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There are a few different ways you could handle this, depending on exact requirements. One simple possibility could be a Read-only Rule on the Status field to stop users changing the Status unless they own the Incident.
$(CurrentLoginId() != Owner)
You could do similar to the Owner field if you wanted the make the current owner hand over to a new owner.
Another option I haven't really looked into would be using a Validation Rule. You could check whether the Status has changed to Resolved/Closed (using the Status:original field qualifier -- Online Help for that), and if you use multiple languages, make sure to take that into account in any string comparisons (using the Local() function). The downside of Validation Rules is that they are only checked after clicking Save, so users may find they've put some effort into the Incident already, only to be unable to save it.
Hope this helps.