Modeling Damage in Self-Regulated Transportation Networks with Tree-like Structure

Self-regulated transportation networks belong to the class of continuous network models and are widely used not only in biological applications such as vascular systems, neural networks or tissue regeneration, but also in urban infrastructure and in communication technologies. Their well-established tree structure prevents the formation of loops, which limits their ability to capture an important feature observed in real systems: when a disruption or damage occurs, the network should be able to reorganize to restore transport pathways. In this work, we propose alternative modeling strategies to incorporate this capability. These approaches allow for the network to adapt to perturbations by modifying its structure and, in some cases, by creating alternative routes that compensate for damaged regions. Numerical results illustrate how the modified models can reproduce self-repair mechanisms that are not captured by standard formulations.