Bifurcation analysis of a multidelayed HIV model in presence of immune response and understanding of in‐host viral dynamics

Abstract

In this paper, we proposed a multidelayed in‐host HIV model to represent the interaction between human immunodeficiency virus and immune response. One delay was considered to incorporate the time required by the virus for various intracellular events to make a host cell productively infective, and the second delay was introduced to take into account the time required for adaptive immune system to respond against infection. We extensively analyzed this multidelayed model analytically and numerically. We show that delay may have both destabilizing and stabilizing effects even when the system contains a single immune response delay. It happens when there exists two sequences of critical values of this delay. If the system starts with stable state in absence of delay, then the smallest value of these critical delays causes instability and the next higher value causes stability. The system may also show stability switching for different values of the virus replication factor. These results demonstrate the possible reasons of intrapatients and interpatients variability of CD4+ T cells and virus counts in HIV‐infected patients.

Global stability of delay‐distributed viral infection model with two modes of viral transmission and B‐cell impairment

“…We mention that there are several forms of the cell‐free and cell‐to‐cell infection rates ω 1 Θ 1 ( U , P ) and ω 2 Θ 2 ( U , I ) which can satisfy (A1) to (A4) such as bilinear incidence ω 1 UP , ω 2 UI , saturated incidence , , Crowley‐Martin incidence , , and Hill‐type incidence ,, where ω 1 , ω 2 , α 1 , α 2 , κ , c 1 , c 2 , c 3 , and c 4 are positive constants.…”

Stability of a discrete-time general delayed viral model with antibody and cell-mediated immune responses

“…where r < β [53,54]. (ii) Incidence rate function Λ(F, H): bilinear incidence κFH [55], saturated incidence κFH 1+uH [56], (iii) Holling-type II incidence κFH 1+wF [57], Beddington-DeAngelis incidence κFH 1+uH+wF [58], Crowley-Martin incidence κFH (1+uH)(1+wF) [59], Hill-type incidence κF H ζ +F [60], where κ, u, w, ζ , and are positive constants. (iii) Function i (ρ): linear i (ρ) = υ i ρ [1] and quadratic i (ρ) = υ i ρ + υ i ρ 2 [15], where υ i and υ i are positive constants.…”

Stability of a general discrete-time HIV dynamics model with three categories of infected CD4 + T-cells and multiple time delays

“…Thus, U n is monotone decreasing sequence. Because U n 0, there is a limit lim [33], and Hill-type incidence κs m p ζ m +s m [1], where κ, η, , ζ, and m are positive constants.…”