Stability and Hopf bifurcation analysis of an SVEIR epidemic model with vaccination and multiple time delays

Zhang, Zizhen; Kundu, Soumen; Tripathi, Jai Prakash; Bugalia, Sarita

doi:10.1016/j.chaos.2019.109483

Cited by 53 publications

(26 citation statements)

References 40 publications

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“…In the last few decades, the nonlinear phenomenon in chaos has been widely considered in engineering, sciences, and applied mathematics [1,2]. When a deterministic system exhibits a strange phenomenon of aperiodic trajectories, this is called chaos [3][4][5]. Chaotic system sensitivity is introduced when the initial conditions and system parameters have a strong influence on chaotic systems; however, even a minor alteration in the starting situation can have a significant impact on the final result [6].…”

Section: Introductionmentioning

confidence: 99%

A New Fractional-Order Chaotic System with Its Analysis, Synchronization, and Circuit Realization for Secure Communication Applications

et al. 2021

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This article presents a novel four-dimensional autonomous fractional-order chaotic system (FOCS) with multi-nonlinearity terms. Several dynamics, such as the chaotic attractors, equilibrium points, fractal dimension, Lyapunov exponent, and bifurcation diagrams of this new FOCS, are studied analytically and numerically. Adaptive control laws are derived based on Lyapunov theory to achieve chaos synchronization between two identical new FOCSs with an uncertain parameter. For these two identical FOCSs, one represents the master and the other is the slave. The uncertain parameter in the slave side was estimated corresponding to the equivalent master parameter. Next, this FOCS and its synchronization were realized by a feasible electronic circuit and tested using Multisim software. In addition, a microcontroller (Arduino Due) was used to implement the suggested system and the developed synchronization technique to demonstrate its digital applicability in real-world applications. Furthermore, based on the developed synchronization mechanism, a secure communication scheme was constructed. Finally, the security analysis metric tests were investigated through histograms and spectrograms analysis to confirm the security strength of the employed communication system. Numerical simulations demonstrate the validity and possibility of using this new FOCS in high-level security communication systems. Furthermore, the secure communication system is highly resistant to pirate attacks. A good agreement between simulation and experimental results is obtained, showing that the new FOCS can be used in real-world applications.

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Section: Introductionmentioning

confidence: 99%

A New Fractional-Order Chaotic System with Its Analysis, Synchronization, and Circuit Realization for Secure Communication Applications

et al. 2021

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“…That is, reinfection likely occurs [6,7]. It is shown that time delay is of great significance in many biological modelling, and its change may affect the dynamic behavior of the system [4][5][6][9][10][11][12][13][14][15][16][17][18][19], such as stability, uniqueness, and oscillation of solution. So, it is instructive to consider a mathematical model with time delays to research the influence of immunity on disease control of malaria transmission.…”

Section: Introductionmentioning

confidence: 99%

Stability and Hopf Bifurcation Analysis of a Vector-Borne Disease Model with Two Delays and Reinfection

Yan-xia

Huang

et al. 2021

Computational and Mathematical Methods in Medicine

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In this paper, a vector-borne disease model with two delays and reinfection is established and considered. First of all, the existence of the equilibrium of the system, under different cases of two delays, is discussed through analyzing the corresponding characteristic equation of the linear system. Some conditions that the system undergoes Hopf bifurcation at the endemic equilibrium are obtained. Furthermore, by employing the normal form method and the center manifold theorem for delay differential equations, some explicit formulas used to describe the properties of bifurcating periodic solutions are derived. Finally, the numerical examples and simulations are presented to verify our theoretical conclusions. Meanwhile, the influences of the degree of partial protection for recovered people acquired by a primary infection on the endemic equilibrium and the critical values of the two delays are analyzed.

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“…From another perspective, in comparison with ordinary differential equations, delayed differential equations present more complex dynamics. In fact, delayed differential equations have been applied in various fields, for example, mathematical biology [27][28][29][30], epidemiology [31][32][33], and computer virus [34][35][36][37]. All the work above revealed that delay can influence dynamics of the systems significantly.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation and optimal control analysis of a delayed drinking model

2020

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Alcoholism is a social phenomenon that affects all social classes and is a chronic disorder that causes the person to drink uncontrollably, which can bring a series of social problems. With this motivation, a delayed drinking model including five subclasses is proposed in this paper. By employing the method of characteristic eigenvalue and taking the temporary immunity delay for alcoholics under treatment as a bifurcation parameter, a threshold value of the time delay for the local stability of drinking-present equilibrium and the existence of Hopf bifurcation are found. Then the length of delay has been estimated to preserve stability using the Nyquist criterion. Moreover, optimal strategies to lower down the number of drinkers are proposed. Numerical simulations are presented to examine the correctness of the obtained results and the effects of some parameters on dynamics of the drinking model.

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Stability and Hopf bifurcation analysis of an SVEIR epidemic model with vaccination and multiple time delays

Cited by 53 publications

References 40 publications

A New Fractional-Order Chaotic System with Its Analysis, Synchronization, and Circuit Realization for Secure Communication Applications

A New Fractional-Order Chaotic System with Its Analysis, Synchronization, and Circuit Realization for Secure Communication Applications

Stability and Hopf Bifurcation Analysis of a Vector-Borne Disease Model with Two Delays and Reinfection

Bifurcation and optimal control analysis of a delayed drinking model

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