  Optimal control of interdependent epidemics spreading over complex networks
is a critical issue. We first establish a framework to capture the coupling
between two epidemics, and then analyze the system's equilibrium states by
categorizing them into three classes, and deriving their stability conditions.
The designed control strategy globally optimizes the trade-off between the
control cost and the severity of epidemics in the network. A gradient descent
algorithm based on a fixed point iterative scheme is proposed to find the
optimal control strategy. The optimal control will lead to switching between
equilibria of the interdependent epidemics network. Case studies are used to
corroborate the theoretical results finally.
