In the discrete one-infected example, what are the initial values of S, I, and R?

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.

Reasoning, step by step

1. Identify the total population size as N.
2. Set the number of infected individuals to exactly one: $I=1$.
3. Deduce that the remaining individuals are susceptible: $S=N-1$.
4. Note that at the very beginning, no individuals have entered the recovered or removed compartment: $R=0$.

Example

The lecturer says, 'maybe the very beginning is if we really have a discrete population is that S is N minus one. So if we really don't have a huge population, I can actually count them. I might say S is N minus one. There's one infected person, everyone else is susceptible.' The board shows $S=N-1$, $I=1$, and $R=0$.

Common misconceptions

• Assuming R starts at a non-zero value.
• Thinking S equals N when there is an infected person.

Watch the explanation

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