A ”plasma needle” is a cold plasma source operating at atmospheric pressure. Such sources interact strongly with living cells, but experimental studies on bacterial samples show that this interaction has a surprising pattern resulting in circular or annular killing structures. This paper presents numerical simulations showing that this pattern occurs because biologically active reactive oxygen and nitrogen species are produced dominantly where effluent from the plasma needle interacts with ambient air. A novel solution strategy is utilised coupling plasma produced neutral(uncharged) reactive species to the gas dynamics solving for steady state profiles at the treated biological surface. Numerical results are compared with experimental reports corroborating evidence for atomic oxygen as a key bactericidal species. Surface losses are considered for interaction of plasma produced reactants with reactive solid and liquid interfaces. Atomic oxygen surface reactions on a reactive solid surface with adsorption probabilities above 0.1 are shown to be limited by the flux of atomic oxygen from the plasma. Interaction of the source with an aqueous surface showed hydrogen peroxide as the dominant species at this interface.