Sustained and transient oscillations and chaos induced by delayed antiviral immune response in an immunosuppressive infection model

Abstract

Sustained and transient oscillations are frequently observed in clinical data for immune responses in viral infections such as human immunodeficiency virus, hepatitis B virus, and hepatitis C virus. To account for these oscillations, we incorporate the time lag needed for the expansion of immune cells into an immunosuppressive infection model. It is shown that the delayed antiviral immune response can induce sustained periodic oscillations, transient oscillations and even sustained aperiodic oscillations (chaos). Both local and global Hopf bifurcation theorems are applied to show the existence of periodic solutions, which are illustrated by bifurcation diagrams and numerical simulations. Two types of bistability are shown to be possible: (i) a stable equilibrium can coexist with another stable equilibrium, and (ii) a stable equilibrium can coexist with a stable periodic solution.

$\mathcal{P}\mathcal{T}$ -symmetric model of immune response

“…It is also worth mentioning that in Ref. [26] a twodimensional dynamical system describing the immune response to a virus is considered; this FIG. 16: An organism that survives an antigen attack.…”

Nonlinear Models for the Delayed Immune Response to a Viral Infection

“…Ref. [20] analyzed oscillations and chaotic behavior triggered by delayed immune response and [21] the dynamics of a model with delayed CTL response and immune circadian rhythm was considered. Delayed responses are essential for a good description of the immune system as the stimulation generating CTLs need a delay τ , such that the response in time t is a function of the concentration of antigens in time t − τ .…”

Dynamics of a delayed predator‐prey model with Allee effect and Holling type II functional response

“…Moreover, predator-prey models modeled by delay differential equations exhibit much more complicated dynamics than ordinary differential equations. 39,[41][42][43][44][45][46][47][48] For example, delays can cause the loss of stability and can induce various oscillations and periodic solutions (see Ruan, 39 Shu et al, 46 Wolkowicz and Xia, 48 Liao et al, 49 Shu et al, 50 Tian, 51 Xiao and Ruan, 52 and Yamaguchi et al 53 and the references therein). The models mentioned above only assume that the predation population can instantaneously convert the consumption into its growth.…”