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The current transport properties of DNA molecules are of considerable interest. The key reason for this appears to be linked to the universality of DNA molecules in living organisms, their self-assembly properties, and potential applications as nanoscale devices. The modelling of the I-V characteristics of a DNA molecule using equivalent circuits is reported. The advantages of the proposed model are that non-linear current behaviour can be included together with potential piece-wise solutions. The model includes the use of transistors to mimic current discontinuities at transition points. The simulated results closely resemble measured I-V curves and do not invoke resonant tunneling which contradicts observed temperature dependences. An equivalent-circuit model which includes the use of active devices is shown to be effective way to mimic non-linear current transport in biological molecules.