Spatial epidemic project
Spatial models allow epidemic variables to depend on location as well as time. A simple reaction–diffusion susceptible-infectious system is
\[\frac{\partial S}{\partial t}=-\beta SI+D_S\nabla^2S,\qquad \frac{\partial I}{\partial t}=\beta SI-\gamma I+D_I\nabla^2I.\]The reaction terms describe local infection and recovery; diffusion terms represent spatial movement.
Experiment
Start infection in a localised region and solve the equations numerically on a spatial domain with specified boundary conditions. Visualise \(I(x,t)\) at successive times.
Compare movement
Change \(D_I\) and examine how the spatial speed and shape of epidemic spread change.
Project outcome. Connect local epidemic dynamics with movement to produce a spatially propagating infection pattern.