Could competition between antibiotic-vulnerable and antibiotic-resistant infections be used to manage resistance? Hypothetically, treating co-infected individuals those carrying both strains at once could promote antibiotic resistance. In the mathematical model, fitness tradeoffs between strains and different structures in the host population represent the effects of treatment schemes, with people divided into four compartments: susceptible, infected with one strain or the other, or infected with both simultaneously. We use the next generation matrix method to calculate R0 for the resistant and vulnerable strains, looking for situations where they experience competitive exclusion or coexistence, and focusing on those where resistance can invade. The model supports the hypothesis that treating doubly-infected individuals promotes antibiotic resistance, and in the future some simplifying assumptions shall be relaxed (perfect treatment implementation, for example) and in general more realistic treatment strategies that physicians use will be considered.