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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.

The basic SIR model is written as a system of ordinary differential equations describing transfers between compartments: susceptibles decrease by infection, infecteds gain infections and lose cases by recovery or removal, and recovereds increase by removal from the infected class. The equations are $\frac{dS}{dt}=-\beta SI$, $\frac{dI}{dt}=\beta SI-\gamma I$, and $\frac{dR}{dt}=\gamma I$.

Conditions: The population is modeled as well mixed.; The dynamics are represented by global rate equations rather than spatially resolved equations.

The basic SIR model is written as a system of ordinary differential equations describing transfers between compartments: susceptibles decrease by infection, infecteds gain infections and lose cases by recovery or removal, and recovereds increase by removal from the infected class. The equations are $\frac{dS}{dt}=-\beta SI$, $\frac{dI}{dt}=\beta SI-\gamma I$, and $\frac{dR}{dt}=\gamma I$.

Conditions: The population is modeled as well mixed.; The dynamics are represented by global rate equations rather than spatially resolved equations.

In the displayed SIR equations, $\beta$ represents the transmission rate per pair of people, one infected and one susceptible, which governs the flow of new infections. $\gamma$ represents the removal or recovery rate, which governs the flow of infected individuals leaving the infected compartment to join the recovered or removed compartment.

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.

In the displayed SIR equations, $\beta$ represents the transmission rate per pair of people, one infected and one susceptible, which governs the flow of new infections. $\gamma$ represents the removal or recovery rate, which governs the flow of infected individuals leaving the infected compartment to join the recovered or removed compartment.

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.