SIR Model — Susceptible

This equation says the susceptible group shrinks at a rate proportional to how many people are susceptible and how many infected people are currently present. The minus sign appears because contacts between susceptible and infected individuals move people out of the susceptible compartment into the infected compartment, so the susceptible fraction must decrease. The transmission rate β bundles together how often people make effective contacts and how likely those contacts are to cause infection.

Use this when modeling the early or mid-stage spread of an infectious disease in a well-mixed population with no births, deaths, or immunity changes beyond the SIR transitions. It is especially useful in deterministic epidemic models for estimating how quickly susceptibility is depleted under different transmission assumptions.

• Forgetting the negative sign and interpreting dS/dt as an increase
• Using population counts instead of fractions without adjusting the model form
• Treating β as a pure probability rather than a rate parameter that reflects contact frequency and transmission likelihood