The influence of time delay on epidemic spreading under limited resources

While epidemic spreading naturally involves time delay due to the order of propagation, its control depends on the resource amount to be devoted. However, it is unclear how time delay impacts epidemic spreading under limited resources. Here we analyze a simple model of epidemic spreading on a two-layer network, which considers both the time delay between the layers and the resource amount. Interestingly, we find that the delay can induce first-order, continuous and hybrid phases as well as transitions among them, depending on the resource amount, the connection strength between layers and their internal structures. In addition, we find that there is a critical threshold of time delay such that even a small resource amount can effectively control the epidemic spreading if the delay is beyond this threshold, and a large resource amount is needed otherwise. These findings would provide useful guidelines for government decisions on the control of epidemic spreading.