Vectored Immunoprophylaxis and Cell-to-Cell Transmission in HIV Dynamics

2020 ◽  
Vol 30 (13) ◽  
pp. 2050185
Author(s):  
Yancong Xu ◽  
Zirui Zhu ◽  
Yu Yang ◽  
Fanwei Meng
Keyword(s):  
Hopf Bifurcation ◽  
Homoclinic Bifurcation ◽  
Hiv Disease ◽  
Hiv Model ◽  
Hiv Dynamics ◽  
Dynamical Behaviors ◽  
Cell Transmission ◽  
Parameter Interval ◽  
Local And Global Bifurcations ◽  
Main Factor

We consider local and global bifurcations in a HIV model with cell-to-cell transmission and vectored immunoprophylaxis. Both theoretical and numerical analyses are conducted to explore various dynamical behaviors including backward bifurcation, Hopf bifurcation, homoclinic bifurcation, Bogdanov–Takens bifurcation, hysteresis and isola bifurcation. The isola bifurcation of periodic orbits was first detected numerically in HIV model, which means that there is a parameter interval with the same oscillations. It is shown that the effect of vectored immunoprophylaxis in this model is the main cause of the periodic symptoms of HIV disease. Moreover, it is shown that the increase of cell-to-cell transmission may be the main factor causing Hopf bifurcation to disappear, and thus eliminating oscillation behavior. Also, several patterns of dynamical behaviors are found in different parameter intervals including the bistability.

scholarly journals Modelling HIV dynamics with cell-to-cell transmission and CTL response

2021 ◽  
Author(s):  
Zirui Zhu ◽  
Ranchao Wu ◽  
Yu Yang ◽  
Yancong Xu
Keyword(s):  
Hopf Bifurcation ◽  
Cell Interaction ◽  
Backward Bifurcation ◽  
Hiv Treatment ◽  
Hiv Model ◽  
Ctl Response ◽  
Hiv Dynamics ◽  
Subcritical Hopf Bifurcation ◽  
Cell Transmission ◽  
New Type

In most HIV models, the emergence of backward bifurcation means that the control for basic reproduction number less than one is no longer effective for HIV treatment. In this paper, we study an HIV model with CTL response and cell-to-cell transmission by using the dynamical approach. The local and global stability of equilibria is investigated, the relations of subcritical Hopf bifurcation and supercritical bifurcation points are revealed, especially, the so-called new type bifurcation is also found with two Hopf bifurcation curves meeting at the same Bogdanov-Takens bifurcation point. Forward and backward bifurcation, Hopf bifurcation, saddle-node bifurcation, Bogdanov-Takens bifurcation are investigated analytically and numerically. Two limit cycles are also found numerically, which indicates that the complex behavior of HIV dynamics. Interestingly, the role of cell-to-cell interaction is fully uncovered, it may cause the oscillations to disappear and keep the so-called new type bifurcation persist. Finally, some conclusions and discussions are also given.

scholarly journals Hopf bifurcation in a diffusive predator–prey model with Smith growth rate and herd behavior

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Heping Jiang ◽  
Huiping Fang ◽  
Yongfeng Wu
Keyword(s):  
Hopf Bifurcation ◽  
Neumann Boundary ◽  
Herd Behavior ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Dynamical Behaviors ◽  
Prey System ◽  
Prey Model ◽  
Homogeneous Neumann Boundary Condition ◽  
The Stability

Abstract This paper mainly aims to consider the dynamical behaviors of a diffusive delayed predator–prey system with Smith growth and herd behavior subject to the homogeneous Neumann boundary condition. For the analysis of the predator–prey model, we have studied the existence of Hopf bifurcation by analyzing the distribution of the roots of associated characteristic equation. Then we have proved the stability of the periodic solution by calculating the normal form on the center of manifold which is associated to the Hopf bifurcation points. Some numerical simulations are also carried out in order to validate our analysis findings. The implications of our analytical and numerical findings are discussed critically.

Turing Instability and Hopf Bifurcation in Cellular Neural Networks

2021 ◽  
Vol 31 (08) ◽  
pp. 2150143
Author(s):  
Zunxian Li ◽  
Chengyi Xia
Keyword(s):  
Neural Networks ◽  
Hopf Bifurcation ◽  
Turing Instability ◽  
Cellular Neural Networks ◽  
Bifurcation Theorem ◽  
Decoupling Method ◽  
Dynamical Behaviors ◽  
The Stability ◽  
Approximate Expressions ◽  
Zero Equilibrium

In this paper, we explore the dynamical behaviors of the 1D two-grid coupled cellular neural networks. Assuming the boundary conditions of zero-flux type, the stability of the zero equilibrium is discussed by analyzing the relevant eigenvalue problem with the aid of the decoupling method, and the conditions for the occurrence of Turing instability and Hopf bifurcation at the zero equilibrium are derived. Furthermore, the approximate expressions of the bifurcating periodic solutions are also obtained by using the Hopf bifurcation theorem. Finally, numerical simulations are provided to demonstrate the theoretical results.

scholarly journals The number of limit cycles for a class of quintic Hamiltonian systems under quintic perturbations

2002 ◽  
Vol 73 (1) ◽  
pp. 37-54 ◽  
Author(s):  
Guowei Chen ◽  
Yongbin Wu ◽  
Xinan Yang
Keyword(s):  
Hopf Bifurcation ◽  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Limit Cycles ◽  
Homoclinic Bifurcation

AbstractThe Hopf bifurcation and homoclinic bifurcation of the quintic Hamiltonian system is analyzed under quintic perturbations by using unfolding theory in this paper. We show that a quintic system can have at least 29 limit cycles.

