My new iPhone 5 has a virus or trojan. IT IS NOT JAIL BROKEN!

My phone starts to open and close apps on its own. When I press a key an unrelated key responds. The settings area has locked me out of the reset area. I can not close apps. If I turn the phone on and off, this is all sometimes fixed for a short period of time. I have rest set the settings when I can get in. I have the security code on. Can apple look through my apps and find out where the virus/trojan is coming from and get rid of it? I have erased all of the content on my phone and started over. How do I prevent this from happening again.