In general, "stroke" can be used as a non-countable noun with respect to the medical condition. As an example that directly answers your question (emphases mine):
Hamilton Health Sciences: Creating a world without stroke
For decades, our teams have been tackling stroke head-on. Their discoveries have set the compass for how we treat and prevent stroke worldwide.
Cutting stroke in half
Can you imagine a world without stroke? Dr. Jackie Bosch can, and she’s leading a mission to make that vision a reality.
While research has made great strides in finding new and better ways to treat stroke, prevention is even more important. Dr. Bosch has led worldwide studies showing that certain safe, inexpensive, easily accessible medications (e.g. blood pressure-lowering and cholesterol-lowering drugs) are better at reducing the risk of stroke than previously believed. Together, these medications have the potential to prevent 50 per cent of all strokes, which equates to tens of thousands of lives saved each year.
Stopping stroke in its tracks, sooner
When a stroke happens, millions of brain cells die with each minute that passes. In other words, the quicker a person receives emergency treatment, the less likely they are to suffer severe, potentially disabling brain damage. In recent years, the discovery of clot-busting drugs and special clot removal procedures have benefited countless patients by limiting the effects of stroke once it happens, but their effectiveness depends on how quickly the person receives treatment. Dr. Michael Sharma and his team are testing new drugs that act even faster and more effectively against a stroke to limit progression, giving more stroke victims a chance at life and, for many, a full recovery.
Treating the worst strokes, better
Strokes are devastating, but some are worse than others. Hemorrhagic strokes, which happen when blood vessels rupture and cause bleeding in the brain, are more likely to lead to death and severe disability, yet fewer researchers have ventured into understanding them. Dr. Ashkan Shoamanesh is one of those few, and he leads a Canada-wide research group aimed at exploring how to prevent hemorrhagic strokes and to better treat people who suffer from them.
HHS & McMaster researchers find “simple” methods to prevent heart attack & stroke
Three simple methods to prevent heart attack and stroke have been proven by an international team led by Hamilton Health Sciences (HHS) and McMaster University researchers.
As such, with respect to the non-countable concept of "stroke," use "a world without stroke." (As demonstrated in the article, the same would go for "a world without heart attack." Like you mention, it's a little awkward without the plural, but if you're referring to the phenomenon as a concept to eradicate, the singular is correct.)
From “Any” followed by singular or plural countable nouns?:
According to the books I've used (specifically Smart Choice by Oxford University Press and English in Mind by Cambridge), "any" is used only for uncountable nouns and plurals and when the sentence is a question or a negative. In the example above about "Do you have any ideas? / Do you have any idea?" consider that "Do you have any idea?" is using idea as a synonym of notion which in turn is uncountable. You would never use "any" for a singular noun you can count. Could you say "Do you have any books? / Do you have any book?"?
If you were asking a patient about their medical history, you might say "have you had any strokes?" because you're referencing a countable quantity (as with "any books" in the example above). In the case of your question, "stroke," in the context of "a world without," describes the absence of a concept but not a specific quantity (you could argue that quantity is zero, but I think this makes more sense a purely theoretical statement).