Models & Qualitative Behavior · Superchallenge problem

A fish stock follows $P' = 0.4P\left(1 - \dfrac{P}{1000}\right) - h$ ($t$ in years), and it is harvested at a constant rate $h$ equal to its maximum sustainable yield (the largest $h$ for which an equilibrium exists), sitting at that equilibrium. A disease then suddenly kills $100$ fish. If the harvest rate is not changed, how many years later does the stock collapse to $0$?