Travelling waves of activity in neural circuits have been proposed as a mechanism underlying a variety of neurological disorders, including epileptic seizures, migraine auras and brain injury. The highly influential Wilson-Cowan cortical model describes the dynamics of a network of excitatory and inhibitory neurons. The Wilson-Cowan equations predict travelling waves of activity in rate-based models that have sufficiently reduced levels of lateral inhibition. Travelling waves of excitation may play a role in functional changes in the auditory cortex after hearing loss. We propose that down-regulation of lateral inhibition may be induced in deafferented cortex via homeostatic plasticity mechanisms. We use the Wilson-Cowan equations to construct a spiking model of the primary auditory cortex that includes a novel, mathematically formalized description of homeostatic plasticity. In our model, the homeostatic mechanisms respond to hearing loss by reducing inhibition and increasing excitation, producing conditions under which travelling waves of excitation can emerge. However, our model predicts that the presence of spontaneous activity prevents the development of long-range travelling waves of excitation. Rather, our simulations show short-duration excitatory waves that cancel each other out. We also describe changes in spontaneous firing, synchrony and tuning after simulated hearing loss. With the exception of shifts in characteristic frequency, changes after hearing loss were qualitatively the same as empirical findings. Finally, we discuss possible applications to tinnitus, the perception of sound without an external stimulus.