  We propose a mathematical framework, based on conic geometric programming, to
control a susceptible-infected-susceptible viral spreading process taking place
in a directed contact network with unknown contact rates. We assume that we
have access to time series data describing the evolution of the spreading
process observed by a collection of sensor nodes over a finite time interval.
We propose a data-driven robust convex optimization framework to find the
optimal allocation of protection resources (e.g., vaccines and/or antidotes) to
eradicate the viral spread at the fastest possible rate. In contrast to current
network identification heuristics, in which a single network is identified to
explain the observed data, we use available data to define an uncertainty set
containing all networks that are coherent with empirical observations. Our
characterization of this uncertainty set of networks is tractable in the
context of conic geometric programming, recently proposed by Chandrasekaran and
Shah, which allows us to efficiently find the optimal allocation of resources
to control the worst-case spread that can take place in the uncertainty set of
networks. We illustrate our approach in a transportation network from which we
collect partial data about the dynamics of a hypothetical epidemic outbreak
over a finite period of time.
