Global stability of a virus dynamics model with Beddington–DeAngelis incidence rate and CTL immune response

Abstract

In this paper, the global stability of virus dynamics model with Beddington-DeAngelis infection rate and CTL immune response is studied by constructing Lyapunov functions. We derive the basic reproduction number R 0 and the immune response reproduction number R 0 for the virus infection model, and establish that the global dynamics are completely determined by the values of R 0 . We obtain the global stabilities of the disease-free equilibrium E 0 , immunefree equilibrium E 1 and endemic equilibrium E * when R 0 ≤ 1, R 0 > 1, R 0 > 1, respectively.

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

“…Since spatial diffusion does not change the number and location of constant equilibria, we can establish the existence of nonnegative equilibria of (1.4), which is consistent with the results in [18]. (i) the model always has the disease-free equilibrium E 0 = (λ/d, 0, 0, 0); (ii) if the basic reproductive number R 0 > 1, then there exists an immune-free equilibrium E 1 = (u 1 , w 1 , v 1 , 0), where…”

“…In truth, the delayed model without diffusion is presented and the existence of Hopf bifurcation is investigated in [24]. Besides, the model in the present paper is more generalized than those in [7,11,18,19].…”

“…And in most virus infections, cytotoxic lymphocyte cells (CTLs) and antibody cells play a critical part in antiviral defense [11]. Therefore, Wang et al [18] proposed the following system with nonlinear incidence rate describing immune response against infected cells:…”

“…For example, Huang et al [7] analyzed the global properties of system (1.2) in the absence of CTL immune response and spatial diffusion. Wang et al [18] studied the global stability of nonnegative equilibria in system (1.3) without considering the spatial diffusion. In [19], Wang et al ignored the immune response and established the existence of traveling waves when α = β = 0.…”

Global Analysis for an HIV Infection Model with CTL Immune Response and Infected Cells in Eclipse Phase

“…In [12], the authors consider the interaction between CTL, viruses and macrophages and study the global stability in a model with a mass action infection term. With a saturated infection term, the same mathematical question was tackled in [13] with a model consisting of four ordinary differential equations with a Beddington-DeAngelis infection term.…”