SEIR Epidemic Model with Vaccination & Herd Immunity (2D)

This 2D companion runs a genuine four-compartment SEIR model — susceptible, exposed, infectious, recovered — instead of the simpler SIR curve, so it captures the incubation delay that real diseases like measles or COVID-19 have before a newly infected person becomes contagious. A continuous vaccination-rate control moves susceptibles straight into the immune pool from day zero, and the live readout computes the actual herd-immunity threshold (1 − 1/R0) and effective reproduction number Rt = R0·S(t) from the current state, so you can watch vaccination coverage push Rt below 1 and flatten or fully prevent the outbreak rather than just react to a canned animation.