Penoxycycline offers true immunity to plague & sleeping sickness for 12 hours, and malaria for 8 hours. After that period, it reduces the probably of that particular pawn getting sick (diseases cannot be acquired at 60%+ immunity, and Penoxy sets it to 61%, so there is a brief time before it decays below the threshold)
The weird part is that the game first picks how many pawns will get sick, regardless of immunity, and then next picks which pawns get sick, weighted by immunity. If only one of your pawns has taken penoxy, and took it 24 hours ago, that pawn is 1/50th as likely to get sick as the other pawns. But if all of your pawns have taken it 24 hours ago, they're all just as likely to get sick and the same number of pawns total will get sick. But they'll still be starting at 59% immunity, pretty much guaranteeing survival, and a very short period of actual sickness. (A young, healthy pawn will be at 90%+ immunity when the plague/sleeping sickness is revealed; malaria never revealed at all).
For plague & sleeping sickness, I would not recommend Penoxycycline prophylaxis for all healthy pawns; it can be taken reactively and still add 30%+ immunity, eliminating the need for bed rest or treatment to survive (and if treatment is provided it won't reach serious stages).
Malaria does need proactive Penoxycycline. A healthy pawn will develop 55% immunity in the 4.6 days it takes to reveal itself, so reactive penoxy only adds 5%. Penoxy taken every 5 days will maintain a minimum of 46% immunity to malaria, so healthy pawns will never have a visible Malaria infection. But taken every 9 days, a healthy pawn will still develop immunity before malaria hits Major severity without any treatment or bed rest. A solo jungle explorer looking to conserve their supply might stretch it out to every 12 days (which will avoid extreme without any treatment or bed rest), or if they're particularly brave/desperate, every 15 days (but then there is a small risk that bed rest will be necessary). Taken every 20 days, Penoxy offers no guaranteed immunity, but on average will cut off 2.5 days before immunity is acquired.