Global dynamics of a discretized SIRS epidemic model with time delay

Sekiguchi, Masaki; Ishiwata, Emiko

doi:10.1016/j.jmaa.2010.05.007

Cited by 71 publications

(58 citation statements)

References 21 publications

(34 reference statements)

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“…However, since a discrete model generally can exhibit more complicated dynamical behavior than continuous models such as bifurcations and chaos (see [25,28] and references therein). Fortunately, a nonstandard finite difference scheme (NSFD) has been proposed by Mickens [29] and received much attention (see [20,[30][31][32][33][34][35][36][37][38] and references therein). One important advantage of Mickens' scheme is that it performs well in preserving the major dynamical properties of the approximated original continuous models (see [20,[35][36][37][38]).…”

Section: G(i) Imentioning

confidence: 99%

Dynamic consistent NSFD scheme for a viral infection model with cellular infection and general nonlinear incidence

Hou

Geng

et al. 2018

Adv Differ Equ

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We study a discrete-time model with diffusion that describe the dynamics of viral infections by using nonstandard finite difference (NSFD) scheme. The original model we considered was a viral infection model with cellular infection and general nonlinear incidence. We analyze thoroughly the dynamical properties of both discrete and original continuous models and show that the discrete system is dynamically consistent with the original continuous model, including positivity and boundedness of solutions, equilibria, and their global properties. The results imply that the NSFD scheme can efficiently preserve the global dynamics properties of the corresponding continuous model. Some numerical simulations are carried out to validate the theoretical results.

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Section: G(i) Imentioning

confidence: 99%

Dynamic consistent NSFD scheme for a viral infection model with cellular infection and general nonlinear incidence

Hou

Geng

et al. 2018

Adv Differ Equ

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“…Small modifications to these assumptions can easily be handled but would alter an optimal control. Discrete and distributed time delays may be considered in the incidence term, but these modifications would require some different estimates and control analysis [5,32]. The control of alternative disease dynamics, such as vector-host relationships which may be represented by parabolic PDE systems, can be studied with the techniques outlined here.…”

Section: Discussionmentioning

confidence: 99%

Optimal vaccine distribution in a spatiotemporal epidemic model with an application to rabies and raccoons

Neilan¹,

Lenhart²

2011

Journal of Mathematical Analysis and Applications

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We formulate an S-I-R (Susceptible, Infected, Immune) spatiotemporal epidemic model as a system of coupled parabolic partial differential equations with no-flux boundary conditions. Immunity is gained through vaccination with the vaccine distribution considered a control variable. The objective is to characterize an optimal control, a vaccine program which minimizes the number of infected individuals and the costs associated with vaccination over a finite space and time domain. We prove existence of solutions to the state system and existence of an optimal control, as well as derive corresponding sensitivity and adjoint equations. Techniques of optimal control theory are then employed to obtain the optimal control characterization in terms of state and adjoint functions. To illustrate solutions, parameter values are chosen to model the spread of rabies in raccoons. Optimal distributions of oral rabies vaccine baits for homogeneous and heterogeneous spatial domains are compared. Numerical results reveal that natural land features affecting raccoon movement and the relocation of raccoons by humans can considerably alter the design of a cost-effective vaccination regime. We show that the use of optimal control theory in mathematical models can yield immediate insight as to when, where, and what degree control measures should be implemented.Published by Elsevier Inc.

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“…Recently, some discrete-time models from nonstandard finite difference techniques have received much attention (see [6,22,23,25,26,32], and the references cited therein). Sekiguchi and Ishiwata derived a discretized SIRS epidemic model with time delay by applying a nonstandard finite difference scheme and analyzed its global dynamics [26].…”

Section: Introductionmentioning

confidence: 99%

“…Sekiguchi and Ishiwata derived a discretized SIRS epidemic model with time delay by applying a nonstandard finite difference scheme and analyzed its global dynamics [26]. Strictly speaking, everything in the real world has a relevance with time.…”

Section: Introductionmentioning

confidence: 99%

Permanence and extinction in a nonautonomous discrete SIRVS epidemic model with vaccination

Zhang

2015

Applied Mathematics and Computation

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Global dynamics of a discretized SIRS epidemic model with time delay

Cited by 71 publications

References 21 publications

Dynamic consistent NSFD scheme for a viral infection model with cellular infection and general nonlinear incidence

Dynamic consistent NSFD scheme for a viral infection model with cellular infection and general nonlinear incidence

Optimal vaccine distribution in a spatiotemporal epidemic model with an application to rabies and raccoons

Permanence and extinction in a nonautonomous discrete SIRVS epidemic model with vaccination

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