Why does the lecture say $S+I+R=N$ in the SIR model?

Conditions

• No births, deaths unrelated to removal, immigration, or emigration are included in the displayed accounting.
• N is treated as the total population size.

Reasoning, step by step

1. Identify the three compartments: $S(t)$, $I(t)$, and $R(t)$.
2. Note that the model tracks disease spread within a fixed population.
3. Observe that the sum of the three compartment sizes is constrained to equal the total population N.
4. Conclude that this expresses the conservation of total population under the displayed model assumptions.

Example

The board writes '$S + I + R = N$' below the system. The lecturer says, 'if there are N people in the population,' and later remarks that they add up to N.

Common misconceptions

• Assuming the model includes demographic processes like births or deaths unrelated to the disease.
• Thinking N changes over time as people move between compartments.

Watch the explanation

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