This　article　is　concerned　with　the　optimal　control　problem　of　age-structured　population　dynamics　for　the　spread　of　universally　fatal　diseases.　The　existence　and　uniqueness　of　solution　of　the　system,　which　consists　of　a　group　of　partial　differential　equations　with　nonlocal　boundary　conditions,　is　proved.　The　Dubovitskii　and　Milyutin　functional　analytical　approach　is　adopted　in　the　investigation　of　the　Pontryagin　maximum　principle　of　the　system.　The　necessary　condition　is　presented　for　the　optimal　control　problem　in　fixed　final　horizon　case.　Finally,　a　remark　on　how　to　utilize　the　obtained　results　is　also　made.