  Ending the HIV/AIDS pandemic is among the Sustainable Development Goals for
the next decade. In order to overcome the gap between the need for care and the
available resources, better understanding of HIV epidemics is needed to guide
policy decisions, especially for key populations that are at higher risk for
HIV infection. Accurate HIV epidemic estimates for key populations have been
difficult to obtain because their HIV surveillance data is very limited. In
this paper, we propose a so-called joint spatial conditional auto-regressive
model for estimating HIV prevalence rates among key populations. Our model
borrows information from both neighboring locations and dependent populations.
As illustrated in the real data analysis, it provides more accurate estimates
than independently fitting the sub-epidemic for each key population. In
addition, we provide a study to reveal the conditions that our proposal gives a
better prediction. The study combines both theoretical investigation and
numerical study, revealing strength and limitations of our proposal.
