  Type 1 diabetes (T1D) is an autoimmune disease of the beta cells of the
pancreas. The nonobese diabetic (NOD) mouse is a commonly used animal model,
with roughly an 80% incidence rate of T1D among females. In 100% of NOD mice,
macrophages and T-cells invade the islets in a process called insulitis. It can
be several weeks between insulitis and T1D, and some mice do not progress at
all. It is thought that this delay is mediated by regulatory T-cells (Tregs)
and that a gradual loss of effectiveness in this population leads to T1D.
However, this does not explain why some mice progress and others do not. We
propose a simple mathematical model of the interaction between beta cells and
the immune populations, including regulatory T-cells. We find that individual
mice may enter one of two stable steady states: a `mild' insulitis state that
does not progress to T1D and a `severe' insulitis state that does. We then run
a sensitivity analysis to identify which parameters affect incidence of T1D
versus those that affect age of onset. We also test the model by simulating
several experimental manipulations found in the literature that modify
insulitis severity and/or Treg activity. Notably, we are able to match a
reproduce a large number of phenomena using a relatively small number of
equations. We finish by proposing experiments that could help validate or
refine the model.
