We present a biologically plausible model of binocular rivalry consisting of a network of Hodgkin-Huxley type neurons. Our model accounts for the experimentally and psychophysically observed phenomena: (1) it reproduces the distribution of dominance durations seen in both humans and primates, (2) it exhibits a lack of correlation between lengths of successive dominance durations, (3) variation of stimulus strength to one eye influences only the mean dominance duration of the contralateral eye, not the mean dominance duration of the ipsilateral eye, (4) increasing both stimuli strengths in parallel decreases the mean dominance durations. We have also derived a reduced population rate model from our spiking model from which explicit expressions for the dependence of the dominance durations on input strengths are analytically calculated. We also use this reduced model to derive an expression for the distribution of dominance durations seen within an individual.