Medicine and faith are not compatible. You turn either to faith or to medicine, but medicine is not a work of faith, it is a mechanical, carnal tool. If we were living the vision that God had, we would be doing the same works that Jesus Christ did and even greater, and the world would be full of Christians walking around healing the sick and raising the dead.Also to your other point about their disbelief. If you think about it, faith these days have been waining for many, many years, even centuries. This lack of faith put a dent in the ability of godly men to heal people of sicknesses, and move mountains through miracles. So for one issue of sickness, I do believe God made provisions for man by given doctors the ability to heal through science. I don't think it's a mistake that these doctors are driven to find cures for society, and I believe it is the work of the Holy Spirit in the world, although some don't even believe in God. But nonetheless, God chooses unbelievers to carry out His purposes. Think about the millions of babies/young children that would have died if children vaccines had not been discovered. And the man who discovered penicillin. Think about the millions of diseases that penicillin cured. I believe God took measures in his own hands to save mankind from massive death due to the lack of faith in the world.