Table 1 Parameters.

r _T

source rate of Only-Top MSM

96667

estimate

r _V

source rate of Versatile MSM

603950

estimate

r _B

source rate of Only-Bottom MSM

70817

estimate

d _M

death rate of susceptible MSM

0.022

estimate

d _I

death rate of infected MSM

0.105

estimate

n _T

number of AI sex partners per year of Only-Top MSM

11.5

[16]

n _V

number of AI sex partners per year of Versatile MSM

12.4

[16]

n _B

number of AI sex partner per year of Only-Bottom MSM

13.6

[16]

c _T

number of AI acts with each sex partners per year of Only-Top MSM

4.4

[16]

c _V

number of AI acts with each sex partners per year of Versatile MSM

4.5

[16]

c _B

number of AI acts with each sex partners per year of Only-Bottom MSM

4.2

[16]

h _TB

transmissibility of HIV from Top to Bottom

0.01

[9, 20]

h _VB

transmissibility of HIV from Versatile to Bottom

0.01

[9, 20]

h _TV

transmissibility of HIV from Top to Versatile

0.01

[9, 20]

h _BT

transmissibility of HIV from Bottom to Top

0.005

[9, 20]

h _VT

transmissibility of HIV from Versatile to Top

0.005

[9, 20]

h _BV

transmissibility of HIV from Bottom to Versatile

0.005

[9, 20]

h _VV

transmissibility of HIV from Versatile to Versatile

0.0075

estimate

α _y

proportion of infected MSM who know they are infected

0.15

[16]

η ^c

condom efficacy

0.9

[16]

ρ ^c

rate of condom use

0.3

[16]

ψ ^s

proportion with STI

0.158

[16]

μ ^s

multiplication factor of STI for HIV

2.89

[21]

ν _y

proportion of infected MSM who begin to control their behaviour

0.5

[16]