  During an epidemic control, the containment of the disease is usually
achieved through increasing devoted resource to shorten the duration of
infectiousness. However, the impact of this resource expenditure has not been
studied quantitatively. Using the well-documented cholera data, we observe
empirically that the recovery rate which is related to the duration of
infectiousness has a strong positive correlation with the average resource
devoted to the 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 the less contagious diseases, which usually
correspond to the most fatal ones. Furthermore, we find that even for a single
infection source, public resource needs to meet a significant amount, which is
proportional to the whole population size to ensure epidemic containment. Our
findings provide a theoretical foundation for efficient epidemic containment
strategies in the early stage.
