Finalist Award — Top ~7% globally at the 2023 High School Mathematical Contest in Modeling.
The Model
We constructed a Dandelion Spread PDE Model (DSM) — a system of four coupled partial differential equations that model population densities of:
- Settled dandelion seeds
- Dandelion plants
- Puffballs
- Drifting seeds
We corrected the Fisher model by multiplying a logistic term to obtain a logistic population growth that depicts the effect of intraspecific competition on the dandelion population.
For the PDE of drifting seeds, we used the advection-diffusion equation by adding Brownian Random Dispersal. This allows us to effectively predict the spread of dandelions in various kinds of winds.
Computation & Analysis
We used FEniCS to obtain the final predictions of the DSM model, followed by a sensitivity analysis. Finally, we used the Analytic Hierarchy Process to measure the dandelions’ invasiveness, with total biomass calculated using the DSM model.