose and analyze a new mathematical model formulated by fractional differential equations (FDEs) that describes the dynamics of oncolytic M1 virotherapy. The well-posedness of the proposed model is proved through existence, uniqueness, nonnegativity, and boundedness of solutions. Furthermore, we study all equilibrium points and conditions needed for their existence. We also analyze the global stability of these equilibrium points and investigate their instability conditions. Finally, we state some numerical simulations in order to exemplify our theoretical results.

scholarly journals On The Mathematical Model of Two- Prey and Two-Predator Species

2020 ◽  
pp. 608-619
Author(s):  
A. G. Frahan
Keyword(s):  
Mathematical Model ◽  
Local Stability ◽  
Equilibrium Points ◽  
Basin Of Attraction ◽  
Predator Species ◽  
Numerical Examples ◽  
Group Defense ◽  
The Mathematical Model ◽  
Interior Points ◽  
Theoretical Results

In this work, we study two species of predator with two species of prey model, where the two species of prey live in two diverse habitats and have the ability to group-defense. Only one of the two predators tends to switch between the habitats. The mathematical model has at most 13 possible equilibrium points, one of which is the point of origin, two are axial, tow are interior points and the others are boundary points. The model with , where n is the switching index, is discussed regarding the boundedness of its solutions and the local stability of its equilibrium points. In addition, a basin of attraction was created for the interior point. Finally, three numerical examples were given to support the theoretical results.

Coping experiences of graduate students on full-time employment and full-time academic programmes

2020 ◽  
Vol 39 (5-6) ◽  
pp. 605-618
Author(s):  
Samuel Amponsah ◽  
Alex Kumi-Yeboah ◽  
Stephen O. Adjapong ◽  
Chris Olusola Omorogie
Keyword(s):  
Graduate Students ◽  
Full Time ◽  
Full Time Employment

scholarly journals On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
S. M. Al-Mekhlafi ◽  
A. O. Albalawi ◽  
D. Baleanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Weighted Average ◽  
Necessary Optimality Conditions ◽  
Numerical Approach ◽  
Population Number ◽  
Infected People ◽  
The Stability ◽  
Novel Coronavirus ◽  
Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

scholarly journals On a predator-prey system interaction under fluctuating water level with nonselective harvesting

2020 ◽  
Vol 18 (1) ◽  
pp. 458-475
Author(s):  
Na Zhang ◽  
Yonggui Kao ◽  
Fengde Chen ◽  
Binfeng Xie ◽  
Shiyu Li
Keyword(s):  
Water Level ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Optimal Harvesting ◽  
Positive Equilibrium ◽  
Predator Population ◽  
Model Interaction ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fluctuating Water Level

Abstract A predator-prey model interaction under fluctuating water level with non-selective harvesting is proposed and studied in this paper. Sufficient conditions for the permanence of two populations and the extinction of predator population are provided. The non-negative equilibrium points are given, and their stability is studied by using the Jacobian matrix. By constructing a suitable Lyapunov function, sufficient conditions that ensure the global stability of the positive equilibrium are obtained. The bionomic equilibrium and the optimal harvesting policy are also presented. Numerical simulations are carried out to show the feasibility of the main results.

scholarly journals Stochastic and deterministic mathematical model of cholera disease dynamics with direct transmission

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Getachew Teshome Tilahun ◽  
Woldegebriel Assefa Woldegerima ◽  
Aychew Wondifraw
Keyword(s):  
Mathematical Model ◽  
Stochastic Model ◽  
Deterministic Model ◽  
Equilibrium Points ◽  
Invariant Solution ◽  
Stochastic Approach ◽  
Disease Dynamics ◽  
Treatment Rate ◽  
Invariant Region ◽  
Contact Transmission

AbstractIn this paper we develop a stochastic mathematical model of cholera disease dynamics by considering direct contact transmission pathway. The model considers four compartments, namely susceptible humans, infectious humans, treated humans, and recovered humans. Firstly, we develop a deterministic mathematical model of cholera. Since the deterministic model does not consider the randomness process or environmental factors, we converted it to a stochastic model. Then, for both types of models, the qualitative behaviors, such as the invariant region, the existence of a positive invariant solution, the two equilibrium points (disease-free and endemic equilibrium), and their stabilities (local as well as global stability) of the model are studied. Moreover, the basic reproduction numbers are obtained for both models and compared. From the comparison, we obtained that the basic reproduction number of the stochastic model is much smaller than that of the deterministic one, which means that the stochastic approach is more realistic. Finally, we performed sensitivity analysis and numerical simulations. The numerical simulation results show that reducing contact rate, improving treatment rate, and environmental sanitation are the most crucial activities to eradicate cholera disease from the community.

scholarly journals Gains in employment status following antidepressant medication or cognitive therapy for depression

2015 ◽  
Vol 206 (4) ◽  
pp. 332-338 ◽  
Author(s):  
Jay C. Fournier ◽  
Robert J. DeRubeis ◽  
Jay Amsterdam ◽  
Richard C. Shelton ◽  
Steven D. Hollon
Keyword(s):  
Cognitive Therapy ◽  
Employment Status ◽  
Antidepressant Medication ◽  
Relative Advantage ◽  
Full Time ◽  
Treatment Interaction ◽  
Effect Of Treatment ◽  
Using Data ◽  
A Site ◽  
Full Time Employment

BackgroundDepression can adversely affect employment status.AimsTo examine whether there is a relative advantage of cognitive therapy or antidepressant medication in improving employment status following treatment, using data from a previously reported trial.MethodRandom assignment to cognitive therapy (n = 48) or the selective serotonin reuptake inhibitor paroxetine (n = 93) for 4 months; treatment responders were followed for up to 24 months. Differential effects of treatment on employment status were examined.ResultsAt the end of 28 months, cognitive therapy led to higher rates of full-time employment (88.9%) than did antidepressant medication among treatment responders (70.8%), χ21 = 5.78, P = 0.02, odds ratio (OR) = 5.66, 95% CI 1.16–27.69. In the shorter-term, the main effect of treatment on employment status was not significant following acute treatment (χ21 = 1.74, P = 0.19, OR = 1.77, 95% CI 0.75–4.17); however, we observed a site×treatment interaction (χ21 = 6.87, P = 0.009) whereby cognitive therapy led to a higher rate of full-time employment at one site but not at the other.ConclusionsCognitive therapy may produce greater improvements in employment v. medication, particularly over the longer term.

scholarly journals Nonlinear Dynamics of a PI Hydroturbine Governing System with Double Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Hongwei Luo ◽  
Jiangang Zhang ◽  
Wenju Du ◽  
Jiarong Lu ◽  
Xinlei An
Keyword(s):  
Hopf Bifurcation ◽  
Equilibrium Points ◽  
Bifurcation Theorem ◽  
Center Manifold Theorem ◽  
Governing System ◽  
Normal Form Method ◽  
The Stability ◽  
System Frequency ◽  
Realistic Significance ◽  
Theoretical Results

A PI hydroturbine governing system with saturation and double delays is generated in small perturbation. The nonlinear dynamic behavior of the system is investigated. More precisely, at first, we analyze the stability and Hopf bifurcation of the PI hydroturbine governing system with double delays under the four different cases. Corresponding stability theorem and Hopf bifurcation theorem of the system are obtained at equilibrium points. And then the stability of periodic solution and the direction of the Hopf bifurcation are illustrated by using the normal form method and center manifold theorem. We find out that the stability and direction of the Hopf bifurcation are determined by three parameters. The results have great realistic significance to guarantee the power system frequency stability and improve the stability of the hydropower system. At last, some numerical examples are given to verify the correctness of the theoretical results.

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