MODELING AND SIMULATION OF INDIVIDUALS BEHAVIOUR ON BIOLOGICAL NETWORKS

Here we present some studies on the behavior of individuals in a biological networks. The first study is about Physarum polycephalum slime mold and its
ability to find the shortest path in a maze. Here we present a PDE chemotaxis model that reproduce its behavior in a network, schematized as a planar graph,
(1). In particular, suitable transmission and boundary conditions at each node of the graph are considered to mimic the choice of such an organism to move from
an arc to another arc of the network, motivated by the search for food. Several numerical tests are presented for special network geometries to show the qualitative
agreement between our model and the laboratory observed behavior of the mold. The second study is about tumor associated macrophages and the mathematical
modeling of the behavior of cell populations in a microfluidic chip, an environment constructed in laboratory to mimic complex biological systems. In particular,
the developed model consists of reaction-diffusion-transport equations with chemotaxis: birth/death processes, interaction with chemoattractant, interaction
and competition between species. Suitable transmission conditions are included in the algorithm and numerical tests are presented.