scholarly journals A non-standard numerical scheme for an age-of-infection epidemic model

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Eleonora Messina ◽  
Mario Pezzella ◽  
Antonia Vecchio
Keyword(s):  
Finite Differences ◽  
Epidemic Model ◽  
Numerical Scheme ◽  
Continuous Model ◽  
Step Length ◽  
Qualitative Behavior ◽  
Convergence Properties ◽  
Integral Term ◽  
Age Of Infection ◽  
Continuous Dynamic

<p style='text-indent:20px;'>We propose a numerical method for approximating integro-differential equations arising in age-of-infection epidemic models. The method is based on a non-standard finite differences approximation of the integral term appearing in the equation. The study of convergence properties and the analysis of the qualitative behavior of the numerical solution show that it preserves all the basic properties of the continuous model with no restrictive conditions on the step-length <inline-formula><tex-math id="M1">\begin{document}$ h $\end{document}</tex-math></inline-formula> of integration and that it recovers the continuous dynamic as <inline-formula><tex-math id="M2">\begin{document}$ h $\end{document}</tex-math></inline-formula> tends to zero.</p>

scholarly journals Analysis of Atangana–Baleanu fractional-order SEAIR epidemic model with optimal control

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Chernet Tuge Deressa ◽  
Gemechis File Duressa
Keyword(s):  
Numerical Simulation ◽  
Optimal Control ◽  
Fractional Order ◽  
Control Strategy ◽  
Epidemic Model ◽  
Numerical Scheme ◽  
Order Derivative ◽  
Control Analysis ◽  
Fractional Order Derivative ◽  
Fractional Orders

AbstractWe consider a SEAIR epidemic model with Atangana–Baleanu fractional-order derivative. We approximate the solution of the model using the numerical scheme developed by Toufic and Atangana. The numerical simulation corresponding to several fractional orders shows that, as the fractional order reduces from 1, the spread of the endemic grows slower. Optimal control analysis and simulation show that the control strategy designed is operative in reducing the number of cases in different compartments. Moreover, simulating the optimal profile revealed that reducing the fractional-order from 1 leads to the need for quick starting of the application of the designed control strategy at the maximum possible level and maintaining it for the majority of the period of the pandemic.

INITIAL IMPROVEMENT OF THE HYBRID ACCELERATED GRADIENT DESCENT PROCESS

2018 ◽  
Vol 98 (2) ◽  
pp. 331-338 ◽  
Author(s):  
STEFAN PANIĆ ◽  
MILENA J. PETROVIĆ ◽  
MIROSLAVA MIHAJLOV CAREVIĆ
Keyword(s):  
Gradient Descent ◽  
Line Search ◽  
Initial Step ◽  
Step Length ◽  
Descent Method ◽  
Gradient Descent Method ◽  
Convergence Properties ◽  
Backtracking Line Search ◽  
Initial Improvement ◽  
Accelerated Gradient

We improve the convergence properties of the iterative scheme for solving unconstrained optimisation problems introduced in Petrovic et al. [‘Hybridization of accelerated gradient descent method’, Numer. Algorithms (2017), doi:10.1007/s11075-017-0460-4] by optimising the value of the initial step length parameter in the backtracking line search procedure. We prove the validity of the algorithm and illustrate its advantages by numerical experiments and comparisons.

scholarly journals Global stability of a DS–DI epidemic model with age of infection

2012 ◽  
Vol 385 (2) ◽  
pp. 655-671 ◽  
Author(s):  
Jun-Yuan Yang ◽  
Xue-Zhi Li ◽  
Maia Martcheva
Keyword(s):  
Global Stability ◽  
Epidemic Model ◽  
Age Of Infection

Theoretical and Numerical Solutions of Maglev Train Induced Vibration

2013 ◽  
Vol 459 ◽  
pp. 271-277
Author(s):  
S.H. Ju ◽  
C.C. Leong ◽  
Y.S. Ho
Keyword(s):  
Control System ◽  
Numerical Scheme ◽  
Large Time ◽  
Numerical Solutions ◽  
Step Length ◽  
Dynamic Interaction ◽  
Maglev Train ◽  
Time Step ◽  
Large Time Step ◽  
Interaction Problem

This paper proposed an efficient method based on theoretical equations to solve the dynamic interaction problem between the Timoshenko beam and maglev vehicles. A systematic PI numerical scheme is developed for the control system of the maglev train. The major advantage is that only one simple equation required in the control calculation, although the original control system is fairly complicated. Numerical simulations indicate that a large time step length can be used in the proposed method to obtain stable and accurate results.

