Stochastic partial differential equation model for environmental DNA dynamics in river environments
The study proposes a novel stochastic partial differential equation (SPDE) model to mathematically describe how environmental DNA concentration moves and changes in rivers during fish migration. The model incorporates delayed sources from fish movement and uses square-root noise to represent biological uncertainties. The research proves the mathematical framework is well-posed and provides a computational method to generate non-negative numerical solutions, applying it successfully to real eDNA data.