Current along an axon
As far as I was able to find there exists two models of the action potential by using RC circuits. Do note that there is no flow of electrons per se across a tube, but rather a migration of potential. See this.

The Hodgkins Huxley model :


  The Hodgkin–Huxley model, or conductance-based model, is a mathematical model that describes how action potentials in neurons are initiated and propagated. It is a set of nonlinear differential equations that approximates the electrical characteristics of excitable cells such as neurons and cardiac myocytes, and hence it is a continuous time model


http://en.wikipedia.org/wiki/Hodgkin%E2%80%93Huxley_model

The Fitzhugh-Nagumo model:


  The FitzHugh–Nagumo model is a simplified version of the Hodgkin–Huxley model which models in a detailed manner activation and deactivation dynamics of a spiking neuron. In the original papers of FitzHugh, this model was called Bonhoeffer–van der Pol oscillator...


http://en.wikipedia.org/wiki/FitzHugh%E2%80%93Nagumo_model

http://en.wikipedia.org/wiki/Quantitative_models_of_the_action_potential

Hodgkin, Allan L., and Andrew F. Huxley. "Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo." The Journal of physiology 116.4 (1952): 449-472.

Now, I have not dealt with differential equations in quite a while, and hence may not be the best source for explaining the model itself, but I'll try and update the post with what (if anything) I understand.