Antivirus not prominent on iOS devices

Solution 1:

Due to application sandboxing in iOS, which restricts applications to just their individually allocated areas on the filesystem (and prevents access to any other application's or the OS' files as well as memory, network communication, etc.), an app written to be like an antivirus cannot really read anything outside of its own sandbox.

Due to limited multitasking in iOS, an app written to be like an antivirus cannot really run in the background for a long time to scan the system continuously.

Both these factors together make it impossible to make an antivirus like app for iOS unless the device is jailbroken.

Any antivirus, if at all deemed necessary, would have to be made by Apple. Third party app developers are limited to the restrictions mentioned above.

Further to the comments on the question, it may be worth one's while to look at this presentation titled "The Android vs. Apple iOS Security Showdown - July 2012" (especially slides #20 through #33).

Solution 2:

The brief answer is Apple provides a developer kit (SDK) that makes this sort of program very limited in functionality and doesn't allow programs to plug in and modify the OS as has proven popular for desktop OS scanning tools.

Antivirus software is limited by the sandbox

As Kaspersky explains, the way apps are currently sandboxed within the app store, there is no way for an antivirus package to scan outside of its sandbox. It would not be able to scan files downloaded from Safari, other apps, Mail, or anything else.

But that's ok.

Apple's sandbox limits malware

The sandbox also limits what any malware could do. Since apps need to be signed, and the APIs they're allowed access to limit their access, there's not much room for a virus or other malware to sneak in. Right now, there are no known iOS viruses.