scholarly journals Mathematical Model for Coronavirus Disease 2019 (COVID-19) Containing Isolation Class

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Anwar Zeb ◽  
Ebraheem Alzahrani ◽  
Vedat Suat Erturk ◽  
Gul Zaman
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Local Stability ◽  
Dynamical Behavior ◽  
Order Method ◽  
Human Contact ◽  
Proposed Model ◽  
Fourth Order Method ◽  
Nsfd Scheme ◽  
Nonstandard Finite Difference

The deadly coronavirus continues to spread across the globe, and mathematical models can be used to show suspected, recovered, and deceased coronavirus patients, as well as how many people have been tested. Researchers still do not know definitively whether surviving a COVID-19 infection means you gain long-lasting immunity and, if so, for how long? In order to understand, we think that this study may lead to better guessing the spread of this pandemic in future. We develop a mathematical model to present the dynamical behavior of COVID-19 infection by incorporating isolation class. First, the formulation of model is proposed; then, positivity of the model is discussed. The local stability and global stability of proposed model are presented, which depended on the basic reproductive. For the numerical solution of the proposed model, the nonstandard finite difference (NSFD) scheme and Runge-Kutta fourth order method are used. Finally, some graphical results are presented. Our findings show that human to human contact is the potential cause of outbreaks of COVID-19. Therefore, isolation of the infected human overall can reduce the risk of future COVID-19 spread.

scholarly journals Optimal Fourth, Eighth and Sixteenth Order Methods by Using Divided Difference Techniques and Their Basins of Attraction and Its Application

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 322 ◽  
Author(s):  
Yanlin Tao ◽  
Kalyanasundaram Madhu
Keyword(s):  
Dynamical Behavior ◽  
Computational Cost ◽  
Basins Of Attraction ◽  
Order Method ◽  
Eighth Order ◽  
Projectile Motion ◽  
First Derivative ◽  
Iteration Functions ◽  
Optimal Launch Angle ◽  
Fourth Order Method

The principal objective of this work is to propose a fourth, eighth and sixteenth order scheme for solving a nonlinear equation. In terms of computational cost, per iteration, the fourth order method uses two evaluations of the function and one evaluation of the first derivative; the eighth order method uses three evaluations of the function and one evaluation of the first derivative; and sixteenth order method uses four evaluations of the function and one evaluation of the first derivative. So these all the methods have satisfied the Kung-Traub optimality conjecture. In addition, the theoretical convergence properties of our schemes are fully explored with the help of the main theorem that demonstrates the convergence order. The performance and effectiveness of our optimal iteration functions are compared with the existing competitors on some standard academic problems. The conjugacy maps of the presented method and other existing eighth order methods are discussed, and their basins of attraction are also given to demonstrate their dynamical behavior in the complex plane. We apply the new scheme to find the optimal launch angle in a projectile motion problem and Planck’s radiation law problem as an application.

scholarly journals Dynamics of a Nonstandard Finite-Difference Scheme for a Limit Cycle Oscillator with Delayed Feedback

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Yuanyuan Wang ◽  
Xiaohua Ding
Keyword(s):  
Finite Difference ◽  
Limit Cycle ◽  
Euler Method ◽  
Delayed Feedback ◽  
Dimensional System ◽  
Two Dimensional ◽  
Limit Cycle Oscillator ◽  
The Stability ◽  
Nsfd Scheme ◽  
Nonstandard Finite Difference

We consider a complex autonomously driven single limit cycle oscillator with delayed feedback. The original model is translated to a two-dimensional system. Through a nonstandard finite-difference (NSFD) scheme we study the dynamics of this resulting system. The stability of the equilibrium of the model is investigated by analyzing the characteristic equation. In the two-dimensional discrete model, we find that there are stability switches on the time delay and Hopf bifurcation when the delay passes a sequence of critical values. Finally, computer simulations are performed to illustrate the theoretical results. And the results show that NSFD scheme is better than the Euler method.

Dynamics of populations with two sexes

2015 ◽  
Vol 08 (04) ◽  
pp. 1550049
Author(s):  
M. Cecilia Pérez ◽  
E. Adriana Saavedra ◽  
Mariano A. Ferrari
Keyword(s):  
Mathematical Model ◽  
Local Stability ◽  
Elephant Seal ◽  
Southern Elephant Seal ◽  
Real Population ◽  
Proposed Model ◽  
Males And Females ◽  
Direct Applicability ◽  
State Existence ◽  
Dynamics Of Populations

A mathematical model is presented in order to describe the dynamics of polygamous populations, bearing in mind single individuals of both sexes and the development of reproductive groups. In this context, the description leads us to consider positive homogeneous dynamical systems, establishing conditions for the stationary state existence and its local stability. A fourth pre-reproductive stage was considered, i.e. males and females spend part of their lives before being in condition to reproduce, as a first step to consider more general models. Finally, we parametrized the proposed model using southern elephant seal data, to analyze the direct applicability to a real population.

scholarly journals A nonstandard finite difference scheme for the modeling and nonidentical synchronization of a novel fractional chaotic system

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Dumitru Baleanu ◽  
Sadegh Zibaei ◽  
Mehran Namjoo ◽  
Amin Jajarmi
Keyword(s):  
Finite Difference ◽  
Numerical Simulations ◽  
Active Control ◽  
Chaotic System ◽  
Equilibrium Points ◽  
Control Technique ◽  
New Model ◽  
Fractional Chaotic System ◽  
Nsfd Scheme ◽  
Nonstandard Finite Difference

AbstractThe aim of this paper is to introduce and analyze a novel fractional chaotic system including quadratic and cubic nonlinearities. We take into account the Caputo derivative for the fractional model and study the stability of the equilibrium points by the fractional Routh–Hurwitz criteria. We also utilize an efficient nonstandard finite difference (NSFD) scheme to implement the new model and investigate its chaotic behavior in both time-domain and phase-plane. According to the obtained results, we find that the new model portrays both chaotic and nonchaotic behaviors for different values of the fractional order, so that the lowest order in which the system remains chaotic is found via the numerical simulations. Afterward, a nonidentical synchronization is applied between the presented model and the fractional Volta equations using an active control technique. The numerical simulations of the master, the slave, and the error dynamics using the NSFD scheme are plotted showing that the synchronization is achieved properly, an outcome which confirms the effectiveness of the proposed active control strategy.

scholarly journals The Dynamics of a Single Species in a Polluted Environment

2020 ◽  
pp. 1-12
Author(s):  
Raid Kamel Naji ◽  
Mona Ghassan Younis ◽  
Mohammad Naeemullah
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Local Stability ◽  
Single Species ◽  
Global Dynamics ◽  
Polluted Environment ◽  
Nonlinear Mathematical Model ◽  
Proposed Model

This article proposed and analysed a nonlinear mathematical model that consist of a single species in a polluted environment (PE). The proposed model was also discussed in terms of its uniqueness, existence, and boundedness of the solution. Also, each possible equilibrium point was analysed for local stability, followed by investigation of the global dynamics of the system using the Lypanov functions. The effects of the presence of toxicants on the dynamics of a single species in the PE was numerically investigated

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