During epidemic control, containment of the disease is usually achieved through increasing a devoted resource to reduce the infectiousness. However, the impact of this resource expenditure has not been studied quantitatively. For disease spread, the recovery rate can be positively correlated with the average amount of resource devoted to infected individuals. By incorporating this relation we build a novel model and find that insufficient resource leads to an abrupt increase in the infected population size, which is in marked contrast with the continuous phase transitions believed previously. Counterintuitively, this abrupt phase transition is more pronounced in less contagious diseases. Furthermore, we find that even for a single infection source, the public resource needs to be available in a significant amount, which is proportional to the total population size, to ensure epidemic containment. Our findings provide a theoretical foundation for efficient epidemic containment strategies in the early stage.