Use simulink to create model. Use matlab to create figures. This problem also requires the use of trim() and linmod().

1. This problem describes the immune response triggered by encountering foreign antigens. This is called the cytotoxic T cell or CTL response. Suppose that z eliminates infected cells. There are 4 variables: uninfected cells, x, infected cells, y, free virus particles v, and CTL cells z. The equations are Uninfected cells are produced at a constant rate , die at a rate dx and are lost to infection at a rate of xv. Infected cells are produced from uninfected cells and free virus at the rate, .v and die at a rate ay and are lost to CTL cells at a rate of pyz. Free virus is produced from infected cells at a rate ky and die at a rate uv. The CTL cells are produced at a rate of c and die at a rate of b. Parameter values are =l; d= 0.01, a= 0.05; = 0.005, p=1; k= 50; u= 5; b = 0.05 a). Let c=0. This produces no CTL response, or what happens without an immune system Simulate the above systems with initial values of x(0) 10 y(0)=1; v(0)=1; z(0) 0 :0)=0 Determine the steady state value by running the simulation and by running the "trim" function. Check answers with the equations. b). Let c=10. This is a strong immune response. Repeat part (a) and compare the steady-state results via simulation and the trim function c). Let c=0.05 to simulate a weak immune response. Repeat part (a) and compare the steady- state results via simulation and the trim function d). For part a, linearize the system using the "linmod" function around the steady-state result for part a