I loves maths, and thus, let me do some simple maths here.
Known figures are:
35 HIV cases detected in 6 months in the CHANGI General Hospital (CGH) among 3 out of 10, or among about 6500 people who opted to be tested.
What does this imply?
It means there might be in total 35 * 10/3 = 116.667 HIV positive among the 6500* 10/3 = 21666.67 patients who visited CGH.
By further extrapolation, it means there might be 116.667 / 21666.67 * 4M = 21538.46 HIV positive people in Singapore.
OK, there is a bias here ... , as patients cannot be used to represent general population. Thus, it needs to be corrected by multiplying by the proportion of people who visited hospital in the past 6 months in Singapore. I don't have it, but let use a low ratio of 1/100, there are about 215.38 HIV positive people in Singapore. This ratio of 1/100 seems too low since 215.38 is only about twice of 116.667 while Singapore has more than 2 similar or larger hospitals like CGH.
Thus, if we use the number of hospitals in Singapore of similar size, which I also don't have the exact figure, but can safely state as > 5, considering SGH, TTSH, AH, CGH, NUH, and many smaller clinics. Then, the number might be 116.667 * 5 ~= 583 HIV positive among only those who visited hospitals in the past 6 months. Note, this is only the estimated number of HIV positive patients, NOT general population.
What we need to pay attention to is not the 35 HIV cases detected. We really need to pay attention to the possibly 116-35=81 undetected HIV cases! From the above estimate, we need to pay attention to the possibly 81*5=405 undetected HIV cases! And if considering the whole population, there are possibly much much more than 405 undetected HIV people who have not visited hospital in the past 6 months, i.e. they are likely to be healthy people.
What are they doing? Without knowing that they are infected, they are living their normal life. What's their "normal" life? At least quite a few of them have a "normal" life of having regular casual sex with multiple partners, including their spouse.
After the first posting, I read this part:
...many of those who did not want the test were elderly or repeat patients who had been tested before. Tests were not offered to those under 21 years old, the age of consent.OK, seems not as bad, but even after discounting, the estimated HIV positive, healthy and sexually people out there who don't know they have the virus are still among the hundreds!!!