Variables and parameters for model.

NOTE. MSM, men who sex with men; UAIC, unprotected anal intercourse.
Value of variables (X, Y1, Y2, Y3, Y4) meant to be initial value for mathematical model. Value of parameters (from nx to fp) meant to be current value for model.
a, s, v3, and v4 are calculated by following equation: If there z% in t years, then the yearly rate r was computed by .
v1, v2, h1, h2, h3, and h4 are calculated by following equation: If it takes t years on average to move to the next compartment, then the yearly rate r was computed by .
K,K1,K2,K3,K4 are calculated by transmission equations supplemented by Fig. S1.
Dimensionless: it has no unit, such as a ratio or a percentage.