No, bluebottle, I don't think that is correct. What you are saying is that the number of people with syphilis aged 15 to 19 outnumbers all the rest combined.

Most indigenous people with syphilis are aged between 15 and 19. Since 2006, infection rates in this group have lessened, and now the group with the highest infection rate is the non-indigenous Australians aged between 30 to 39. ..... Maybe? The spanner in the works is 'since 2006'. Is this causal or temporal? Altogether, some very sloppy and ambiguous writing.

I would rewrite this completely. "Among indigenous people, syphilis reaches its highest prevalence in the 15 to 19 year-old age group.This has been gradually decreasing since 2006. Among non-indigenous Australians the highest prevalence is between 30 and 39."

The use of 'that of' seems fine. It's difficult to understand the rest of the sentence without more context. From what I understand, I would write, "the main population with syphilis is concentrated within the ages of 15 to 19. Since 2006, the prevalence of this population had decreased and that of non-indigenous Australian age is between 30 to 39'. Hope that helps.