Abstract
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.
Highlights
Epidemic spreading is typically a dynamical process
We investigate the influence of resource amount (R) on two final infected subpopulations quantified by ρ1 and ρ2
In contrast to previous studies that considered only single layer networks and did not consider resource factor, the present work considered resource amount invested to epidemic control and a two-layer network consisting of two random networks sharing the same set of nodes
Summary
Epidemic spreading is typically a dynamical process. In previous studies[1,2,3,4,5,6,7,8,9], the spreading was considered to be in single or monoplex networks, which is apparently a simplification since in reality, epidemic diseases spread often through multiple channels, e.g., through different ways of human travelling (airports, train, bus, etc.), just as information may be diffused through different online social mediums such as Twitter and Facebook. Shai et al studied a model of a constrained SIR process on coupled networks where nodes are limited to interact with a maximum number of neighbors[22] They found that in the absence of resource constraint, positive correlation coupling leads to a lower epidemic threshold than a negative one. In the present paper, inspired mainly by the work of ref.[24], we study the effect of resource amount on epidemic control using a modified SIS model This model considers a two-layer network consisting of two random networks A and B sharing the same set of nodes, as shown, where the infected nodes in one subnetwork can pass the disease to their neighbors in another subnetwork until they recover. We find interesting dynamical phenomena, e.g., given a resource amount, the spreading process goes through a first-order phase transition if the infection strength between layers is weak, but a continuous phase transition if the infection strength becomes strong, and the topological structure within a layer network can lead to a multi-phase behavior apart from first-order and continuous phase transitions
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