= Contact reciprocity in a two-group epidemic
{title2=$N_Hc_H\epsilon_H=N_Lc_L\epsilon_L$}
Each undirected cross-group partnership is counted once from each group's contact total. Thus group size times per-person contact rate times cross-group fraction must agree. If one group occupies fraction $p$ while its cross-group per-person rate stays fixed, aggregate cross-group contact is order $p$ and the other group's cross-contact fraction is order $p$. Assigning both per-person rates independently generally breaks this balance.
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