  Our $N$-intertwined model (now called NIMFA) for virus spread in any network
with $N$ nodes is extended to a full heterogeneous setting. The metastable
steady-state nodal infection probabilities are specified in terms of a
generalized Laplacian, that possesses analogous properties as the classical
Laplacian in graph theory. The critical threshold that separates global network
infection from global network health is characterized via an $N$ dimensional
vector that makes the largest eigenvalue of a modified adjacency matrix equal
to unity. Finally, the steady-state infection probability of node $i$ is convex
in the own curing rate $\delta_{i}$, but concave in the curing rates
$\delta_{j}$ of the other nodes $1\leq j\neq i\leq N$ in the network.
