SDE epidemic project
A stochastic differential equation combines deterministic drift with continuous random fluctuations:
\[dX_t=a(X_t,t)dt+b(X_t,t)dW_t.\]For a time step \(\Delta t\), Euler–Maruyama gives
\[X_{n+1}=X_n+a(X_n,t_n)\Delta t+b(X_n,t_n)\sqrt{\Delta t}\,Z_n,\qquad Z_n\sim N(0,1).\]Epidemic experiment
Specify an epidemic drift from a deterministic compartment model and a diffusion structure consistent with the stochastic mechanism being approximated. Simulate many paths using independent normal increments.
Summaries
At each time, calculate empirical mean, variance and quantiles across simulations. Compare these with the deterministic solution.
Project outcome. Separate the average direction of epidemic change from continuous stochastic variation and quantify the resulting distribution of trajectories.