HIV indicators - natural course of an HIV epidemic or results of sociobehavioral changes?

Difficulty in choosing a basic HIV indicator to compare HIV epidemics across countries

What HIV indicators should we use to compare the epidemics across countries & what HIV indicators give us a sense of where the epidemic is?

HIV incidence:

HIV prevalence:

HIV mortality:

A very simple compartmental model for HIV

SID model:

Of course many many assumptions (that are not correct in real life) need to be made to keep it very simple:

S --> Susceptible state:

An S individual is simply someone susceptible to the disease, meaning anyone in the population who is not immune to the disease.

I --> Infectious state:

Once an individual is exposed to the disease, he will develop this disease and become infectious (unless suppressed thanks to ART).

D --> Death state:

HIV infections eventually become AIDS and leads to death.

SID compartmental model disease dynamics

S → I

Individual-level

Going from S to I for an indivudal in a particular year depends on three things:

i(t)=Prevalencei(t) = Prevalence

Although with ART the equation may become:

i(t)=(1ARTcoverage)Prevalencei(t) = (1- ART_{coverage}) * Prevalence
rr
ρ\rho

which combines many factors into one, including:

We can combine the last two into

β=ρr\beta = \rho*r
Population level

On a population-level however, the number of S that will become I also depends on the proportion of S itself in the population (obviously if there are no SS in the first place, no one will can become II).

So we add the following requirement:

s(t)=1HIVPrevalences(t) = 1 - HIV_{Prevalence}

So the change in the number of S in a population in a given year is :

βi(t)s(t)-\beta*i(t)*s(t)

and so HIV incidence can be given by:

HIVIncidence=βi(t)s(t)HIV_{Incidence} = \beta*i(t)*s(t)
    HIVIncidence=βHIVPrevalence(1HIVPrevalence)\iff HIV_{Incidence} = \beta * HIV_{Prevalence} * (1-HIV_{Prevalence})

or

    HIVincidence=β(1ARTcoverage)HIVPrevalence(1HIVPrevalence)\iff HIV_{incidence} = \beta * (1-ART_{coverage}) * HIV_{Prevalence} * (1-HIV_{Prevalence})

A new HIV indicator to compare across countries

As we have data from UNAIDS on ARTcoverageART_{coverage}, HIVincidenceHIV_{incidence}, and HIVprevalenceHIV_{prevalence} from 1990 on, we can easily calculate β\beta as follows:

β=HIVincidenceHIVPrevalenceHIVPrevalence2\beta = \frac{HIV_{incidence}}{HIV_{Prevalence}-HIV_{Prevalence}^2}

And as seen above, β\beta can be considered as a factor representing all socio-behavioral characteristics.