nr. 477 - 2011 - Institut for Natur, Systemer og Modeller (NSM)

12.1 Future Work 121
Adding treatment to Model C
Our initial goal was to modify the DuCa model as presented in chapter 11 and then
proceed to analyze, mathematically, what would be the opportune way of reversing
or arresting the deleterious process in NOD-mice. Based on the analysis we would
determine if any of the treatment strategies presented in chapter 3 would fit the role
laid out by the analysis. And if they could readily be implemented into the model.
E.g. an easy way to implement a drug that reduces the rate of apoptosis (such as GLP-
1) would be to modify the apoptosis term. But if we for a moment think in terms of
humans, then the deleterious process does not become known until quite a large number
of the β-cells are gone. So the term should be modified in such a way as not to take effect
right from birth. Rather the term should take effect at a time that coincides with the
time when the B-concentration is small enough such that symptoms become evident.
A function that comes to mind is hyperbolic tangent – assuming that infusion of the
drug becomes more or less steady after its first application. We could also conceive
of wanting to add a drug such as that initiates β-cell regeneration, replication and/or
differentiation. Again GLP-1 is a prime candidate as we learned in chapter 3. Here we
could add an additional replication term is zero at t = 0 and then grows to whatever
value we can justify based on data.
Regardless of the possible effects of such a drug, accessibility of supporting data is
imperative. In years to come, we hope to see that relevant medical data in this field
will become more readily available to all researchers interested in finding solutions to
major health issues.