  The nervous system is today recognized to play an important role in the
development of cancer. Indeed, neurons extend long processes (axons) that grow
and infiltrate tumors in order to regulate the progression of the disease in a
positive or negative way, depending on the type of neuron considered.
Mathematical modelling of this biological process allows to formalize the
nerve-tumor interactions and to test hypotheses in silico to better understand
this phenomenon. In this work, we introduce a system of differential equations
modelling the progression of pancreatic ductal adenocarcinoma (PDAC) coupled
with associated changes in axonal innervation. The study of the asymptotic
behavior of the model confirms the experimental observations that PDAC
development is correlated with the type and densities of axons in the tissue.
In addition, we study the identifiability of the model parameters. This informs
on the adequacy between the parameters of the model and the experimental data.
It leads to significant insights such that the transdifferentiation phenomenon
accelerates during the development process of PDAC cells. Finally, we give an
example of a simulation of the effects of partial or complete denervation that
sheds lights on complex correlation between the cell populations and axons with
opposite functions.
