Mathematical Modeling Scenario

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Impressed by your previous work, the Ministry of Fisheries is expanding its modeling efforts to support decision making in fisheries management. While the Ministry was hoping to simply adapt the discrete logistic model to be used with other species, a potential issue has been raised. An astute marine biologist recently pointed out that not all species exhibit a life cycle best described by a discrete model. Indeed, in some species, subpopulations spawn at different times of the year. The biologist argued that these new findings suggest that such species are in fact better modeled with the continuous logistic model dN/dt=RN(1N/K), where N denotes the number of fish in generation t,R is the intrinsic rate of growth, and K is the carrying capacity. Your task is to adapt the above model to investigate how harvesting will impact a species of fish that exhibits continuous population growth. As before, two different management strategies have been proposed. The first strategy is to allow harvesting at a fixed rate per year, h; in other words, a fixed number of fish may be harvested each year, regardless of the population size. The second strategy is to allow harvesting at a proportional rate per year, H, meaning a fixed proportion of the total population may be harvested each year. Modify the continuous logistic model to investigate each of these scenarios. Provide a full analysis of each scenario and a recommendation as to the better management strategy and the level of harvesting that should be allowed