Question 1 (15 MARKS) On the island of Mauritius there once lived a population of a flightless bird, known as the dodo. Suppose that the dodo population is described by the delay differential equation a dN (t) = 6N(t T) cN(t T)2 mN(t)?, dt where T > 0) is the time delay between the laying and hatching of a dodo egg, and b, c and m are positive parameters. (a) Give a biological interpretation of the terms of the model. Explain how, according to this model, we can see that the natural life expectancy of the dodo in favourable conditions was very long. (b) Find the equilibria in this model and the ranges of parameter values at which they exist. Question 1 (15 MARKS) On the island of Mauritius there once lived a population of a flightless bird, known as the dodo. Suppose that the dodo population is described by the delay differential equation a dN (t) = 6N(t T) cN(t T)2 mN(t)?, dt where T > 0) is the time delay between the laying and hatching of a dodo egg, and b, c and m are positive parameters. (a) Give a biological interpretation of the terms of the model. Explain how, according to this model, we can see that the natural life expectancy of the dodo in favourable conditions was very long. (b) Find the equilibria in this model and the ranges of parameter values at which they exist