Global Stability and Hopf Bifurcation in a Delayed Viral Infection Model with Cell-to-Cell Transmission and Humoral Immune Response

2019 ◽  
Vol 29 (12) ◽  
pp. 1950161 ◽  
Author(s):  
Jinhu Xu ◽  
Yan Geng ◽  
Suxia Zhang
Keyword(s):  
Immune Response ◽  
Hopf Bifurcation ◽  
Viral Infection ◽  
Humoral Immune Response ◽  
Dynamical Behavior ◽  
Infection Model ◽  
Humoral Immune ◽  
Cell Transmission ◽  
Viral Infection Model ◽  
Intracellular Delays

We have developed a class of viral infection model with cell-to-cell transmission and humoral immune response. The model addresses both immune and intracellular delays. We also constructed Lyapunov functionals to establish the global dynamical properties of the equilibria. Theoretical results indicate that considering only two intracellular delays did not affect the dynamical behavior of the model, but incorporating an immune delay greatly affects the dynamics, i.e. an immune delay may destabilize the immunity-activated equilibrium and lead to Hopf bifurcation, oscillations and stability switches. Our results imply that an immune delay dominates the intracellular delays in the model. We also investigated the direction of the Hopf bifurcation and the stability of the periodic solutions by applying normal form and center manifold theory, and investigated the existence of global Hopf bifurcation by regarding the immune delay as a bifurcation parameter. Numerical simulations are carried out to support the analytical conclusions.

scholarly journals Complex Behaviors of Epidemic Model with Nonlinear Rewiring Rate

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Ding Fang ◽  
Yongxin Zhang ◽  
Wendi Wang
Keyword(s):  
Hopf Bifurcation ◽  
Numerical Simulations ◽  
Bifurcation Analysis ◽  
Epidemic Model ◽  
Multiple Equilibria ◽  
Homoclinic Bifurcation ◽  
Propagation Model ◽  
Bifurcation Curve ◽  
Saddle Node Bifurcation ◽  
Saddle Node

An SIS propagation model with the nonlinear rewiring rate on an adaptive network is considered. It is found by bifurcation analysis that the model has the complex behaviors which include the transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation, and Bogdanov–Takens bifurcation. Especially, a bifurcation curve with “S” shape emerges due to the nonlinear rewiring rate, which leads to multiple equilibria and twice saddle-node bifurcations. Numerical simulations show that the model admits a homoclinic bifurcation and a saddle-node bifurcation of the limit cycle.

scholarly journals Hopf Bifurcation Analysis and Anticontrol of Hopf Circles of the Rössler-Like System

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Ranchao Wu ◽  
Xiang Li
Keyword(s):  
Hopf Bifurcation ◽  
Projective Synchronization ◽  
Linear Feedback ◽  
Normal Form Theory ◽  
Dynamical Behaviors ◽  
Control Scheme ◽  
Stable Periodic ◽  
Form Theory ◽  
Synchronization Scheme ◽  
Bifurcation And Stability

A new Rössler-like system is constructed by the linear feedback control scheme in this paper. As well, it exhibits complex dynamical behaviors, such as bifurcation, chaos, and strange attractor. By virtue of the normal form theory, its Hopf bifurcation and stability are investigated in detail. Consequently, the stable periodic orbits are bifurcated. Furthermore, the anticontrol of Hopf circles is achieved between the new Rössler-like system and the original Rössler one via a modified projective synchronization scheme. As a result, a stable Hopf circle is created in the controlled Rössler system. The corresponding numerical simulations are presented, which agree with the theoretical analysis.

scholarly journals Stability and Hopf Bifurcation in a Computer Virus Model with Multistate Antivirus

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Tao Dong ◽  
Xiaofeng Liao ◽  
Huaqing Li
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Computer Virus ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Local Hopf Bifurcation ◽  
Dynamical Behaviors ◽  
Form Theory ◽  
Virus Model ◽  
Theoretical Results

By considering that people may immunize their computers with countermeasures in susceptible state, exposed state and using anti-virus software may take a period of time, a computer virus model with time delay based on an SEIR model is proposed. We regard time delay as bifurcating parameter to study the dynamical behaviors which include local asymptotical stability and local Hopf bifurcation. By analyzing the associated characteristic equation, Hopf bifurcation occurs when time delay passes through a sequence of critical value. The linerized model and stability of the bifurcating periodic solutions are also derived by applying the normal form theory and the center manifold theorem. Finally, an illustrative example is also given to support the theoretical results.

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