AbstractsMathematics

Type 1 diabetes is a disease with serious personal and socioeconomic consequences that has attracted the attention of modellers recently. But as models of this disease tend to be complicated, there has been only limited mathematical analysis to date. Here we address this problem by providing a bifurcation analysis of a previously published mathematical model for the early stages of type 1 diabetes in diabetes-prone NOD mice, which is based on the data available in the literature. We also show positivity and the existence of a family of attracting trapping regions in the positive 5D cone, converging towards a smaller trapping region, which is the intersection over the family. All these trapping regions are compact sets, and thus, practical weak persistence is guaranteed. We conclude our analysis by proposing 4 novel treatment strategies: increasing the phagocytic ability of resting macrophages or activated macrophages, increasing the phagocytic ability of resting and activated macrophages simultaneously and lastly, adding additional macrophages to the site of inflammation. The latter seems counter-intuitive at first glance, but nevertheless it appears to be the most promising, as evidenced by recent results.; Type 1 diabetes is a disease with serious personal and socioeconomic consequences that has attracted the attention of modellers recently. But as models of this disease tend to be complicated, there has been only limited mathematical analysis to date. Here we address this problem by providing a bifurcation analysis of a previously published mathematical model for the early stages of type 1 diabetes in diabetes-prone NOD mice, which is based on the data available in the literature. We also show positivity and the existence of a family of attracting trapping regions in the positive 5D cone, converging towards a smaller trapping region, which is the intersection over the family. All these trapping regions are compact sets, and thus, practical weak persistence is guaranteed. We conclude our analysis by proposing 4 novel treatment strategies: increasing the phagocytic ability of resting macrophages or activated macrophages, increasing the phagocytic ability of resting and activated macrophages simultaneously and lastly, adding additional macrophages to the site of inflammation. The latter seems counter-intuitive at first glance, but nevertheless it appears to be the most promising, as evidenced by recent results.