Effects of Viral and Cytokine Delays on Dynamics of Autoimmunity

Abstract

Abstract:A major contribution to the onset and development of autoimmune disease is known to come from infections. An important practical problem is identifying the precise mechanism by which the breakdown of immune tolerance as a result of immune response to infection leads to autoimmunity. In this paper, we develop a mathematical model of immune response to a viral infection, which includes T cells with different activation thresholds, regulatory T cells (Tregs), and a cytokine mediating immune dynamics. Particular emphasis is made on the role of time delays associated with the processes of infection and mounting the immune response. Stability analysis of various steady states of the model allows us to identify parameter regions associated with different types of immune behaviour, such as, normal clearance of infection, chronic infection, and autoimmune dynamics. Numerical simulations are used to illustrate different dynamical regimes, and to identify basins of attraction of different dynamical states. An important result of the analysis is that not only the parameters of the system, but also the initial level of infection and the initial state of the immune system determine the progress and outcome of the dynamics.

Quantifying the Role of Stochasticity in the Development of Autoimmune Disease

“…However, earlier work of Iwami et al [10,11] has shown that, while this behaviour can be observed for both types of growth functions in the absence of infection or immune reaction, their specific functional form does have a significant effect on the overall dynamics of autoimmune disease. Thus, we have chosen to use a logistic form for the growth function of healthy organ cells, in agreement with Iwami et al [10] and our earlier work on autoimmunity [34][35][36][37][38][39][40].…”

“…Blyuss and Nicholson [34,35] used a TAT-based model to investigate autoimmunity arising through a mechanism of molecular mimicry from immune response to a viral infection. To capture a dynamical regime where autoimmunity arises as a by-product of viral infection but after that initial infection has already been cleared by the immune system, Fatehi et al [36][37][38][39][40] developed this model further by including cytokines mediating T cell proliferation, as well as time delays associated with various aspects of the immune response.…”

Stochastic dynamics in a time-delayed model for autoimmunity

“…While regulatory T cells may block the expression of IL-2 by T cells by suppressing IL-2 mRNA, thus restricting T cell proliferation [82,83,84], similarly to other studies that analysed the role of IL-2 in T cell dynamics [85,86,87], we do not explicitly include this mechanism in our model not to increase its complexity. This effect can, however, be included as an additional term (−γT reg I) in the equation for IL-2 [24,25], though our earlier analysis of an analogous model has shown that this effect may be smaller compared to other contributions, such as the suppressive effect of regulatory T cells on autoreactive T cells [47].…”

“…This has also provided practically important insights into how variance of stochastic oscillations depends on different parameters, which is very important for comparison with clinical observations of individual realisations of progression of autoimmune disease. A complementary analysis has been performed by Fatehi et al [47,48] to investigate the role played by time delays associated with different aspects of immune response and virus cycle dynamics.…”

Bifurcations and Multistability in a Model of Cytokine-Mediated Autoimmunity

“…Therefore, in this model we assume that T nor and T aut produce IL-2 at rates σ 1 and σ 2 . On the other hand, whilst regulatory T cells do not produce IL-2, similar to other T cells they need this cytokine for their activation and proliferation [94,95]. Thus, we assume that IL-2 promotes proliferation of T reg , T nor and T aut at rates ρ 1 , ρ 2 and ρ 3 , respectively.…”