Consider a disease infecting a population with \( N \) individuals, where \( S(t) \) is the number of individuals that are healthy (susceptible to the disease) at time \( t \), \( I(t) \) is the number of individuals that have been already infected at time \( t \), \( \langle k \rangle \) is the number of contacts that an individual usually has, and \( \beta \) is the rate of transmission.
Under the homogeneous mixing hypothesis, what is the probability that an infected person encounters a healthy individual?
- \( S(t)I(t) \)
- \( S(t)/N \)
- \( I(t)/N \)
- \( \beta \langle k \rangle S(t) I(t) / N \)
- None of the above
Original idea by: Leandro Stival
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