Mathematical modeling of type 1 diabetes in the NOD mouse: separating incidence and age of onset

Type 1 diabetes (T1D) is an autoimmune disease of the β-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 β-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.