Hello !
I just read your paper and, forgive me if I'm wrong, but I think there is a slight flaw in the logic with respect to its title.
The paper aims at providing the "optimal Safari Zone strategy" but what it actually does is providing the catching probability of a single Pokémon encoutered in the Safari Zone depending on the action of the player (ball, bait or rock), which is a different thing in my opinion. In my understanding, an "optimal Safari Zone strategy" should focus on optimizing the player actions to catch as many of the Pokémon you're looking for in a single Safari Zone run.
For example, let's say I want to catch a rare Safari Zone Pokémon (e.g. Tauros). I may run around for like 5 minutes and waste like 200 steps to finally get one to appear. When it does appear, your paper is probably right that my best strategy to catch this particular one Pokémon is just to throw balls at it. However, it fails to account for the cost of failure. If the Pokémon does flee, then I'm down for 5 more minutes of running around and wasting 200 more steps. I am most well served by first throwing a bait then throw balls while the Pokémon is eating (and repeat when it stops eating) because that reduces the flee rate and having the pokémon flee in this scenario is costly in terms of time and money.
The opposite example is let's say I want to catch a very common Safari Zone Pokémon (e.g. Magikarp). In this case the limiting factor of my run is the number of Safari Balls because I don't really care if the Magikarp flees as I can just fish up a new one directly. That means I am most well served by throwing a rock at it first because that means I will have to throw less Safari Balls overall, which means more Magikarps caught on a single run, thus being a more optimal run.
Because of the above, I think the flee rate should be weighted in some way by the encounter rate (e) to truly be an optimal strategy. I expect you would end up with a formula with c, f, and e rather than "only throw balls". To decide which is the optimal Safari Zone strategy to farm for a given Pokémon, you'd then need to enter its values for c, f and e in the formula and, depending on the result, I expect either "bait then balls" (for low encounter rates and high flee rates) or "rock then balls" (for high encounter rates and low flee rates) to be the optimal strategy.
What do you think ? To be honest, I'm too lazy (and less capable than you) to actually do the actual maths for those.