Abstract
We study a discrete-time model with diffusion that describe the dynamics of viral infections by using nonstandard finite difference (NSFD) scheme. The original model we considered was a viral infection model with cellular infection and general nonlinear incidence. We analyze thoroughly the dynamical properties of both discrete and original continuous models and show that the discrete system is dynamically consistent with the original continuous model, including positivity and boundedness of solutions, equilibria, and their global properties. The results imply that the NSFD scheme can efficiently preserve the global dynamics properties of the corresponding continuous model. Some numerical simulations are carried out to validate the theoretical results.
Highlights
The classical within-host virus dynamics model is a system that includes three variables: uninfected cells T(t), infected cells I(t), and free virus particles V (t) at time t.to take some features into consideration of a real system, such as delay between the moment of infection and the moment when the infected cell begins to produce the virus, additional classes of cells may be added to the system
Where T(t), W (t), I(t), and V (t) denote concentrations of uninfected cells, exposed cells, productively infected cells, and free virus particles at time t, respectively, λ is the recruitment rate of the uninfected cells, β1 is the virus-to-cell infection rate. d, δ, p, and c are the mortality rate of uninfected cells, exposed cells, infected cells, and free virus particles, Xu et al Advances in Difference Equations (2018) 2018:108 respectively, and 1/γ is the average time of the latent state
It is necessary to study the effect of spatial structure on virus dynamics, and much attention has been attracted by many researchers
Summary
The classical within-host virus dynamics model is a system that includes three variables: uninfected cells T(t), infected cells I(t), and free virus particles V (t) at time t (see [1, 2]). Theorem 2.3 If R0 ≤ 1, the infection-free steady state E0 is globally asymptotically stable. Theorem 2.4 If R0 > 1, the infection steady state E∗ is globally asymptotically stable. The global asymptotic stability of the infection steady state E∗ follows from LaSalle’s invariance principle. Theorem 3.2 Given t > 0 and x > 0, if R0 ≤ 1, the infection-free equilibrium E0 of system (8) is globally asymptotically stable.
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