I think, that the infection progresses faster, when the patient is already seriously injured. Connor was basically dead the moment he got infected, so the "virus" just took over. On the other hand Adam and Linus seem healthy except that one bite, so their immune system may still be trying to fight the infection and at least slow down the progress. This theory could work even for the lady and her baby. She didn't seem infected, while that baby looked absolutely rotten. She probably got infected on the same day as the baby, (since infants need to be breastfed multiple times a day) but her adult immune system is much stronger, than the babie's and is therefore fighting the infection better.
just sharing some observation points since I see some people are confused in the comments... (contains spoliers)
The black haired man with the eye patch from the very first chapter is in fact adam the policeman. The story with linus and conner is set before adam got infected and during that time he was in love with mark who very much resembles william. My guess is that adam's cause of infection was mark (maybe not who knows) but tbh highkey fuck mark for dumping adam to get married but also fuck adam for being a rapist zombie and hurting poor william!!
About linus and conner, the image of conner looking normal and not zombie-like is only linus's imagination. Conner is in fact a rotten corpse from the very beginning linus digs him up, which is when conner ends up biting linus on the neck. Conner doesn't attack linus because they're both infected and infected ones only attack humans, also they're both consuming human flesh. You can also tell linus is completely delusional when he says that if the world were to take conner away from him he would become like the woman they killed (delusional from grief) but then he says that he would never allow himself to become like her which is crazy talk cause he's already like her. The infection process is slow in linus's case which is why the policemen thought he was still human and let him go.
Kinda hope that adam and william don't end up like linus and conner, that's kinda sad so I'm rooting for william to get a grip and kill adam. Also I do wonder what's causing the slowed down infection process for adam and linus... I hope it's not sex cause that be a let down and entirely lame :c
I've got high expectations for this manga, so far it's 10/10 hope it doesn't go downhill from here