Write a mini-lecture on the Logistic differential equation with non-constant harvesting and itsapplication. Your mini-lecture should be aimed at an audience of third year mathematical sciencesstudents (who might not be

taking the course). You should discuss either one or two types of non-constant harvesting functions. A discussion of equilibrium solutions and a derivation of the exact solution(s) to the equation(s) (where possible) should be included. The mini-lecture should also include a detailed description of at least one example in which a logistic model with non-constant harvesting is used (HINT, see fisheries management). You may either use the exact solution or a numerical approximation to the solution to demonstrate the use of the equation in this example. Asa guideline, in addition to what has already been requested, your mini-lecture could include some of the following: Historical/background information on the equation(s) and their use; an overview of some modelling uses of the equation(s); derivation of the equation(s); an explanation of terms such as yield-effort curve and maximum sustainable yield. Cite all sources of information using a Harvard referencing style and do not rely solely on Wikipedia for your information. Each mini-lecture should be appropriate for a final year undergraduate student in mathematics. The guide length for this mini-lecture is 1000 words. Marks for this question will be allocated as follows: Content: (including appropriateness of the presentation for the intended audience) 8marks. Writing Style (including readability, grammar, punctuation, spelling): 5 marks. • Referencing: 2 marks.