arXiv:2610.35206v1 Announce Type: cross Abstract: This paper presents a macroscopic approach for modeling pedestrian movement. A convection-diffusion partial differential equation (PDE) is described and used to model the flow of runners along a marathon course. A marathon is a good modeling case study for human movement because the location of runners is only known in sparse locations, so an accurate model is needed to know where people are at all times. As well, marathons offer many safety and logistical problems that can be solved by modeling human movement. Data is obtained from the 2023 Columbus Marathon, and model improvements are made to include a temporally varying convection term. Results show an increase in model accuracy which can allow for better resource allocation and safety measures.