  Resource diffusion is an ubiquitous phenomenon, but how it impacts epidemic
spreading has received little study. We propose a model that couples epidemic
spreading and resource diffusion in multiplex networks. The spread of disease
in a physical contact layer and the recovery of the infected nodes are both
strongly dependent upon resources supplied by their counterparts in the social
layer. The generation and diffusion of resources in the social layer are in
turn strongly dependent upon the state of the nodes in the physical contact
layer. Resources diffuse preferentially or randomly in this model. To quantify
the degree of preferential diffusion, a bias parameter that controls the
resource diffusion is proposed. We conduct extensive simulations and find that
the preferential resource diffusion can change phase transition type of the
fraction of infected nodes. When the degree of interlayer correlation is below
a critical value, increasing the bias parameter changes the phase transition
from double continuous to single continuous. When the degree of interlayer
correlation is above a critical value, the phase transition changes from
multiple continuous to first discontinuous and then to hybrid. We find
hysteresis loops in the phase transition. We also find that there is an optimal
resource strategy at each fixed degree of interlayer correlation where the
threshold reaches a maximum and under which the disease can be maximally
suppressed. In addition, the optimal controlling parameter increases as the
degree of inter-layer correlation increases.
