most rape cases are done by locals. Immigrants are a very small percentage of these cases.

Not only that, Immigrants are a very good reason a country is advancing. Take a look at the US, thousands of rape and killing cases, almost none of them done by Asians. Many great scientists and inventors are Asians.
Germany is also a good example, their medical system is almost based on Syrian people.

For sure people do bad things, but it's not because they are immigrants, it's because they are sick on the head.

If you can get some real statistics from the US, UK, Germany France and other countries, you'll see clearly that these numbers aren't high at all, they're as much as nativers if not lower.