Stability analysis in a class of discrete SIRS epidemic models

Hu, Zengyun; Teng, Zhidong; Jiang, Haijun

doi:10.1016/j.nonrwa.2011.12.024

Cited by 124 publications

(75 citation statements)

References 32 publications

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“…In the last years, the study of discrete-time (epidemic) models has increased (see for instance ([15] or [16]) due to different considerations (see [17]). First of all, statistical data on epidemics are collected in discrete time.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, to describe epidemics using such discrete models seems to be convenient. In addition, more accurate numerical simulation results are maybe obtained using discrete-time models, although the dynamic behaviors of such discrete models are often more complex [16]. Furthermore, numerical simulations of continuous-time models are obtained by discretizing these models.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A discrete epidemic model for bovine Babesiosis disease and tick populations

Aranda¹,

Trejos²,

Valverde³

2017

Open Physics

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Abstract:In this paper, we provide and study a discrete model for the transmission of Babesiosis disease in bovine and tick populations. This model supposes a discretization of the continuous-time model developed by us previously. The results, here obtained by discrete methods as opposed to continuous ones, show that similar conclusions can be obtained for the discrete model subject to the assumption of some parametric constraints which were not necessary in the continuous case. We prove that these parametric constraints are not artificial and, in fact, they can be deduced from the biological significance of the model. Finally, some numerical simulations are given to validate the model and verify our theoretical study.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A discrete epidemic model for bovine Babesiosis disease and tick populations

Aranda¹,

Trejos²,

Valverde³

2017

Open Physics

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“…There are many discretization methods that have been used to construct the discretetime model using continuous-time methods such as explicit and implicit Euler's method, Runge-Kutta method, predictor-corrector method and nonstandard finite difference methods [33][34][35][36][37]. Some of them are approximation for the derivative and some for the integral.…”

Section: Discretization Processmentioning

confidence: 99%

Bifurcations and chaos in a discrete SI epidemic model with fractional order

et al. 2018

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In this study, a new discrete SI epidemic model is proposed and established from SI fractional-order epidemic model. The existence conditions, the stability of the equilibrium points and the occurrence of bifurcation are analyzed. By using the center manifold theorem and bifurcation theory, it is shown that the model undergoes flip and Neimark-Sacker bifurcation. The effects of step size and fractional-order parameters on the dynamics of the model are studied. The bifurcation analysis is also conducted and our numerical results are in agreement with theoretical results.

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“…All authors read and approved the manuscript. 1 School of Mathematics and Statistics, Central China Normal University, Wuhan, China. 2 College of Mathematics and System Sciences, Xinjiang University, Urumqi, China.…”

Section: Competing Interestsmentioning

confidence: 99%

“…Recently, many investigations have demonstrated that the incidence rate is a primary factor in generating the abundant dynamical behaviors (such as bistability and periodicity phenomena, which are very important dynamical features) of epidemic models [1][2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Bifurcations of an SIRS model with generalized non-monotone incidence rate

Teng

2018

Adv Differ Equ

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We consider an SIRS epidemic model with a more generalized non-monotone incidence: χ (I) = κI p 1+I q with 0 < p < q, describing the psychological effect of some serious diseases when the number of infective individuals is getting larger. By analyzing the existence and stability of disease-free and endemic equilibrium, we show that the dynamical behaviors of p < 1, p = 1 and p > 1 distinctly vary. On one hand, the number and stability of disease-free and endemic equilibrium are different. On the other hand, when p ≤ 1, there do not exist any closed orbits and when p > 1, by qualitative and bifurcation analyses, we show that the model undergoes a saddle-node bifurcation, a Hopf bifurcation and a Bogdanov-Takens bifurcation of codimension 2. Besides, for p = 2, q = 3, we prove that the maximal multiplicity of weak focus is at least 2, which means at least 2 limit cycles can arise from this weak focus. And numerical examples of 1 limit cycle, 2 limit cycles and homoclinic loops are also given.

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Stability analysis in a class of discrete SIRS epidemic models

Cited by 124 publications

References 32 publications

A discrete epidemic model for bovine Babesiosis disease and tick populations

A discrete epidemic model for bovine Babesiosis disease and tick populations

Bifurcations and chaos in a discrete SI epidemic model with fractional order

Bifurcations of an SIRS model with generalized non-monotone incidence rate

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