What do the parameters beta and gamma represent in the displayed SIR equations?

Conditions

• $\beta$ is the transmission rate per pair.
• $\gamma$ is the removal/recovery rate.
• The displayed model treats the population as divided into S, I, and R compartments.

Reasoning, step by step

1. Identify $\beta$ as the transmission rate (per pair) multiplying the interaction term $SI$.
2. Identify $\gamma$ as the removal/recovery rate multiplying the infected population $I$.
3. Note that the total infection flow is $\beta SI$, decreasing S and increasing I.
4. Note that the total removal flow is $\gamma I$, decreasing I and increasing R.

Example

The board writes '$\beta$ = transmission rate (per pair)' and '$\gamma$ = removal/recovery rate' next to the differential equations. The lecturer explains that infection is passed between a pair of people at rate $\beta$, and individuals are removed at rate $\gamma I$.

Common misconceptions

• Assuming $\beta$ is the total infection rate rather than the per-pair rate.
• Thinking $\gamma$ only represents medical recovery and excludes death or other removals.

Watch the explanation

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