  In this paper, we study the $SIS$ (susceptible-infected-susceptible) and
$SIR$ (susceptible-infected-removed) epidemic models on undirected, weighted
networks by deriving pairwise-type approximate models coupled with
individual-based network simulation. Two different types of
theoretical/synthetic weighted network models are considered. Both models start
from non-weighted networks with fixed topology followed by the allocation of
link weights in either (i) random or (ii) fixed/deterministic way. The pairwise
models are formulated for a general discrete distribution of weights, and these
models are then used in conjunction with network simulation to evaluate the
impact of different weight distributions on epidemic threshold and dynamics in
general. For the $SIR$ dynamics, the basic reproductive ratio $R_0$ is
computed, and we show that (i) for both network models $R_{0}$ is maximised if
all weights are equal, and (ii) when the two models are equally matched, the
networks with a random weight distribution give rise to a higher $R_0$ value.
The models are also used to explore the agreement between the pairwise and
simulation models for different parameter combinations.
