The most obvious inherited health issues of the Peke-face Persian: BAS.

Although the Peke-face Persian (flat-faced Persian) can suffer from all or one of 16 inherited diseases, the one highlighted in the infographic below is the most obvious. It is perhaps the classic consequence of breeding cats with unnaturally shaped heads and faces to try and meet an aesthetic which pleases the eye of some. Heavens knows why because the Peke-face is certainly uglier than the Doll-face.

There is no cure for this or the other Peke-face Persian inherited diseases because they are caused by a distorted face and head due to extreme breeding. You have to change the breeding practices over a long time if you are to 'cure' this shameful state of affairs where the cat fancy have abdicated their responsibilities to ensure that they breed healthy cats. In fact I think you'll see that the CFA demands in their breed standards that health should not be compromised BUT IT IS (in the most gross way)! And has been for decades in really serious ways causing distress and unhappiness in these cats. 

Brachycephalic Airway Syndrome (BAS) in Peke-face Persian cats by Michael Broad

If you click on this link: Infographics on Peke-face Persian health problems, you'll see some more health issues associated with this breed, if that interests you. Each one is a 60 second read. The goal is to explain sometimes complicated medical information in studies in an infographic. I want everyone to have access to this kind of information as it is good for cat welfare and to educate potential adopters of purebred cats.

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P.S. please forgive the occasional typo. These articles are written at breakneck speed using Dragon Dictate. I have to prepare them in around 20 mins. Also: sources for news articles are carefully selected but the news is often not independently verified. Also, I rely on scientific studies but they are not 100% reliable.