Human scabies is a major global public health issue, with an estimated 300 million cases per year worldwide. Prevalence rates are particularly high in many third-world regions and within various indigenous communities in developed countries. Infestation with Sarcoptes Scabiei is associated with group-A streptococcal pyoderma which in turn predisposes to rheumatic fever, acute glomerulonephritis and their respective long-term sequelae: rheumatic heart disease and chronic renal insufficiency. The documented difficulties inherent in achieving scabies control within affected communities have motivated us to develop a network-dependent Monte-Carlo model of the scabies contagion, with the dual aims of gaining insight into its dynamics, and in determining the effects of various treatment strategies. Here we show that scabies burden is adversely affected by increases in average network degree, prominent network clustering, and by a person-to-person transmissibility of greater magnitude. We demonstrate that creating a community-specific model allows for the determination of an effective treatment protocol that can satisfy any pre-defined target prevalence. We find frequent low-density treatment protocols are inherently advantageous in comparison with infrequent mass screening and treatment regimes: prevalence rates are lower when compared with protocols that administer the same number of treatments over a given time interval less frequently, and frequent low-density treatment protocols have economic, practical and public acceptance advantages that may facilitate their long-term implementation. This work demonstrates the importance of stochasticity, community structure and the heterogeneity of individuals in influencing the dynamics of the human scabies contagion, and provides a practical method for investigating the outcomes of various intervention strategies.