Stability analysis in a diffusional immunosuppressive infection model with delayed antiviral immune response

Tian, Canrong; Gan, Weiqun; Zhu, Ping

doi:10.1002/mma.4279

Cited by 4 publications

(3 citation statements)

References 39 publications

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“…Following this, many scholars continuously modified the immunosuppressive infection model [10][11][12]. Due to the immune system requiring a time lag to generate new immune cells through a series of events [13], Shu et al [10] proposed an assumption that the activation rate of immune cells at time t is dependent on both the virus load and the number of immune cells at time t − τ.…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal Dynamics of a Diffusive Immunosuppressive Infection Model with Nonlocal Competition and Crowley–Martin Functional Response

Xue,

Xu,

Ding

2023

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In this paper, we introduce the Crowley–Martin functional response and nonlocal competition into a reaction–diffusion immunosuppressive infection model. First, we analyze the existence and stability of the positive constant steady states of the systems with nonlocal competition and local competition, respectively. Second, we deduce the conditions for the occurrence of Turing, Hopf, and Turing–Hopf bifurcations of the system with nonlocal competition, as well as the conditions for the occurrence of Hopf bifurcations of the system with local competition. Furthermore, we employ the multiple time scales method to derive the normal forms of the Hopf bifurcations reduced on the center manifold for both systems. Finally, we conduct numerical simulations for both systems under the same parameter settings, compare the impact of nonlocal competition, and find that the nonlocal term can induce spatially inhomogeneous stable periodic solutions. We also provide corresponding biological explanations for the simulation results.

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Section: Introductionmentioning

confidence: 99%

Spatiotemporal Dynamics of a Diffusive Immunosuppressive Infection Model with Nonlocal Competition and Crowley–Martin Functional Response

Xue,

Xu,

Ding

2023

Axioms

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“…Time‐dependent coupled partial differential equations (PDEs) play a crucial role in modeling various chemical and biological processes 1–12 . The coupled Brusselator model is one such nonlinear coupled PDE that seeks applications in cooperative processes of chemical kinetics or biochemical reactions 13 .…”

Section: Introductionmentioning

confidence: 99%

“…Time-dependent coupled partial differential equations (PDEs) play a crucial role in modeling various chemical and biological processes. [1][2][3][4][5][6][7][8][9][10][11][12] The coupled Brusselator model is one such nonlinear coupled PDE that seeks applications in cooperative processes of chemical kinetics or biochemical reactions. 13 For example, in the patterns formation on animal skins with and without cross-diffusion, in the creation of ozone by atomic oxygen through a triple collision, in enzymatic reactions, in plasma and laser physics.…”

Section: Introductionmentioning

confidence: 99%

Analytical modeling of the approximate solution behavior of multi‐dimensional reaction–diffusion Brusselator system

Hussain

2022

Math Methods in App Sciences

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This article presents an effective and simple approximation scheme to analytically approximate solution behavior of a multi‐dimensional reaction–diffusion Brusselator system. This system has applications in cooperative processes of chemical kinetics and biochemical reaction processes. The proposed residual power series method is based on multiple power series expansion and residual error function formulation. The convergence properties and error bounds of the proposed scheme are theoretically established and numerically verified. Two benchmark problems in two‐ and three‐dimensional space are considered to validate the efficiency and accuracy of the proposed scheme. The obtained results verified reliability, accuracy, and simplicity of the proposed scheme against the available results in literature.

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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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Stability analysis in a diffusional immunosuppressive infection model with delayed antiviral immune response

Cited by 4 publications

References 39 publications

Spatiotemporal Dynamics of a Diffusive Immunosuppressive Infection Model with Nonlocal Competition and Crowley–Martin Functional Response

Spatiotemporal Dynamics of a Diffusive Immunosuppressive Infection Model with Nonlocal Competition and Crowley–Martin Functional Response

Analytical modeling of the approximate solution behavior of multi‐dimensional reaction–diffusion Brusselator system

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

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