  Predicting Pandemic evolution involves complex modeling challenges, often
requiring detailed discrete mathematics executed on large volumes of
epidemiological data. Differential equations have the advantage of offering
smooth, well-behaved solutions that try to capture overall predictive trends
and averages. We further simplify one of those equations, the SIR model, by
offering quasi-analytical solutions and fitting functions that agree well with
the numerics, as well as COVID-19 data across a few countries. The equations
provide an elegant way to visualize the evolution, by mapping onto the dynamics
of an overdamped classical particle moving in the SIR configuration space,
drifting down gradient of a potential whose shape is set by the model and
parameters in hand. We discuss potential sources of errors in our analysis and
their growth over time, and map those uncertainties into a diffusive jitter
that tends to push the particle away from its minimum. The combined physical
understanding and analytical expressions offered by such an intuitive
drift-diffusion model could be particularly useful in making policy decisions
going forward.
