Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 207 / 2 / e

Table of contents
- Solution e

Solution

Under frequency-dependent mass-action kinetics, if

I (t)

of the

N (t)

individuals are infectious, the force of infection is

λ (t) = β \frac{I ( t )}{N ( t )} .

One newly infectious person in an otherwise susceptible population transmits at total rate approximately

β

for mean infectious duration

1/ γ

. Hence the basic reproduction number is

R_{0} = \frac{β}{γ} = β d_{I},

where

d_{I}

is the infectious, rather than latent-plus-infectious, duration.

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