Bifurcation analysis in a discrete SIR epidemic model with the saturated contact rate and vertical transmission

Du, Wenju; Zhang, Jiangang; Qin, Shuang; Yu, Jing

doi:10.22436/jnsa.009.07.02

Cited by 12 publications

(2 citation statements)

References 18 publications

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“…In recent years, due to infectious diseases data collected based on periods of days, weeks, months, and years, we have seen more attention being given to a great deal of practical real life problems in epidemiology depicted by discrete-time epidemic models described using difference equations. Although, in recent times, an increasing attention has been given to the discrete epidemic models (see [2,8] and the references cited therein), the research in the context of the nonlinear dynamic characteristics of the discrete systems is relatively few, compared with the amount of studies performed in the literature about the continuous systems. With their unique dynamic characteristics, the discrete systems are able to depict many practical problems in the real life, in particular in the context of epidemiology (see [9][10][11][12] and the references cited therein)…”

Section: Introductionmentioning

confidence: 99%

On the Dynamical Complexity of a Seasonally Forced Discrete SIR Epidemic Model with a Constant Vaccination Strategy

et al. 2018

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In this article, we consider the discretized classical Susceptible-Infected-Recovered (SIR) forced epidemic model to investigate the consequences of the introduction of different transmission rates and the effect of a constant vaccination strategy, providing new numerical and topological insights into the complex dynamics of recurrent diseases. Starting with a constant contact (or transmission) rate, the computation of the spectrum of Lyapunov exponents allows us to identify different chaotic regimes. Studying the evolution of the dynamical variables, a family of unimodal-type iterated maps with a striking biological meaning is detected among those dynamical regimes of the densities of the susceptibles. Using the theory of symbolic dynamics, these iterated maps are characterized based on the computation of an important numerical invariant, the topological entropy. The introduction of a degree (or amplitude) of seasonality, ε, is responsible for inducing complexity into the population dynamics. The resulting dynamical behaviors are studied using some of the previous tools for particular values of the strength of the seasonality forcing, ε. Finally, we carry out a study of the discrete SIR epidemic model under a planned constant vaccination strategy. We examine what effect this vaccination regime will have on the periodic and chaotic dynamics originated by seasonally forced epidemics.

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Section: Introductionmentioning

confidence: 99%

On the Dynamical Complexity of a Seasonally Forced Discrete SIR Epidemic Model with a Constant Vaccination Strategy

et al. 2018

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“…They have studied stability and Neimark-Sacker bifurcation of a discrete-time predator-prey model. The analysis of bifurcations has already received much attention during the last few years [20,[22][23][24][25][26][27][28][29]. Bifurcation and stability analysis are examined in detail in [20,[22][23][24][30][31][32][33][34][35][36][37][38][39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Neimark–Sacker bifurcation and stability analysis of a discrete-time prey–predator model with Allee effect in prey

Kangalgil

2019

Adv Differ Equ

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In this paper, the dynamical behaviors of a discrete-time prey-predator model with Allee effect on the prey population are investigated. The existence and topological classification of the fixed points of the model are analyzed. It is shown that the model can undergo a Neimark-Sacker bifurcation at the unique positive fixed point by choosing a as a bifurcation parameter. The conditions of the existence for Neimark-Sacker bifurcation and the direction of bifurcation via bifurcation theory are presented. Also, some numerical simulations are presented to support of the analytical finding. Then bifurcation diagrams and phase portraits of the model are given. MSC: 39A28; 39A30; 92B05

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Complex dynamics analysis for a two-stage Cournot duopoly game of semi-collusion in production

et al. 2017

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Bifurcation analysis in a discrete SIR epidemic model with the saturated contact rate and vertical transmission

Cited by 12 publications

References 18 publications

On the Dynamical Complexity of a Seasonally Forced Discrete SIR Epidemic Model with a Constant Vaccination Strategy

On the Dynamical Complexity of a Seasonally Forced Discrete SIR Epidemic Model with a Constant Vaccination Strategy

Neimark–Sacker bifurcation and stability analysis of a discrete-time prey–predator model with Allee effect in prey

Complex dynamics analysis for a two-stage Cournot duopoly game of semi-collusion in production

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