  Memristors are an electronic device whose resistance depends on the voltage
history that has been applied to its two terminals. Despite its clear advantage
as a computational element, a suitable transport model is lacking for the
special class of interface-based memristors. Here, we adapt the widely-used
Yakopcic compact model by including transport equations relevant to
interface-type memristors. This model is able to reproduce the qualitative
behaviour measured upon Nb-doped SrTiO$_3$ memristive devices. Our analysis
demonstrates a direct correlation between the devices' characteristic
parameters and those of our model. The model can clearly identify the charge
transport mechanism in different resistive states thus facilitating evaluation
of the relevant parameters pertaining to resistive switching in interface-based
memristors. One clear application of our study is its ability to inform the
design and fabrication of related memristive devices.
