Modeling and analysis of recurrent autoimmune disease Many autoimmune diseases are characterized by a pattern of recurrence and remis sion, in which periods of apparent selftolerance are punctuated by intervals of recurring autoimmu nity. We introduce a newly discovered class of terminally differentiated regulatory T cells, HLADR  TReg cells, into an existing autoimmune disease model. Our newly developed 4dimensional model exhibits recurrent dynamics, which are preserved in a reduced and rescaled 3dimensional model as well. Applying dynamical systems theory, we analyze the dynamics underlying this behavior in both the 4dimensional and 3dimensional models and further prove that the recurrent behavior (or oscillation) arises due to a Hopf bifurcation or a persistent oscillation rather than from homoclinic orbits. Numerical simulations are conducted to verify the analytical results and identify the recurrent parameter region.

Exploiting Stochastic Petri Net formalism to capture the Relapsing Remitting Multiple Sclerosis variability under Daclizumab administration It is well known that the response of individuals to disease varies, either because of unpredictable exogenous events, such as possibly unknown environmental effects, or just because of endogenous factors, i.e. different genetic background. In particular, when a treatment effectiveness has to be validated, the individual variability should be taken into account by exploiting stochastic models. Relapsing Remitting Multiple Sclerosis (RRMS) is an unpredictable and complex disease, whose random behaviour perfectly fits the study with stochastic models. RRMS is the most common form of Multiple Sclerosis (MS), an immunemediated inflammatory disease of the central nervous system, characterized by alternate episodes of symptom exacerbation (relapses) with periods of disease stability (remission). Several treatments were proposed to contrast the disease progression. Among these, Daclizumab initially exhibited promising results. However, due to the risk of serious side effects the treatment has been retired. We propose a stochastic and an hybrid extension, based on a generalization of the high level Petri Net formalism, of an existing model of Daclizumab effects on RRMS. The model is developed to investigate the complex mechanisms and unpredictable behaviour characterizing the RRMS disease and its relapsing, especially under the Daclizumab administration.