= Farm-size stratified SIR model
{title2=$\dot S_n=-\beta s(n)S_n\sum_m i(m)I_m$}
Here $s(n)$ and $i(n)$ weight susceptibility and infectiousness of a farm with $n$ animals, with size distribution $P_n$ and recovery rate $\gamma$. The rank-one next-generation matrix has reproduction number $\mathcal R_0=(\beta/\gamma)\sum_n s(n)i(n)P_n$. Susceptibility proportional to size preferentially depletes large susceptible farms. Infectivity heterogeneity alone leaves an exactly homogeneous aggregate SIR trajectory for representative initial infections. When both weights equal size, the second rather than first size moment governs invasion.
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