Ragweed is an Invasive Alien Species natively growing in North America which is at risk of being introduced in Denmark thru import of bird seeds. The plant produces a high amount of pollen which causes allergy and asthma and is considered a very potent allergy source. It is estimated that 100.000 new cases of allergy and asthma will emerge if rag weed is fully established in Denmark leading to significant socio economic costs. As ragweed has not yet established in Denmark the management options are open for discussion. In this paper two basic options are analyzed: a. Prevention of introduction or b. Do nothing and treat the allergy symptoms thru standard medical care. The analysis shows that the costs of preventing introduction of ragweed thru yearly control campaigns is significantly lower than the costs of treating the allergy symptoms, implying that preventing introduction is the efficient and preferable management strategy. The robustness of the conclusions is tested by sensitivity analysis of the driving assumptions and is show that the conclusions hold even if the control costs are doubled and the benefits are reduced by 50%.