Permissions are done at a project level in general.
You can overrride permissions for issue types, but it's not an easy job - you have to create a workflow for each type of issue you want to have different permissions, associate them with issues in the workflow scheme, and then use "workflow properties" to alter the project permissions on each and every status in it.
As Joe says though - delete permissions aren't worth the effort - they should be severely limited to a smal set of users who can check before doing it, or simply not allowed. Because you will be bitten by a user deleting the wrong thing and then whining that they can't get it back.
There is no issue type level security as a whole. You can use security schemes assigned to issues. HOWEVER, I strongly advise against allowing anyone to delete issues. It WILL come back to bite you. The forum is full of people looking for ways to get a deleted issue back. There aren't any good ones.
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