Type 1 diabetes (T1D) is an autoimmune disease in which immune cells
target and kill the insulin-secreting pancreatic beta cells.
Recent investigation of diabetes-prone (NOD) mice reveals large cyclic
fluctuations in the levels of T cells (cells of the adaptive
immune system) weeks before the onset of the disease. We extend
a previous mathematical model for T-cell dynamics to account for the
gradual killing of beta cells, and show how such cycles can arise
as a natural consquence of feedback between self-antigen and T-cell
populations. The model has interesting nonlinear dynamics
including Hopf and homoclinic bifurcations in biologically reasonable
regimes of parameters. The model fits into a larger program of
investigation of type 1 diabetes, and suggests experimental tests.