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Plasmodium (P.) falciparum and P. vivax are the two most common causes of malaria. While the majority of deaths and severe morbidity are due to P. falciparum, P. vivax poses a greater challenge to eliminating malaria outside of Africa due to its ability to form latent liver stage parasites (hypnozoites), which can cause relapsing episodes within an individual patient. In areas where P. falciparum and P. vivax are co-endemic, individuals can carry parasites of both species simultaneously. These mixed infections complicate dynamics in several ways; treatment of mixed infections will simultaneously affect both species, P. falciparum can mask the detection of P. vivax, and it has been hypothesised that clearing P. falciparum may trigger a relapse of dormant P. vivax. When mixed infections are treated for only blood-stage parasites, patients are at risk of relapse infections due to P. vivax hypnozoites. We present a stochastic mathematical model that captures interactions between P. falciparum and P. vivax, and incorporates both standard schizontocidal treatment (which targets blood-stage parasites) and radical treatment (which additionally targets liver-stage parasites). We apply this model to assess the implications of different treatment coverage of radical cure for mixed and P. vivax infections and a so-called "unified radical cure" treatment strategy for P. falciparum, P. vivax and mixed infections. We find that a unified radical cure strategy, with G6PD screening, leads to a substantially lower incidence of malaria cases and deaths overall. We perform a one-way sensitivity analysis to highlight important model parameters.