Table 2.

Transition rates for the k-group, s-stage SIS model

Event	State transition	Transition rate
Infection in group j	$I_{j1}\to I_{j1}+1$	$\frac{\beta }{N}\left({\sum }_{m=1}^k{\lambda }_m{\sum }_{v=1}^s{I}_{\mathit{mv}}\right){\mu }_j\left(N_j-{\sum }_{v=1}^s{I}_{\mathit{jv}}\right)$
Transition to next infectious stage	$\left(I_{j,v-1},I_{\mathit{jv}}\right)\to (I_{j,v-1}-1,I_{\mathit{jv}}+1)$	$s\gamma I_{j,v-1}$ for $v=2,3,\dots ,s$
Recovery in group j	$I_{\mathit{js}}\to I_{\mathit{js}}-1$	$s\gamma I_{\mathit{js}}$