| Abstract | Regulatory T cells have been identified as playing a key role in preventing autoimmune disease. We present an ordinary differential equation (ODE) model of their action within a system also including self antigen, professional antigen presenting cells, and autoreactive effector T cells. Deterministically, qualitative long-term behaviour is predicted by the basic reproductive ratio (R0): when R0<1, solutions converge to the trivial equilibrium (interpreted as self tolerance), while when R0>1, solutions converge to a non-trivial equilibrium (interpreted as chronic autoimmunity); bistability does not occur. However, a stochastic treatment of the model demonstrates, through Monte Carlo simulation and a branching process approximation, that either long-term tolerance or chronic autoimmunity may arise from the same initial conditions, and that the probability of mounting a chronic repsonse depends on the initial "dose" of self antigen or autoreactive effector T cells. This result parallels observations of dose dependence reported in the biological literature, suggesting that stochastic effects may provide a straightforward explanation for experimental results, in lieu of a more complex ODE model exhibiting deterministic bistability. |
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