lnfectious diseases. such as influenza' can spread according to the autonomous differential equation % : BI (N I) .u,I. I denotes the number of infected people' Ndenotes the total size of the population being modeled' ,6 is a raterofrtransmission constant. and p. is the recovery rate from infection (20m Find all equilibria if B : 0.01, N : 1000, and u : 2. Determine the stability of these equilibria using the stability criterion (b)[3] Draw the phase plot fa) versus Iwhere HI) : I' with ,3: 0.01, N : 1000, and p : 2. On the plot identify the equilibria and whether they are unstable or locally stable Also' draw direction arrows for the case where the number of infected people is I = 500 and for the case where I = 900. You may find it helpful to use Desmos or Wolfram Alpha to plot the graph of f(I) versus I, or you can plot it by hand ifyou like (QM The baSic reproduction numberi R0 represents the expected number of new infections that an infected indiVidual will produce when introduced into a completely susceptible population Show that by rearranging the condition for f : 0 to be unstable, an inequality of the form RD > 1 is obtained where R0 : 'BTN