Stability preserving NSFD scheme for a delayed viral infection model with cell-to-cell transmission and general nonlinear incidence

2017 ◽  
Vol 23 (5) ◽  
pp. 893-916 ◽  
Author(s):  
Jinhu Xu ◽  
Yan Geng
Keyword(s):  
Viral Infection ◽  
Infection Model ◽  
Nonlinear Incidence ◽  
Cell Transmission ◽  
Nsfd Scheme ◽  
Viral Infection Model

scholarly journals Dynamic Consistent NSFD Scheme for a Delayed Viral Infection Model with Immune Response and Nonlinear Incidence

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Jinhu Xu ◽  
Yan Geng
Keyword(s):  
Immune Response ◽  
Viral Infection ◽  
Discrete Time ◽  
Discrete Model ◽  
Continuous Model ◽  
Infection Model ◽  
Time Step ◽  
Nonlinear Incidence ◽  
Nsfd Scheme ◽  
Viral Infection Model

In this paper, a discrete-time model has been proposed by applying nonstandard finite difference (NSFD) scheme to solve a delayed viral infection model with immune response and general nonlinear incidence. It is shown that the discrete model has equilibria which are exactly the same as those of the original continuous model. Using discrete-time analogue of Lyapunov functionals, the global asymptotic stability of the equilibria of the discrete model is fully determined by the basic reproduction number of the virus and immune response, R0 and R1, with no restriction on the time step size, which implies that the NSFD scheme preserves the qualitative dynamics of the corresponding continuous model.

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 Global dynamics for a class of infection-age model with nonlinear incidence

2018 ◽  
Vol 24 (1) ◽  
pp. 47-72 ◽  
Author(s):  
Yuji Li ◽  
Rui Xu ◽  
Jiazhe Lin
Keyword(s):  
Viral Infection ◽  
Reproduction Number ◽  
Infection Model ◽  
Uniform Persistence ◽  
Global Dynamics ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Infection Age ◽  
Age Model ◽  
Viral Infection Model

In this paper, we propose an HBV viral infection model with continuous age structure and nonlinear incidence rate. Asymptotic smoothness of the semi-flow generated by the model is studied. Then we caculate the basic reproduction number and prove that it is a sharp threshold determining whether the infection dies out or not. We give a rigorous mathematical analysis on uniform persistence by reformulating the system as a system of Volterra integral equations. The global dynamics of the model is established by using suitable Lyapunov functionals and LaSalle's invariance principle. We further investigate the global behaviors of the HBV viral infection model with saturation incidence through numerical simulations.

A delayed reaction–diffusion viral infection model with nonlinear incidences and cell-to-cell transmission

2021 ◽  
Author(s):  
Qing Ge ◽  
Xia Wang ◽  
Libin Rong
Keyword(s):  
Viral Infection ◽  
Traveling Wave Solutions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Infection Model ◽  
Threshold Dynamics ◽  
Delayed Reaction ◽  
Homogeneous Neumann Boundary Condition ◽  
Cell Transmission ◽  
Viral Infection Model

In this paper, we propose a reaction–diffusion viral infection model with nonlinear incidences, cell-to-cell transmission, and a time delay. We impose the homogeneous Neumann boundary condition. For the case where the domain is bounded, we first study the well-posedness. Then we analyze the local stability of homogeneous steady states. We establish a threshold dynamics which is completely characterized by the basic reproduction number. For the case where the domain is the whole Euclidean space, we consider the existence of traveling wave solutions by using the cross-iteration method and Schauder’s fixed point theorem. Finally, we study how the speed of spread in space affects the spread of cells and viruses. We obtain the existence of the wave speed, which is dependent on the diffusion coefficient.

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