Epidemic Modeling
Dynamics of Infectious Deseases with the SIR model
The SIR (Susceptible, Infected, Recovered) models are a class of differential equations for modeling the spread of infectious diseases. In the model, the population is divided into groups which may transition to other groups. Susceptible becomes infected at a certain rate, infected becomes recovered (and immune) at a certain rate, and this relation is written (S->I->R). Variations and modifications of this simple model help inform the spread of various recurrent epidemic illnesses such as measles and influenza, and now much more recently, Covid 19. Dimensional analysis on infection rates can establish how virulant the diseases is, and whether `Epidemic' will (may) occur. Presented above is the phase diagram and some example trajectories of the S->I->R->S model, where the recovered population loses its immunity to the illness at a certain rate. Here one observes, absent any external input, that the infected population settles down to a constant nonzero value, and the illness is not eradicated.