Stability and bifurcation control analysis of a delayed fractional-order eco-epidemiological system

Qi, Hao; Zhao, Wencai

doi:10.1140/epjp/s13360-022-03154-z

Cited by 6 publications

(17 citation statements)

References 38 publications

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“…The results showed that both the delay and the feedback gain coefficient could suppress the emergence of Hopf bifurcation. Moreover, in [43], Qi H and Zhao W considered the factor of manual intervention and proposed a delayed fractional-order eco-epidemiological model with a feedback controller, which verified the critical role of the controller for the stability of the system.…”

Section: Introductionmentioning

confidence: 89%

Stability and Bifurcation Control for a Generalized Delayed Fractional Food Chain Model

Li,

Liu,

Zhao

et al. 2024

Fractal Fract

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In this paper, a generalized fractional three-species food chain model with delay is investigated. First, the existence of a positive equilibrium is discussed, and the sufficient conditions for global asymptotic stability are given. Second, through selecting the delay as the bifurcation parameter, we obtain the sufficient condition for this non-control system to generate Hopf bifurcation. Then, a nonlinear delayed feedback controller is skillfully applied to govern the system’s Hopf bifurcation. The results indicate that adjusting the control intensity or the control target’s age can effectively govern the bifurcation dynamics behavior of this system. Last, through application examples and numerical simulations, we confirm the validity and feasibility of the theoretical results, and find that the control strategy is also applicable to eco-epidemiological systems.

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Section: Introductionmentioning

confidence: 89%

Stability and Bifurcation Control for a Generalized Delayed Fractional Food Chain Model

Li,

Liu,

Zhao

et al. 2024

Fractal Fract

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“…From the definition of fractional derivative, it is not difficult to see that the fractional derivative is associated with the whole time domain, while the integer derivative is only related to a particular time, so a fractional differential system has the function of long-term memory or short-term memory [15][16][17]. At the same time, because the fractional system has a broader stability region than the traditional integer-order system [18,19], it is therefore widely used in physics and viscoelastic materials, control and artificial intelligence, biology and dynamic systems, etc. [14,[20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Stability and Optimal Control of a Fractional SEQIR Epidemic Model with Saturated Incidence Rate

Sun

Zhao

2023

Fractal Fract

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The fractional differential equation has a memory property and is suitable for biomathematical modeling. In this paper, a fractional SEQIR epidemic model with saturated incidence and vaccination is constructed. Firstly, for the deterministic fractional system, the threshold conditions for the local and global asymptotic stability of the equilibrium point are obtained by using the stability theory of the fractional differential equation. If R0<1, the disease-free equilibrium is asymptotically stable, and the disease is extinct; when R0>1, the endemic equilibrium is asymptotically stable and the disease persists. Secondly, for the stochastic system of integer order, the stochastic stability near the positive equilibrium point is discussed. The results show that if the intensity of environmental noise is small enough, the system is stochastic stable, and the disease will persist. Thirdly, the control variables are coupled into the fractional differential equation to obtain the fractional control system, the objective function is constructed, and the optimal control solution is obtained by using the maximum principle. Finally, the correctness of the theoretical derivation is verified by numerical simulation.

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“…There exists a large volume of literature on ecological models with time delays present in the governing equations. Time-delayed eco-epidemiological models have been investigated in [25,38,12,4,13,29,51]. Qi and Zhao [38] formulated a delayed fractional eco-epidemic model with an extended feedback controller.…”

mentioning

confidence: 99%

“…Time-delayed eco-epidemiological models have been investigated in [25,38,12,4,13,29,51]. Qi and Zhao [38] formulated a delayed fractional eco-epidemic model with an extended feedback controller. In this study, they investigated the stability and the Hopf bifurcation where the digestion delay is the bifurcation parameter.…”

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confidence: 99%

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A brief discussion about a predator-prey model including disease in predators with the delay effect

Das,

Chakraborty

2023

NACO

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Prey-predator interactions in an ecosystem are greatly influenced by the gestation delay and disease. To analyze the complex dynamics of the prey-predator interaction, we have proposed a three-tire delayed eco-epidemic model including disease in the predator population. During the study of this model, we establish the positivity and boundedness of the proposed model and also find all possible equilibrium points with their local and global stability condition in absence and presence of gestation delay. Analytical and numerical studies explain the existence of Transcritical and Hopf-bifurcations. Using sensitivity analysis, we examine the positive and negative impact of all model parameters and identify the most significant parameters. The main objective is to understand how disease and gestation delay influence the populations of this proposed model and also examine the combined effect of both gestation delay and disease infection rate. Furthermore, we incorporate the disease transmission delay and explore the combined effect of both gestation delay and disease transmission delay on the solutions of the proposed system. Numerically, we have demonstrated that the system experiences only steady and periodic behavior under the influence of gestation delay, but under the combined impact of both gestation delay and disease transmission delay, the system undergoes stable, one-periodic, two-periodic, and chaotic regimes.

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Stability and bifurcation control analysis of a delayed fractional-order eco-epidemiological system

Cited by 6 publications

References 38 publications

Stability and Bifurcation Control for a Generalized Delayed Fractional Food Chain Model

Stability and Bifurcation Control for a Generalized Delayed Fractional Food Chain Model

Stability and Optimal Control of a Fractional SEQIR Epidemic Model with Saturated Incidence Rate

A brief discussion about a predator-prey model including disease in predators with the delay effect

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