Hi, Brady. If you have a good selection of tools, it is not too difficult to put in a "dutchman" to replace the section of missing or destroyed jamb. Basically, what you want to do is remove any stop molding that might be in the way then cut out a section with your power circular saw. Set the saw to cut at a 45 degree angle toward the strike plate and for a depth equal to the jamb. Make one saw cut above and one below the bad section and remove it. Buy a piece of pine equal to the width of the jamb and make corresponding cuts so it fits into the gap you created. Glue and nail the piece in, replace the strike plate, prime and paint.
The saw cuts can be kind of tricky. If you have any concern at all about making them, hire someone to do this part. It is a lot easier to worry about how you are going to pay for his time than to count your fingers after the cuts.