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The SIR model is a model that depicts the susceptibility, the infection, and the recovery stages of a given disease. The SIR model is relatively flexible, and variables can be bent and rearranged as seen fit to whatever disease it may be describing. In terms of HIV, a widely accepted SIR model is not a 'SIR' to begin with. In reality, HIV's SIR is a SI - since there is no a true 'recovery' phase. Refer to the following image(1):
Since there is no true 'recovery,' and as stated in previous posts, HIV has different 'stages' of infection, the model is S - everyone on Earth is susceptible - I1 - first stage of infection, which can either resort to the face treatment for HIV to help control, or it can move on to - I2 - the second stage of infection, which can follow suit with ART treatment or it can progress to - I3 - the third stage of infection. Once an individual has reached the third stage of infection - AIDS - treatment is still available, but chances of survival by that point are significantly slim and usually the third stage of infection usually results in death (in which case, the model should indicate from off of the I3 that the result is death and not just a perpetual state of third stage infection).
In SIR models, there is a variable outside of the model itself - an equational factor - known as R0, or the basic reproduction number. It is said that if R0 is greater than value "1" then it is infectious in a population. R0 is calculated from SIR models by using the parameters: R0= p/a, where p is equal to the infection rate, and a is equal to the removal rate. HIV has an R0 of anywhere from 2-5, depending(2). Because HIV is a sexually transmitted disease, pinpointing the exact basic reproduction number is somewhat fickle.
1. http://www.idmod.org/docs/hiv/hiv-model-overview.html#ref29
2. https://en.wikipedia.org/wiki/Basic_reproduction_number
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