Question: Imagine that a genetically-engineered form of white-blood cell has been developed for therapeutic use in fighting the SARS-CoV-2 virus. When introduced into the body, these white blood cells feed on other cells that have been invaded by the virus. A simple model that characterizes the growth of these two cell populations is given below: = - 2 = 2 - Here, "x" represents the fraction of lung cells that have been infected by the virus, while "y" represents the fraction of the genetically-engineered white blood cells. Note that, without therapeutic intervention (y=0), x would grow exponentially. In contrast, the therapeutic cells are self-limiting but the growth rate (dy/dt) of their population is enhanced by the number of virally- infected lung cells. (a) Determine the values of the cell populations at which there will be no net growth in the population of both cell types. (b) Determine whether the equilibrium points determined in (a) are stable or unstable. As well, deduce the nature of stability at these points (ie. are they stable/unstable foci or nodes, or saddle points, etc.). (c ) Sketch the phase plane diagram for this system, showing clearly the x- and y-nullclines, as well as the general directions. Need Assignment Help?