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The lecture states $S+I+R=N$ to express the conservation of total population in the displayed SIR model. It means that individuals move among the susceptible, infected, and recovered compartments, but the total counted population remains fixed at $N$, assuming no births, deaths unrelated to removal, immigration, or emigration are included in the accounting.

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

The lecture states $S+I+R=N$ to express the conservation of total population in the displayed SIR model. It means that individuals move among the susceptible, infected, and recovered compartments, but the total counted population remains fixed at $N$, assuming no births, deaths unrelated to removal, immigration, or emigration are included in the accounting.

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