Plasmodium vivax poses unique challenges for malaria control and elimination, notably the potential for relapses to maintain transmission in the face of drug-based treatment and vector control strategies. We developed an individual-based mathematical model of P. vivax transmission calibrated to epidemiological data from Papua New Guinea (PNG). In many settings in PNG, increasing bed net coverage is predicted to reduce transmission to less than 0.1% prevalence by light microscopy, however there is substantial risk of rebounds in transmission if interventions are removed prematurely. In several high transmission settings, model simulations predict that combinations of existing interventions are not sufficient to interrupt P. vivax transmission. This analysis highlights the potential options for the future of P. vivax control: maintaining existing public health gains by keeping transmission suppressed through indefinite distribution of interventions; or continued development of strategies based on existing and new interventions to push for further reduction and towards elimination.