Vagal nerve stimulation in cardiac therapy involves delivering electrical current to the vagal sympathetic complex in patients experiencing heart failure. The therapy has shown promise but the mechanisms by which any benefit accrues is not understood. In this paper we model the response to increased levels of stimulation of individual components of the vagal sympathetic complex as a differential activation of each component in the control of heart rate. The model provides insight beyond what is available in the animal experiment in as much as allowing the simultaneous assessment of neuronal activity throughout the cardiac neural axis. The results indicate that there is sensitivity of the neural network to low level subthreshold stimulation. This leads us to propose that the chronic effects of vagal nerve stimulation therapy lie within the indirect pathways that target intrinsic cardiac local circuit neurons because they have the capacity for plasticity.