Agreeing with all that has been said. In case you want to fit a model, of course the brian2modelfitting library might come handy 
. But as @rth pointed out, you cannot really use the Izhikevich model (or similar I&F models) to fit the details of a membrane potential trace. This is even evident in Izhikevich’s examples, e.g. in Fig. 1 of Izhikevich (2003) – the experimental recording of the RS neuron has a much lower resting potential compared to the model. On the other hand, these types of models can be used to fit the spiking response. I don’t know the paper you linked in Implementation of Izhikevich neuron model - #16 by lann591, but it seems that they did only that, i.e. recreate ISIs.
2 Likes