This project aims to characterize the speed of spreading driven by dispersal events with broadly distributed jump distances that undergo length-dependent constraints. We employ lattice-based simulations and scaling arguments to investigate the impact on the range of the dispersal kernel. While numerous models have been developed to describe spreading phenomena ranging from plant dispersal to viruses in computer networks, these models rarely incorporate the constraint of distance traveled. However, in various scenarios such as epidemics and plant dispersal, the distance traveled plays a crucial role. In this project, we present two stochastic models for spreading: one occurring on a fixed network and another exhibiting more homogeneous behavior in space and time. By employing different functions to represent the importance of distances traveled or the length of the links, we demonstrate how diverse patterns can emerge. Additionally, assuming a controlled approach to implementing the cost, we provide theoretical results supported by simulations, whether the objective is to accelerate or decelerate the spreading process.
- Hallatschek Lab