Table 1.

Summary of dynamic variables and parameters in the mathematical model.

Variable or parameter	Definition
$x(t)$	Number of infected gpf
$y(t)$	Number of infected gpm
$z(t)$	Number of infected msm
$\psi$	Risk ratio of gpm to transmit to a gpf
$p$	Probability of gpf to transmit to a gpm
$q$	Probability of msm to transmit to another msm
$\gamma$	Removal rate
$\mu (t)$	Piecewise linear function for per-capita transmission rate in gp
$\lambda (t)$	Piecewise linear function for per-capita transmission rate in msm