Infections with Sarcoptes scabiei, or scabies, remain common in many disadvantaged populations. Mass drug administration (MDA) has been used in such settings to achieve a rapid reduction in infection and transmission, with the goal of eliminating the public health burden of scabies. While prevalence has been observed to fall substantially following such an intervention, in some instances resurgence of infection to baseline levels has occurred over several years. To explore the biology underpinning this phenomenon, we have developed a theoretical model of scabies life-cycle and transmission dynamics in a homogeneously mixing population, and simulate the impact of mass drug treatment strategies acting on egg and mite life cycle stages (ovicidal) or mites alone (non-ovicidal). In order to investigate the dynamics of the system, we first define and calculate the optimal interval between treatment doses. We calculate the probability of eradication as a function of the number of optimally-timed successive treatment doses and the number of years over which a program is run. For the non-ovicidal intervention, we first show that at least two optimally-timed doses are required to achieve eradication. We then demonstrate that while more doses over a small number of years provides the highest chance of eradication, a similar outcome can be achieved with fewer doses delivered annually over a longer period of time. For the ovicidal intervention, we find that doses should be delivered as close together as possible. This work provides a platform for further research into optimal treatment strategies which may incorporate heterogeneity of transmission, and the interplay between MDA and enhancement of continuing scabies surveillance and treatment strategies.