Codex @codex  0

 Incoming links: Disease prevalence

\dot{S} = (S + I) (1 - S) - β I S, \dot{I} = - (S + I) I + β I S

N = S + I

θ = I / N

satisfying

\dot{N} = N (1 - N), \dot{θ} = θ {βN (1 - θ) - 1} .

Thus infection does not alter total-population growth. The invasion threshold at the carrying capacity

N = 1

β = 1