- #1

- 2

- 0

d0 = 0.003,

d1 = 0.008,

d2 = 0.05,

d3 = 1,

ry = 0.008,

ay = 1.6/100,

by = 10/750,

cy = 100,

u = 4 * 10^−8,

y0 = 2.5 * 10^5.

This is my ODE system:

My task says:

**Find algebraically the steady state for the equations. Set y0 = 2.5 * 10^5 and calculate y1, y2, y3 based on the derived equations at the steady state.**

Is it even possible to find the exact value of y1, y2, and y3 with the given information?

I have tried it in R, but it's impossible to get an answer.. How can I do this manually to get the solution for y1, y2, y3 at the steady state?

Code:

```
model <- function(t,x,params){
y0 <- x[1]
y1 <- x[2]
y2 <- x[3]
y3 <- x[4]
ry <- params[1]
mu <- params[2]
d0 <- params[3]
ay <- params[4]
d1 <- params[5]
by <- params[6]
d2 <- params[7]
cy <- params[8]
d3 <- params[9]
m <- rep(0,4)
m[1] = ((ry*(1-mu)) - d0) * y0
m[2] = (ay * y0) - (d1 * y1)
m[3] = (by * y1) - (d2 * y2)
m[4] = (cy * y2) - (d3 * y3)
return(m)
}
x <- ode23(model, y0 = c(y0=250000, y1=y_1, y2=y_2, y3=y_3), t0=0,tf=400, params = c(0.008,4*10^-8,0.003,1.6/100,0.008,10/750,0.05,100,1))
```