If we stop allowing large scale Immigration (particularly) from Muslim Countries. Stop (most) welfare to immigrants, cut social services to 2 children for immigrants and lower income immigrants. Build our nations and other nation Manufacturing Infrastructure. In the medium term get off Muslim and Arab Oil. That is what funds mosques and radicalized Islam. Then ensure you/we have the civilized world has STRONG Borders and Enforcement, and let nature take its course in pre-dominant Islamic countries. We could fly out the Non-Muslims from pre-dominant Islamic countries as well! And ensure if any Western Muslim decides to kick up a sh*tfest in the Western World, they will be harshly dealt with and stripped of their citizenship and kicked out of the Western World/Country!
While many years have been spent trying to stop groups like Al-Qaeda, and recent events has made it seem as though these efforts have been in vain, it does not mean the fight has been lost. New tactics need to be worked out with the countries where the problems are most prevalent, and try and stop these groups by working to prevent people from being radicalized in the first place. If they have no soldiers, spreading their skewed morals would be almost impossible.
Yes, we can stop the spread of Islamic radicalism, if we do our best to spread peace and humanity abroad. There will always be incidents here and there, but it is not inevitable that radical Islam takes over the entire world. We can have strategic military bases, and build up our relationship with Israel.
I believe that no matter how hard we try, we will not be able to contain Ideas. In a chaos ridden region such as the Middle East, violent ideas will spread like wildfire. There has always been violence in the Middle wast (most of it was fueled by the clashing of various religious ideals) and the only way to somewhat contain these ideas would be to have peace in the middle east, which I believe to be almost impossible.
I don't think there is any way we can actually stop the spreading of radical Islamic ideas. More and more people in countries across the world are becoming radicalized. The Internet only makes it easier to recruit new members. All we can do is promote peace and show the world that the top governments will not stand for the violence to continue.
I do not believe we can stop the spread of Islamic radicalism. One need only look to the power of the Christian churches in the past. The Crusades were absolutely radical in their time and there was no stopping those either. I believe this movement is simply something this religion has to make it through much like the Christians did.