You meet Captain Logan after defending your base from the horde.
He first appears South of Spencer's Mill or West of the Farmland's. His first mission requires you to pick up a note off a Cleo drop in a swampish lake area. There are a few zeds and a jugg that you can fight or flee. You can take everything or take the item you need.
Later on when you progress, you will meet him north of Marshal to check out the Plague Wall at the Crashed Plane Site. You will then have to headshot wandering bloaters or sneak up a bloater and hold the interact button. You must quickly collect the sample because the Bloaters will explode. You see the destroyed bridge and later meet the doctor at a rusty barn.
Progressing more, his final mission is to kill the Plague Wall or try to. (Run out of Plague Cure or not). He will then be recruited and inform the doctor that he has transferred to your community.
I believe you cannot deny his recruitment.