Exercises 20.4 Homework
1.
(Theoretical) Expand the Lotka-Volterra model (20.2.1)-(20.2.2) to include a second kind of predator, wolves \(W\text{,}\) which eats both rabbits and foxes. Note that the rate at which wolves eat rabbits would be different from the rate at which they eat foxes.
2.
(Theoretical) The SIR model assumes that any two individuals are equally likely to “mix”, i.e., to meet and potentially transmit the disease. Modify the model to account for different groups within a population (for example, on-campus and off-campus students). This means having two groups of susceptible individuals: \(S_1\) and \(S_2\text{,}\) and two groups of infected ones: \(I_1\) and \(I_2\text{.}\) The recovered/removed ones can be all in one group \(R\) since their interactions do not matter. Since there should be more interaction within each group than between the two groups, the products \(S_1I_1\) and \(S_2I_2\) should have larger coefficients in the system than \(S_1I_2\) and \(S_2I_1\text{.}\)
3.
Choose one of the two models you constructed in the previous exercises, and implement it in Matlab. Try to choose the coefficients and initial conditions so that the change of size of each group is visible on the plot (meaning the plot does not just show a horizontal line).