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enter image description hereCan we generate code for semi-relative local sensitivity for an ODE mathematical model?

This is the ODE system I have:

eqns = {
  T'[t] == Q - α0 (T[t] - T0) - (km T[t])/(k11 + k12 T[t]),
  T1'[t] == (km T[t])/(k11 + k12 T[t]) - α1 T1[t],
  m'[t] == q - α2 (m[t] - m0) + k1 m[t] n[t] - k0 m[t] T1[t],
  n'[t] == q1 - β n[t] - k1 m[t] n[t],
  C1'[t] == q2 - β1 C1[t] - λ1 k1 m[t] n[t] - λ km T[t]/(k11 + k12 T[t])
};


 initConds = {
  T[0] == T0, T1[0] > 0, m[0] == m0, n[0] > 0, C1[0] > 0
};
sol = NDSolve[{eqns, initConds}, {T, T1, m, n, C1}, {t, 0, tf}];

As one can see in the plots, they plotted (a $\frac{\partial T}{\partial a}$). That is what I want to plot. I need the idea to proceed

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    $\begingroup$ I reckon everyone would appreciate it, if you could please provide a minimal code for what you really want. Not everyone may understand what you actually want(your question as it is now is vague) and at best can guess. $\endgroup$ Commented Mar 30 at 6:32
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    $\begingroup$ You could look at ParametricNDSolve but it will be better if you give an example of what you are trying to do. $\endgroup$ Commented Mar 30 at 6:35
  • $\begingroup$ The edit is better, but still missing enough to be able to reproduce the plots. You also need to give typical values of the parameters that you use, such as T0, T1(0) etc. Also Q, k1 etc. The initConds seems badly formatted having > as an initial condition doesnt enable you to find a solution. Please check the documentation for other simple coupled differential equations to work out how the formatting should be correctly implemented. $\endgroup$ Commented Apr 1 at 4:02

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It seems that the model presented by OP is a SIR-type model with "treatment dynamics" (T, T1) and "resource tracking" (C1).

That kind of Sensitivity Analysis (SA) is typically done in System Dynamics (SD). (And related SD epidemiological studies.)

The following notebooks (posts) show how to do SD SA using Wolfram Language over SIR-like models extended with resource dynamics:

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