I am new to Mathematica. I am trying to find out the best-fit values of the parameters appearing in an ODE system of three equations. The three ODE equations are:
{a'[t] == -k[1]*a[t], b'[t] == -k[2]*b[t] + k[1]*a[t], c'[t] == k[2]*b[t]}
The experimental data set for the three equations with respect to time (in minutes) is:
adata = {{0, 1}, {2, 0.88}, {6, .69}, {10, .53}, {20, .28}, {30, .15}, {50, .043}, {70, .012}, {90, 0}, {120, 0}, {150, 0}, {200, 0}}
bdata = {{0, 0}, {2, 0.12}, {6, .29}, {10, .42}, {20, .56}, {30, .57}, {50, .46}, {70, .33}, {90, 0.22}, {120, 0.12}, {150, .06}, {200, 0.02}}
cdata = {{0, 0}, {2, 0.003}, {6, .030}, {10, .050}, {20, .16}, {30, .28}, {50, .50}, {70, .66}, {90, 0.78}, {120, 0.88}, {150, .94}, {200, 0.98}}
(First entry in each pair is time)
The goal here is to solve ODE, and then optimize the parameters (k1, k2) such that the equations can best describe the experimental data.
I would be very thankful to you, if you can spare some of your valuable time and help me with this query.
the objective fuction to be minimzed is as follows