Good Question?!
First of all, I am sure 100% if we were the dominators of the world as you said! and we are the drivers of this knowledge and civilization train most of the diseases which are known today will no longer exists?!!
You ask me how?!
Because our great religion automatically bans the causes of this diseases in our shari'a as it's stated in our comprehensive Book of Medicine (Holy Kuran)
I will give you an example:
All the STDs will no longer exists as it's rate today!!
All the diseases transmitted OFR (oral faecal route)!!
All the psychological diseases will hardly known today!!
the list goes on!!
The causes of all those diseases are prevented and cured in our Prophetic Medicine!!
but the other question that needs to be answered is:
what our ancient muslims those who lived in andalus have done in medical history?
let me tell you their contributions for example:
They translated most of foreign sources into Arabic ( 7th and 8th centuries)
From (9th through the 13 centuries) was the stage of excellence in which the Islamic physicians were the leaders like (Ibn Al-Nafis, Ibn al-Haytham, Al-Kindi, Ibn Sina (Avicenna) was known in the West as "the prince of physicians." and more known physician world wide in that golden centuries.
Who discovered the pulmonary circulation?!
Who had the ability to practice medicine and surgery as well?!
who named public health, preventive medicine as part of medicine? and listed the well known seven principles for the preservation of health!!
Who defined fever and claasified into the known types today like continuous, relapsing, and hectic!!
Who treated measles and smallpox?!!
I can't list all the discoveries here but try
To know more about discoveries by the hand of our great muslim physicians check this article
http://www.bmj.com/cgi/content/full/331/7531/1486http://www.iiim.org/islamed3.html"Today's Western world might look very different without the legacy of Muslim scholars in Baghdad, Cairo, Cordoba, and elsewhere."
thanks
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By: Dr.Mahdi