  In this paper, we study networks of positive linear systems subject to
time-invariant and random uncertainties. We present linear matrix inequalities
for checking the stability of the whole network around the origin with
prescribed probability and decay rate. Based on this condition, we then give an
efficient method, based on geometric programming, to find the optimal
parameters of the probability distribution describing the uncertainty. We
illustrate our results by analyzing the stability of a viral spreading process
in the presence of random uncertainties.
