Type 1
diabetes (T1D) is an autoimmune disease in which immune cells, notably
T-lymphocytes target and kill the insulin-secreting pancreatic beta cells.
Elevated blood sugar levels and full blown diabetes result once a large
enough fraction of these beta cells have been destroyed. Recent investigation
of T1D in animals (the non-obese diabetic (NOD) mice) has revealed large
cyclic fluctuations in the levels of T cells circulating in the blood weeks
before the onset of diabetes, but the mechanism for these oscillations is
unclear. A mathematical model for the immune response suggests a possible
explanation for the cyclic pattern of behaviour. We show that cycles similar
to those observed experimentally can occur when activation of T cells is an
increasing function of self-antigen level, whereas the production of memory
cells declines with that level. Our model extends previous theoretical work
on T cell dynamics in T1D, and leads to interesting nonlinear dynamics,
including Hopf and homoclininc bifurcations in biologically reasonable
regimes of parameters. This is work I accomplished while on sabbatical at the
University of British Columbia with Professor Leah
Keshet.
