The raw number of new infections in a given year is

New infections[n]=β[n]I[n]N[n]S[n]\text{New infections[n]} = \beta[n]*\frac{I[n]}{N[n]}*S[n]

where:

But the data I have (from UNAIDS) gives HIVIncidenceHIV_{Incidence} in "per 1000" so:

HIVIncidence[n]=New infections[n]1000N[n]HIV_{Incidence}[n] = \text{New infections[n]} * \frac{1000}{N[n]}
    HIVIncidence[n]=β[n]I[n]N[n]S[n]N[n]1000\iff HIV_{Incidence}[n] = \beta[n]*\frac{I[n]}{N[n]}* \frac{S[n]}{N[n]} * 1000

I let β\beta absorb the factor of 1000 and I end up with:

β=HIVIncidenceHIVPrevalence(1HIVPrevalence)\beta = \frac{HIV_{Incidence}}{HIV_{Prevalence}*(1-HIV_{Prevalence})}

Example:

2 countries with same β=103\beta = 10^{-3} and HIVPrevalence=20%=0.2HIV_{Prevalence} = 20\% = 0.2 but different total populations:

New infections:

Incidence in "per 1000":