Question

Assignment 8 Remaining Time: 131:53:22 Question 1 Consider a system of differential equations describing the progress of a disease in a population, given by F(x, y) for 1 point How Did I Do? a vector-valued function F. In our particular case, this is: d' = 3 – 3xy - 12 y' = 3xy – 34 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= DS 1 The y-nullclines are y = 0 and x = b) There are two equilibrium points that are biologically meaningful (i.e. whose coordinates are non-negative). They are (21,y]) and (xc2 ,y2), where we order them so that x1 < 22. The equilibrium with the smaller x-coordinate is (21,41) = A The equilibrium with the larger x-coordinate is (x2,42) =

Answer 1

a) n nulleline : 3-Bny - Ilo >) ya 3-n 3n y hulleline : 3ny-zy = 0 3 y Cu-1) 20 b) and n=1 O yao ) N=3 equilibria S, L3,0) for n=1 ) . a S., (1) equilibria, y= 3 = 1 12 بادی (Mi, y) = (1, (12, Y₂ ) = (30) c) 3 (hf, yo )? (where k' = 4, y'=9] for fy ga gy -34-1 -3n 31-3 . A 23(1, 2/2) = d) 2 At at this point 15 1-9 9-3 6 e) A region, (1 2 1 1 2 ) be point l'o) oyko and down word. Similarly at B cit (2, 3), nico, y'lo To the left ard downward ar To the right the left and upward. To at e to the right and upward at