Abstract Ecological and socio-economic impacts from biological invasions are rapidly escalating worldwide. While effective management underpins impact mitigation, such actions are often delayed, insufficient or entirely absent. Presently, management delays emanate from a lack of monetary rationale to invest at early invasion stages, which precludes effective prevention. Here, we provide such rationale by developing a conceptual model, based on logistic growth, to quantify the cost of inaction towards invasive alien species under varying time delays and management efforts. Further, we apply the resulting model to management and damage data from a relatively data-rich genus ( Aedes mosquitoes). Our model confirms that rapid management interventions following invasion drastically minimise costs, and that higher management investments lead to much steeper cost declines. Further, we identify a ‘runaway’ point beyond which costs of inaction slowly approach saturation. Any management action during this phase can be considered severely delayed, resulting in substantial losses. For Aedes , we estimated that a management delay of just 20 years could have accrued additional costs of at least US$ 842 million in 40 years, whereas in the case of no management, inaction costs could have been approximately three-fold higher, totalling US$ 2433 million. These results highlight the need for more timely management of invasive alien species by demonstrating how early investments rapidly reduce long-term economic impacts.