Resource control of epidemic spreading through a multilayer network

While the amount of resource is an important factor in control of contagions, outbreaks may occur when they reach a finite fraction of the population. An unexplored issue is how much the resource amount is invested to control this outbreak. Here we analyze a mechanic model of epidemic spreading, which considers both resource factor and network layer. We find that there is a resource threshold, such that a significant fraction of the total population may be infected (i.e., an outbreak will occur) if the amount of resource is below this threshold, but the outbreak may be effectively eradicated if it is beyond the threshold. The threshold is dependent upon both the connection strength between the layers and their internal structure. We also find that the layer-layer connection strength can lead to the phase transition from the first-order phase to the continuous one or vice versa, whereas the internal connection can result in a different kind of phase transition (i.e., the so-called hybrid phase transition) apart from first-order and continuous one. Our results could have important implications for government decisions on public health resources devoted to epidemic disease control.