Table 1.

State transitions and their rates for patch i in a metapopulation simulation. (S denotes occupied by susceptible hosts, I denotes occupied by infectious hosts and ∅ denotes unoccupied by the host. All patches are characterized by an environmental transmission rate, γ(τ_i), where τ_i is the time since the patch was last occupied by infectious individuals.)

state transition	process	rate
$S\to I$	infection (from contact or reservoir)	δCIi+γ(τi)
$S\to \mathrm{\varnothing }$	extinction (of susceptible)	ESi
$I\to \mathrm{\varnothing }$	extinction (of infectious)	EIi
$\mathrm{\varnothing }\to S$	colonization (by susceptibles)	CSi
$\mathrm{\varnothing }\to I$	colonization (by infectious)	CIi