A note on an NSFD scheme for a mathematical model of respiratory virus transmission

Mickens, Ronald E.; Washington, Talitha M.

doi:10.1080/10236198.2010.515590

Cited by 30 publications

(15 citation statements)

References 7 publications

(21 reference statements)

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“…For us, dynamical consistency means: whenever there is extinction (respectively permanence) of the disease for the continuous-time model the same holds for the discrete-time one. Several papers [5,6,9,10,14,25,26] discuss the dynamical consistency with respect to some particular properties of discrete epidemiological models obtained from continuous models by some NSFD scheme [23]. We note that while the papers cited above consider autonomous models, in the present work we discuss dynamical consistency for a non-autonomous model.…”

Section: Introductionmentioning

confidence: 89%

A Consistent Discrete Version of a Nonautonomous SIRVS Model

Mateus

Silva

Vaz

2018

Discrete Dynamics in Nature and Society

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A family of discrete non-autonomous SIRVS models with general incidence is obtained from a continuous family of models by applying Mickens non-standard discretization method. Conditions for the permanence and extinction of the disease and the stability of disease-free solutions are determined. The consistency of those discrete models with the corresponding continuous model is discussed: if the time step is sufficiently small, when we have extinction (respectively permanence) for the continuous model we also have extinction (respectively permanence) for the corresponding discrete model. Some numerical simulations are carried out to compare the different possible discretizations of our continuous model using real data.

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Section: Introductionmentioning

confidence: 89%

A Consistent Discrete Version of a Nonautonomous SIRVS Model

Mateus

Silva

Vaz

2018

Discrete Dynamics in Nature and Society

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“…Currently, there are various discretization methods to discretize a continuous model, including the standard methods, such as Euler method, Runge-Kutta method, some other standard and nonstandard finite difference scheme (see e.g. [6,7,11,[19][20][21][22][23]27]).…”

Section: Introductionmentioning

confidence: 99%

The stability of a stochastic discrete SIVS epidemic model with general nonlinear incidence

Wen

Teng

Liu

2022

NAMC

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In this paper, based on Euler–Marryama method and theory of stochastic processes, a stochastic discrete SIVS epidemic model with general nonlinear incidence and vaccination is proposed by adding random perturbation and then discretizing the corresponding stochastic differential equation model. Firstly, the basic properties of continuous and discrete deterministic SIVS epidemic models are obtained. Then a criterion on the asymptotic mean-square stability of zero solution for a general linear stochastic difference system is established. As the applications of this criterion, the sufficient conditions on the stability in probability of the disease-free and endemic equilibria for the stochastic discrete SIVS epidemic model are obtained. The numerical simulations are given to illustrate the theoretical results.

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“…This method can be more stable and accurate than the standard method . Moreover, this method can be easier to formulate . The positive applications of NFDM can be found in the fields of physics, chemistry, and engineering .…”

Section: Introductionmentioning

confidence: 99%

A novel variable‐order fractional nonlinear Klein Gordon model: A numerical approach

Sweilam

AL–Mekhlafi

Albalawi

2019

Numerical Methods Partial

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In this article, a novel variable order fractional nonlinear Klein Gordon model is presented where the variable‐order fractional derivative is defined in the Caputo sense. The merit of nonstandard numerical techniques is extended here and we present the weighted average nonstandard finite difference method to study numerically the proposed model. Special attention is paid to study the convergence and to the stability analysis of the numerical technique. Moreover, the truncation error is analyzed. Three test examples are provided. Comparative studies are done between the used numerical technique and the weighted average finite difference method. It is found that the stability regions are larger by using the weighted average nonstandard finite difference method.

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A note on an NSFD scheme for a mathematical model of respiratory virus transmission

Cited by 30 publications

References 7 publications

A Consistent Discrete Version of a Nonautonomous SIRVS Model

A Consistent Discrete Version of a Nonautonomous SIRVS Model

The stability of a stochastic discrete SIVS epidemic model with general nonlinear incidence

A novel variable‐order fractional nonlinear Klein Gordon model: A numerical approach

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