scholarly journals Dynamical analysis of a generalized hepatitis B epidemic model and its dynamically consistent discrete model

2021 ◽  
Author(s):  
Manh Tuan Hoang
Keyword(s):  
Hepatitis B ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Discrete Model ◽  
Reproduction Number ◽  
Continuous Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Nsfd Scheme ◽  
The Basic Reproduction Number

The aim of this work is to study qualitative dynamical properties of a generalized hepatitis B epidemic model and its dynamically consistent discrete model. Positivity, boundedness, the basic reproduction number and asymptotic stability properties of the model are analyzed rigorously. By the Lyapunov stability theory and the Poincare-Bendixson theorem in combination with the Bendixson-Dulac criterion, we show that a disease-free equilibrium point is globally asymptotically stable if the basic reproduction number $\mathcal{R}_0 \leq 1$ and a disease-endemic equilibrium point is globally asymptotically stable whenever $\mathcal{R}_0 > 1$. Next, we apply the Mickens’ methodology to propose a dynamically consistent nonstandard finite difference (NSFD) scheme for the continuous model. By rigorously mathematical analyses, it is proved that the constructed NSFD scheme preserves essential mathematical features of the continuous model for all finite step sizes. Finally, numerical experiments are conducted to illustrate the theoretical findings and to demonstrate advantages of the NSFD scheme over standard ones. The obtained results in this work not only improve but also generalize some existing recognized works.

scholarly journals Numerical solution of advection-diffusion equation using finite difference schemes

2020 ◽  
Vol 55 (1) ◽  
pp. 15-22
Author(s):  
LS Andallah ◽  
MR Khatun
Keyword(s):  
Diffusion Equation ◽  
Numerical Solution ◽  
Numerical Scheme ◽  
Finite Difference Schemes ◽  
Qualitative Behavior ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Nicolson Scheme ◽  
And Diffusion ◽  
Crank Nicolson

This paper presents numerical simulation of one-dimensional advection-diffusion equation. We study the analytical solution of advection diffusion equation as an initial value problem in infinite space and realize the qualitative behavior of the solution in terms of advection and diffusion co-efficient. We obtain the numerical solution of this equation by using explicit centered difference scheme and Crank-Nicolson scheme for prescribed initial and boundary data. We implement the numerical scheme by developing a computer programming code and present the stability analysis of Crank-Nicolson scheme for ADE. For the validity test, we perform error estimation of the numerical scheme and presented the numerical features of rate of convergence graphically. The qualitative behavior of the ADE for different choice of the advection and diffusion co-efficient is verified. Finally, we estimate the pollutant in a river at different times and different points by using these numerical scheme. Bangladesh J. Sci. Ind. Res.55(1), 15-22, 2020

SIV EPIDEMIC MODELS WITH AGE OF INFECTION

2009 ◽  
Vol 02 (01) ◽  
pp. 61-67 ◽  
Author(s):  
JUN-YUAN YANG ◽  
FENG-QIN ZHANG ◽  
XIAO-YAN WANG
Keyword(s):  
Integral Equation ◽  
Infectious Diseases ◽  
Epidemic Model ◽  
Endemic Equilibrium ◽  
Epidemic Models ◽  
Reproductive Number ◽  
Asymptotically Stable ◽  
Age Of Infection

accination is a very important strategy for the elimination of infectious diseases. An SIV epidemic model with age of infection and vaccination has been formulated in this paper. Using the theory of differential and integral equation, we show that the infection-free equilibrium is locally asymptotically stable if the reproductive number R0 < 1, and the endemic equilibrium is locally asymptotically stable if R0 > 1.

A SIMPLE DISCRETE-TIME ANALOGUE PRESERVING THE GLOBAL STABILITY OF A CONTINUOUS SIRS EPIDEMIC MODEL

2013 ◽  
Vol 06 (02) ◽  
pp. 1350001 ◽  
Author(s):  
YOICHI ENATSU ◽  
YOSHIAKI MUROYA
Keyword(s):  
Asymptotic Stability ◽  
Discrete Time ◽  
Epidemic Model ◽  
Discrete Model ◽  
Continuous Model ◽  
The Other ◽  
Infected Population ◽  
Sirs Epidemic Model ◽  
Backward Euler ◽  
Euler Discretization

In this paper, we consider the backward Euler discretization derived from a continuous SIRS epidemic model, which contains a remaining problem that our discrete model has two solutions for infected population; one is positive and the other is negative. Under an additional positiveness condition on infected population, we show that the backward Euler discretization is one of simple discrete-time analogue which preserves the global asymptotic stability of equilibria of the corresponding continuous model.

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