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Table 1 The values or distributions of parameters (partly) for modeling the HIV epidemic.

From: Increasing risk behaviour can outweigh the benefits of antiretroviral drug treatment on the HIV incidence among men-having-sex-with-men in Amsterdam

Parameter

Value

Description

Source

Duration of steady relationships

(1,2)1

The duration of steady partnerships among Amsterdam MSM is reported to have an expected value of 1.5 years.

[20]

Duration of the asymptomatic stage for the untreated

ℬ (26,0.5)2

This stage lasts 13 years for people with a failed treatment or without any therapy.

[24, 25]

Duration of the asymptomatic stage for the successfully treated

ℬ (52,0.5)

This stage lasts a mean value of 22.5 years for people with a successful treatment. And the duration is likely increased to a mean value of 26 years, thanks to the wide use of HAART and the improvement in the therapy regimens.

[26–28]

Frequency of sexual actions per year between steady partners (with infected at stage AP)

(30)3

The frequency of either URAI or UIAI between steady partners is 15 per year.

[20]

Frequency of sexual actions between steady partners in the first 3 months and the last 9 months, respectively (with infected at stage PI)

(8) &(22)

The PI stage lasts for about 3 months which is shorter than the 1-year time step, so that we divide individuals' first year of infection into two periods. Thus, the frequencies in these two periods adds up to 30.

[20]

Transmission probability per URAI/UIAI4 act (with infected at stage PI)

0.22/0.044

 

[29–31]

Transmission probability per URAI/UIAI act (with infected at stage AP)

0.011/0.0022

The infected in the last 9 months of PI contribute the same to transmission possibility per act as they do at stage AP.

[29–31]

Reduction in risky behavior along casual partnerships for men who have a steady partner

0.84

Men may make an agreement with his steady partner to be monogamous or to have no UAI outside the relationship, leading to less risky behavior.

see Sec. 2 in [20]

Moderate (default) treatment-induced infectivity reduction factor5

(0.1,0.5)6

ART can moderately reduce transmission probability by 50-90%.

[32]

Optimistic treatment-induced infectivity reduction factor

(0.01,0.1)

ART can optimistically reduce transmission probability by 90-100%.

[32]

Initial population size

2299

People involved in all substudies add up to 2299.

[22]

The power-law degree distribution's exponent γ in this study

1.6

MSM population follows a power-law degree distribution with a value of γ in the interval between 1.5 and 2.

[17]

The power-law degree distribution's maximum degree kmax

200

We assume so.

 

The fraction of vertices with a degree of 0

0.01

We assume that a small portion in a population not having any contact.

 
  1. 1 (val1, val2) is a discrete uniform distribution with val1 and val2 as the lower and upper bounds.
  2. 2 ℬ (n, p) is a binomial distribution.
  3. 3 (λ) is a Poisson distribution.
  4. 4 URAI, unprotected receptive anal intercourse; UIAI, unprotected insertive anal intercourse.
  5. 5 Those who are receiving treatment can obtain an reduction in infectivity and thus decrease transmission probability per act. For example, 0.3 means a reduction of 70% and 0.055 a reduction of 94.5%. The untreated's infectivity remains on baseline quantities given in [29–31].
  6. 6 (val1, val2) is a continuous uniform distribution with val1 and val2 as the lower and upper bounds.