In this paper we study disease spread over a randomly switched network, which
is modeled by a stochastic switched differential equation based on the so
called N-intertwined model for disease spread over static networks. Assuming
that all the edges of the network are independently switched, we present
sufficient conditions for the convergence of infection probability to zero.
Though the stability theory for switched linear systems can naively derive a
necessary and sufficient condition for the convergence, the condition cannot be
used for large-scale networks because, for a network with n agents, it
requires computing the maximum real eigenvalue of a matrix of size exponential
in n. On the other hand, our conditions that are based also on the spectral
theory of random matrices can be checked by computing the maximum real
eigenvalue of a matrix of size exactly n