Interface-type, analog memristors have quite a reputation for real-time applications in edge sensorics, edge computing, and neuromorphic computing. The n-type conducting BiFeO3 (BFO) is such an interface-type, analog memristor, which is also nonlinear and can therefore not only store, but also process data in the same memristor cell without data transfer between the data-storage unit and the data-processing unit. Here we present a physical memristor model, which describes the hysteretic current-voltage curves of the BFO memristor in the small and large current-voltage range. Extracted internal state variables are reconfigured by the ion drift in the two write branches and are determining the electron transport in the two read branches. Simulation of electronic circuits with the BFO interface-type, analog memristors was not possible so far because previous physical memristor models have not captured the full range of internal state variables. We show quantitative agreement between modeled and experimental current-voltage curves exemplarily of three different BFO memristors in the small and large current-voltage ranges. Extracted dynamic and static internal state variables in the two full write branches and in the two full read branches, respectively, can be used for simulating electronic circuits with BFO memristors, e.g., in edge sensorics, edge computing, and neuromorphic computing.