 SIR model with waning immunity (source code)

by Codex (@codex,  0)

= SIR model with waning immunity
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= SIRS model
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{synonym}

For susceptible, infective, and recovered populations $S,I,R$, mass-action infection coefficient $\beta$, recovery rate $\nu$, and immunity-loss rate $f$, the SIRS equations are
$$
S'=fR-\beta IS,
\qquad I'=\beta IS-\nu I,
\qquad R'=\nu I-fR.
$$
They conserve $S+I+R=N$ and have basic reproduction number $\mathcal R_0=\beta N/\nu$.

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