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The problem in the image asks for a simplified expression to represent the fraction of the total population that remains susceptible to an infection.

### Let's break this down:

- \( I \) people are infected.
- \( R \) people have recovered from infection.
- \( S \) people remain susceptible to infection.
- The total population remains constant.

Initially, the entire population was susceptible. Now, the population consists of:
- Susceptible individuals: \( S \),
- Infected individuals: \( I \),
- Recovered individuals: \( R \).

Thus, the total population \( P \) can be written as:
\[
P = S + I + R
\]

The fraction of the population that is susceptible is the number of susceptible individuals \( S \) divided by the total population \( P \). Hence, the fraction susceptible is:
\[
\text{Fraction susceptible} = \frac{S}{S + I + R}
\]

### Final Answer:
\[
\boxed{\frac{S}{S + I + R}}
\]

Would you like further details on this, or do you have any other questions?

Here are 5 related questions for deeper understanding:
1. How does the fraction susceptible change if the number of infected increases?
2. What happens to the fraction susceptible as the epidemic progresses and more people recover?
3. If the entire population is susceptible at the beginning, how does this expression simplify?
4. How could we model the dynamics of this epidemic over time?
5. How would you calculate the percentage of the population that is infected?

**Tip**: Understanding the relationship between different population groups is key to modeling infectious disease dynamics!

One month into an epidemic, I people are infected, R people have recovered from infection, and S people remain susceptible to infection. Initially, the entire population is susceptible, and no one is infected or has recovered. Assume that once someone is infected or has recovered, he or she cannot be reinfected and that the total number of people remains constant. Write a simplified expression representing the fraction of the total population that are susceptible.

Learn how to derive a simplified expression for the fraction of a population that remains susceptible during an epidemic. This problem involves the key algebraic concept of fractions and applies it to epidemiology. Suitable for high school students.

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