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how can i do parameter evaluation of nonlinear differential equation?

here is my equations:

dx/dt = u*x-a*x
ds/dt = b*u*x+c*x
dp/dt = d*u*x+e*x+f*p

and u = um*s/(km+s+s^2/ki)
the parameters a,b,c,d,e,f is already known, and i have 3 arrays of data of x,s,p, and the parameter i want to identify is um,km,and ki.

i tried Nonlinear Curve fitting ,but i don't know whether it can deal with the differential equation
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