Background: This work used mathematical modelling to explore effective policy for hepatitis C virus (HCV) treatment in Australia in the context of methadone maintenance treatment (MMT).Method: We consider two models to depict HCV in the population of injecting drug users (IDU) within Australia. The first model considers the IDU population as a whole. The second model includes separate components for those that are or are not enrolled in MMT. The impact of different levels of HCV treatment and its allocation dependent on MMT status were then determined in terms of the steady state levels of each of these models.Results: Although increasing levels of HCV treatment decrease chronic infection prevalence, initially numbers of acutely infected can rise. This is caused by the high rate of reinfection. We find that no matter the extent of HCV treatment, HCV prevalence cannot be eliminated without limiting risk behaviour. Assuming equal adherence to HCV therapy between MMT and non-MMT, over 84% of HCV treatment should be allocated to those not in MMT. Only if adherence to HCV therapy in non MMT patients falls below 44% of that in MMT then treatment should be preferentially directed to those in MMT.Conclusions: Contrary to generally held beliefs regarding HCV treatment the majority of therapy should be allocated to those that are still actively injecting. This is due to rates of reinfection and to the high turnover of individuals in MMT. Higher adherence to HCV therapy in MMT would need to be achieved before this changed.

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a b s t r a c tIn this paper we generalize a one-dimensional optimal control problem with DNSS property to a two-dimensional optimal control problem. This is done by taking the direct product of the model with itself, i.e. we combine two similar system dynamics under a joint objective functional that is separable in both states and controls. This framework can be applied to the construction of various optimal control problems, such as optimal marketing of related products, optimal growth of separate but interacting economies, or optimal control of two related capital stocks.We study such a system for a particular case drawn from the domain of drug control. The main result of this paper is that in this domain even a modest amount of interaction can sometimes make a very big difference. Hence, drawing conclusions by simplifying the real world into two independent, one-dimensional models may be problematic.Methodologically the combination of two systems with DNSS property leads to a fascinating series of situations with multiple optimal steady states and associated threshold behavior. These instances reflect some important recent developments in optimal dynamic control theory.