Can anyone explain why my code isn't working?

Questions
1

So I’ve got this question:

Two genes A and B each switch off the other. Their activity also decays with time, but at different rates. The change in A and B expression with time can be described using the following 2 ordinary differential equations.

dA/dt= 0.5/(1+(B/Subscript[K, 1])^n)-0.2A
dB/dt= 1/(1+(A/Subscript[K, 2])^n)-2B

Use Mathematica to numerically solve the above system of ordinary differential equations for t=0 to t=120 minutes.
Plot your solution on a single plot.

Assume:
Initial condition:
At t=0, A=0nmol/m^3 and B=0nmol/(m^3).
Subscript[K, 1]=0.5nmol/m^3
Subscript[K, 2]=2nmol/m^3
n=10

And I’m trying to solve the problem. I’ve got this so far:

N[DSolve[{A'[t] == 0.5/((1 + (B[t]/.5))^10) - 0.2 A[t],  B'[t] == 0.5/(1 + (A[t]/2))^10 - 2 B[t], A[0] == 0,  B[0] == 0}, {A[t], B[t]}, {t, 0, 120}]]

And all it’s doing is returning:

{{A[t] -> InterpolatingFunction[{{0., 120.}}, <>][t], 
  B[t] -> InterpolatingFunction[{{0., 120.}}, <>][t]}}

And Mathematica says it’s still running and has been for about 7 or 8 minutes now. Can anyone explain where I’ve gone wrong or how I can solve this problem correctly?

Thanks

2

Best is to use the function NDSolveValue. For example as follows:

{Asol, Bsol} = 
 NDSolveValue[{A'[t] == 0.5/((1 + (B[t]/.5))^10) - 0.2 A[t], 
   B'[t] == 0.5/(1 + (A[t]/2))^10 - 2 B[t], A[0] == 0, B[0] == 0}, {A,
    B}, {t, 0, 120}]
Plot[{Asol[t], Bsol[t]}, {t, 0, 120}]

and get:

output-2.png
output-2.png1239×1754 19.8 KB

3

You tried to find analytical solution the turning it to numbers N[DSolve… better above or:

In[10]:= sol = 
 NDSolve[{A'[t] == 0.5/((1 + (B[t]/.5))^10) - 0.2 A[t], 
   B'[t] == 0.5/(1 + (A[t]/2))^10 - 2 B[t], A[0] == 0, 
   B[0] == 0}, {A[t], B[t]}, {t, 0, 120}]

Out[10]= {{A[t] -> InterpolatingFunction[{{0., 120.}}, <>][t], 
  B[t] -> InterpolatingFunction[{{0., 120.}}, <>][t]}}

In[11]:= Plot[{A[t], B[t]} /. sol, {t, 0, 120}]

4948Untitled-1.png
4948Untitled-1.png360×221 2.1 KB