How do Forcing Functions Work?

  • Differential equations without forcing functions: n compartment model

    dqi/dt Equation (w/o forcing functions)
  • Differential equations with q1 a forcing function: n compartment model

    dqi/dt Equations (with q1 a forcing function)
This example demonstrated how the forcing function works. Remember that your compartmental model always represents a system of differential equations. The top set of equations is the normal set for the n-compartment model.

Now suppose that compartment 1 is a forcing function. In all equations except dq1/t1, q1 on the right hand side is replaced by q1.FF. The equation dq1/dt does not change (which means, even when you are using a forcing function, there will be a solution for q1; it is the time course that is determined by all the other components of the system, assuming that q1 is empty at the start of the experiment).

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