Non-trivial Resource Amount Requirement in the Early Stage for Containing Fatal Diseases

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.