Consider a system of differential equations describing the progress of a disease in a population, given by In our particular case, this is: x=3-3xy-1x y' = 3xy - 2y where x (t) is the number of susceptible individuals at time t and y(t) is the number of infected individuals at time t. The number of individuals is counted in units of 1,000 individuals. a) Find the nullclines (simplest form) of this system of differential equations. The x-nullcline is y = The y-nullclines are y = and x = b) There are two equilibrium points that are biologically meaningful (i.e. whose coordinates are non-negative). They are (x1, y₁) and (x2, y2), where we order them so that x1 < x2. The equilibrium with the smaller x-coordinate is (x₁, y₁) = The equilibrium with the larger x-coordinate is (x2,42) where A = c) The linearization of the system of differential equations at the equilibrium (1,1) gives a system of the form (+)-^(+). = A ab 0 sin (a) a əx = a F(x, y) for a vector-valued function F. Ω