  In this paper, we propose a model predictive control (MPC) method for
real-time intervention of spreading processes, such as epidemics and wildfire,
over large-scale networks. The goal is to allocate budgeted resources each time
step to minimize the risk of an undetected outbreak, i.e. the product of the
probability of an outbreak and the impact of that outbreak. By using dynamic
programming relaxation, the MPC controller is reformulated as a convex
optimization problem, in particular an exponential cone programming. We also
provide sufficient conditions for the closed-loop risks to asymptotically
decrease and a method to estimate the upper bound of when the risk will
monotonically decrease. Numerical results are provided for a wildfire example.
