# Assumptions for modelling secondary transmissions

Page last updated: 2009

The average age at which IDUs in Australia acquire HCV infection is their early to mid 20s53, 67, 68 and it is likely that IDUs who acquire HIV infection would do so a few years thereafter on average. Approximately pMSM=65% of IDUs with HIV are men who have sex with men, pF=7% are females and the remaining pM=28% are heterosexual males54. For IDUs with HCV infection, approximately pMSM=5% of IDUs with HIV are men who have sex with men, pF=32% are females and the remaining pM=63% are heterosexual males54. It is assumed that the average number of long-term sexual partners each IDU has after acquiring infection is creg=3-5. In addition, it is assumed that each heterosexual IDU would have an average of ccas=5-10 casual short-term sexual partners (each with one penetrative act) after acquiring infection and male homosexual IDUs would have an average of ccas=20-30 casual partners after acquiring infection. Most IDUs who share syringes tend to do so with sexual partners or close friends.69, 70 Therefore, some of the potential partners are not susceptible to transmission because they are already infected (and probably the primary source for the case in question); this complexity is not considered here. It is assumed that HIV transmission rates are βHL=0.01 for heterosexual transmission for long-term partnerships, βML=0.1 for male homosexuals for long-term partnerships, and per-act probabilities of HIV transmission during casual partnerships are βFM=0.0005 for female-to-male transmission, βMF=0.001 for male-to-female transmission, and βMM=0.01 for male-to-male transmission during unprotected sex. 71-77 It is assumed that condom usage is p=80%,78 with efficacy of 95%.79-83 HCV transmission per sexual contact is assumed to be βHCV-a=0.1% per act and βHCV-p=2% per long-term partnership.84-86

The average fertility rate in Australia is f=1.93 babies per woman over her lifetime87 and the median age of all mothers of births is approximately 31 years.88 Based on the average age at infection and the relatively similar infection ages for HIV and HCV, it is assumed that 75% of a woman's births occur after she acquires infection.88 The probability of mother-to-child transmission is βHIV-MTCT=2% for HIV (with the use of antiretrovirals and Caesarean section)89-92 and βHCV-MTCT=5% for HCV.93-95

Therefore, the average number of secondary infections through sexual transmission or mother-to-child transmission per HIV infection is:

SHIV = pMSM (cregβML + ccasβMM) + pM (cregβHL + ccasβMF) + pF (cregβHL + ccasβFM + 0.75 fβHIV-MTCT)

(see below for the plain english version of the HIV equation)

and the average number of secondary HCV transmissions expected per HCV infection is:

SHCV = pMSM (cregβHCV-p + ccasβHCV-a) + pM (cregβHCV-p + ccasβHCV-a) + pF (cregβHCV-p + ccasβHCV-a + 0.75 fβHCV-MTCT)

(see below for the plain english version of the HCV equation)

Substituting parameter estimates leads to 0.44 and 0.11 secondary HIV and HCV cases, respectively, for each primary infection. Top of page

## Plain english version of equation for secondary HIV transmission

The average number of secondary infections through sexual transmission or mother-to-child transmission per HIV infection is:
• the average number of long-term sexual partners each IDU has after acquiring infection times the transmission rate of unprotected male-to-male sex
• plus the average number of short-term sexual partners each IDU has after acquiring infection times the transmission rate of unprotected male-to-male sex
• times the number of IDUs with HIV who are men who have sex with men
plus
• the average number of long-term sexual partners each IDU has after acquiring infection times the transmission rate of unprotected heterosexual sex in long-term relationships
• plus the average number of short-term sexual partners each IDU has after acquiring infection times the transmission rate of unprotected male-to-female sex
• times the number of IDUs with HIV who are men who have sex with women
plus
• the average number of long-term sexual partners each IDU has after acquiring infection times the transmission rate of unprotected heterosexual sex in long-term relationships
• plus the average number of short-term sexual partners each IDU has after acquiring infection times the transmission rate of unprotected female-to-male sex
• plus the probability of mother-to-child transmission times 0.75 of the average fertility rate
• times the number of IDUs with HIV who are women who have sex with men.

## Plain english version of equation for secondary HCV transmission

The average number of secondary infections through sexual transmission or mother-to-child transmission per HCV infection is:
• the average number of long-term sexual partners each IDU has after acquiring infection times the transmission rate of HCV per long-term partnership
• plus the average number of short-term sexual partners each IDU has after acquiring infection times the transmission rate of HCV per sexual act
• times the number of IDUs with HCV who are men who have sex with men
plus
• the average number of long-term sexual partners each IDU has after acquiring infection times the transmission rate of HCV per long-term partnership
• plus the average number of short-term sexual partners each IDU has after acquiring infection times the transmission rate of HCV per sexual act
• times the number of IDUs with HCV who are men who have sex with women
plus
• the average number of long-term sexual partners each IDU has after acquiring infection times the transmission rate of HCV per long-term partnership
• plus the average number of short-term sexual partners each IDU has after acquiring infection times the transmission rate of HCV per sexual act
• plus the probability of mother-to-child transmission times 0.75 of the average fertility rate
• times the number of IDUs with HCV who are women who have sex with men