  The spread of disease on complex networks has attracted widely attention in
the physics community. Recent works have demonstrated that heterogeneous degree
and weight distributions have a significant influence on the epidemic dynamics.
In this study, a novel edge-weight based compartmental approach is developed to
estimate the epidemic threshold and epidemic size (final infected density) on
networks with general degree and weight distributions, and a remarkable
agreement with numerics is obtained. Even in complex network with the strong
heterogeneous degree and weight distributions, this approach is worked. We then
propose an edge-weight based removal strategy with different biases, and find
that such a strategy can effectively control the spread of epidemic when the
highly weighted edges are preferentially removed, especially when the weight
distribution of a network is extremely heterogenous. The theoretical results
from the suggested method can accurately predict the above removal
effectiveness.
