Problem 2 Consider model (7.2). 1. Find the fixed points of this system. 2. What are the conditions on the parameters for these fixed points to be in the first quadrant? What is the biological significance of these conditions? 3. Discuss the linear stability of the fixed point such that y = v = 0.i=Cmvm, d7 d i = w my, (72) da- do 7 = _ 1, d'T y H 7 Akb where C = F, 17 = g, and p, = g are dimensionless parameters. We scaled time according to the death rate of normal cells. Alternatively, we could have scaled time according to the rate at which normal cells are produced by the body, i.e. we could have defined 1' = At/Xg, with X0 = 52/(kb). We could also have used a combination of these two time scales. In general, there is more than one possible way of defining dimensionless variables. The most convenient choice is often that which gives dimensionless parameters of order one, if at all possible