An answer to the question: How do you know your model is correct?
The modeling process is just quantitative hypothesis testing.
We have formulated a hypothesis, converted it to the
corresponding system of equations, and tested it against the
experimental data. What we can say is that the model is
quantitatively consistent with the data.
No model can be said to be "correct", but some models
can be shown to be consistent and
some inconsistent with the data. Inconsistent models can be
rejected; consistent models yield useful information and are
worthy of further experimental testing.
We can easily test any alternative hypothesis that someone would
care to propose. But you should remind them of the enormous
volume of data that an alternative model would have to account
for; you can actually list the data sets you have fitted and the
constraints you have obeyed.
Modeling simply quantifies the comparison of theory with
experiment. Modeling is thus a useful tool in applying
traditional scientific method, but it has all of the well-known
limitations of scientific method. In particular, no theory is
ever proven correct. This is because it may not account for data
from future experiments. Modeling is powerful, but it is not
magic. When you present a model, you must remain a scientist.
Don't let the audience hold you to a higher standard than they
apply to their own work. Can you imagine what would happen if a
questioner asked at the end of a talk: "How do you know your
explanation is correct as opposed to several alternative
explanations?" Unless the presenter has already tested the
proposed alternatives and found them inconsistent, it would have
to be admitted that the alternative explanations are possible. No
scientist is ever certain that his or her explanation or model or
theory is correct.
There is more detail on these issues in my chapter on the Rationale for Kinetic Modeling