In the discrete one-infected example, the initial values are S=N−1, I=1, and R=0. This corresponds to a small population where exactly one person is infected, everyone else is susceptible, and nobody has yet recovered or been removed.
Conditions: Total population scale is N.; There is one infected person.; Everyone else is susceptible at the beginning.; No one has yet recovered or been removed in this initial example.
In the discrete one-infected example, the initial values are S=N−1, I=1, and R=0. This corresponds to a small population where exactly one person is infected, everyone else is susceptible, and nobody has yet recovered or been removed.
Conditions: Total population scale is N.; There is one infected person.; Everyone else is susceptible at the beginning.; No one has yet recovered or been removed in this initial example.
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 lecture decides that an epidemic occurs if the time derivative of the infected compartment is positive, i.e., dtdI>0. This means the number of infected people is growing in the early stages of the outbreak, when the susceptible population is close to the total population and the infected population is small.
Conditions: The model is the displayed SIR system.; The relevant comparison is made in the early stages of the outbreak, where S is close to N and I is small compared with N.
The lecture decides that an epidemic occurs if the time derivative of the infected compartment is positive, i.e., dtdI>0. This means the number of infected people is growing in the early stages of the outbreak, when the susceptible population is close to the total population and the infected population is small.
Conditions: The model is the displayed SIR system.; The relevant comparison is made in the early stages of the outbreak, where S is close to N and I is small compared with N.