The description of that first physical (or ideal) model is a math model.The way you validate a mathematical model is to test it against measured results. The way engineers do that is first study the physical model and then from first principles (the physical and mathematical laws of physics) derive the mathematical model.
Derivations from that initial model then incorporate new physical test measurements and observations (especially so in complex biological systems). There is then no need to verify that model because a properly built one has already taken observations and measurements into account.
It seems you've tried taking a short-cut which has then driven you to construct a purely theoretical model, which you then know you need to 'verify'. This is not a scientific, nor engineering approach to modelling.
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