Predicting pandemic evolution involves complex modeling challenges, typically involving detailed discrete mathematics executed on large volumes of epidemiological data. Making them physics based provides added intuition as well as predictive value. Differential equations have the advantage of offering smooth, well-behaved solutions that try to capture overall predictive trends and averages. In this paper, the canonical susceptible-infected-recovered model is simplified, in the process generating quasi-analytical solutions and fitting functions that agree well with the numerics, as well as infection data across multiple countries. The equations provide an elegant way to visualize the evolution, by mapping onto the dynamics of an overdamped classical particle moving in the susceptible-infected-recovery configuration space, drifting down gradient of a potential whose shape is set by the model and parameters in hand. Potential sources of errors and their growth over time are identified, and the uncertainties are mapped 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 sets the foundation for their eventual extension to a multi-patch model while offering practical error bounds and could thus be useful in making policy decisions going forward.