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

Table of contents
- i d
  - Solution i
- ii d
  - Solution ii
- iii d
  - Solution iii

i

Solution

The SIR model is

S λ (t) I γ R .

The expected infectious duration is

d = 1/ γ

.

ii

Solution

The SEIR model inserts a latent exposed state:

S λ (t) E σ I γ R .

The expected time from infection through the end of infectiousness is

d = 1/ σ + 1/ γ

; the duration during which transmission occurs is

1/ γ

.

iii

Solution

The SIRS model has waning immunity:

S λ (t) I γ R ω S .

An infection lasts

d = 1/ γ

, while immunity lasts

1/ ω

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