Propagation of HBV with spatial dependence

Wang, Kaifa; Wang, Wendi

doi:10.1016/j.mbs.2007.05.004

Cited by 179 publications

(121 citation statements)

References 37 publications

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“…The model here is much more generalized than those in [16,17,30]. Some new dynamic behavior, i.e., time periodic phenomenon, has been generated by spatial diffusion and time delay.…”

Section: Discussionmentioning

confidence: 99%

“…Next, we discuss whether the cross-diffusion has effect on the dynamics of cross-diffusion System (16) or not.…”

Section: The Cross-diffusion System Without Time Delaymentioning

confidence: 99%

“…The famous Turing instability, which was first proposed in [15], is the archetypical behavior driven by spatial diffusion. Therefore, Wang and co-workers [16,17] introduced the random mobility of viruses into (1) and considered the following non-dimensional diffusive model:…”

Section: Introductionmentioning

confidence: 99%

“…The System (2) indicates that the flux of viruses is proportional to their concentration gradient, and they go from regions of high concentration to regions of low concentration. The spatiotemporal dynamics have been investigated without or with time delay in [16,17], respectively. Then, some modified diffusive models with time delay and nonlinear functional response have been proposed; see [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

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Spatiotemporal Dynamics of a Delayed and Diffusive Viral Infection Model with Logistic Growth

Zhuang

2017

MCA

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Abstract:Viruses have important influences on human health: they not only cause some common diseases, but also cause serious illnesses. Moreover, the conventional medicines usually fail to prevent or treat them, and viral infections are hard to treat because viruses live inside the body's cells. However, some mathematical models can help to understand the viral transmission mechanism and control viral diseases. In this paper, a delayed viral infection model with spatial diffusion and logistic growth is presented. The asymptotic stability of nonnegative uniform steady states is investigated by utilizing the linearized method and constructing the proper Lyapunov functional, respectively. The existence of Hopf bifurcation from the positive equilibrium point is established by analyzing the corresponding characteristic equation and the direction of bifurcation, and the properties of bifurcating periodic solutions are derived by the aid of the normal form theory for partial functional differential equations. Then, the cross-diffusion system is introduced. Furthermore, some numerical simulations are carried out and discussions are given.

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“…The model here is much more generalized than those in [16,17,30]. Some new dynamic behavior, i.e., time periodic phenomenon, has been generated by spatial diffusion and time delay.…”

Section: Discussionmentioning

confidence: 99%

“…Next, we discuss whether the cross-diffusion has effect on the dynamics of cross-diffusion System (16) or not.…”

Section: The Cross-diffusion System Without Time Delaymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spatiotemporal Dynamics of a Delayed and Diffusive Viral Infection Model with Logistic Growth

Zhuang

2017

MCA

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“…Furthermore, the influences of spatial structures on virus dynamics can not be ignored [19]. But so far, there have been very few results about the influences of spatial structures on virus dynamics with immune response and Beddington-DeAngelis incidence rate.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a diffusive viral model with Beddington-DeAngelis incidence rate and CTL immune response

Zhuang¹

2017

J. Nonlinear Sci. Appl.

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In this paper, a four-dimensional system of viral model with cytotoxic lymphocyte (CTL) immune response is investigated. This model is a reaction-diffusion system with Beddington-DeAngelis incidence rate and free diffusion in a bounded domain. With the help of comparison principle and Lyapunov function method, the well-posedness of solutions and sufficient conditions for global stability of nonnegative equilibria are established. It can be found that free diffusion has no influence on the global stability of the system with homogeneous Neumann boundary conditions.

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Spatial patterns caused by the intracellular time delay in a super‐diffusive HBV model with logistic hepatocyte growth

Gan,

Jin,

Tian

2024

Math Methods in App Sciences

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A super‐diffusive HBV model with the intracellular time delay and logistic hepatocyte growth is studied. We discuss the local asymptotic stability of the unique positive equilibrium and prove that the intracellular time delay can cause spatial patterns. Furthermore, we find that system undergoes a Hopf bifurcation when the time delay increase to a critical value. By the normal form theory and the center manifold theorem, we investigate the stability and direction of the bifurcating periodic solutions. Finally, we present how the initial condition, time delay, superdiffusion coefficient and the exponent of superdiffusion affect spatial patterns by numerical simulations.

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Propagation of HBV with spatial dependence

Cited by 179 publications

References 37 publications

Spatiotemporal Dynamics of a Delayed and Diffusive Viral Infection Model with Logistic Growth

Spatiotemporal Dynamics of a Delayed and Diffusive Viral Infection Model with Logistic Growth

Dynamics of a diffusive viral model with Beddington-DeAngelis incidence rate and CTL immune response

Spatial patterns caused by the intracellular time delay in a super‐diffusive HBV model with logistic hepatocyte growth

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