Question

Please help with step by step explanation

Suppose there is a lake with some fish that are attractive to the fishermen. We wish to model the fish-fishermen interaction given the following assumptions: Assumptions:

• Fish grow exponentially in the absence of fishing.. The presence of the fishermen depresses the fish growth at a rate jointly proportional to the fish and fishermen populations.
• Fishermen are attracted to the lake at a rate directly proportional to the amount of fish in the lake.
• Fishermen leave the lake at a rate proportional to the number of fishermen already there.

(a) Formulate a mathematical model with continuous in time for this situation. Label all the unknowns and state any assumptions that you make about all the parameters

(b) Is there a population level of the fish and the fishermen (fishing at this lake) at which there is no change in either of the populations? If yes, please determine these population levels.

Answer 1

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