Optimal Network-based Intervention in the Presence of Undetectable Viruses

This letter presents an optimal control framework to reduce the spread of viruses in networks. The network is modeled as an undirected graph of nodes and weighted links. We consider the spread of viruses in a network as a system, and the total number of infected nodes as the state of the system, while the control function is the weight reduction leading to slow/reduce spread of viruses. Our epidemic model overcomes three assumptions that were extensively used in the literature and produced inaccurate results. We apply the optimal control formulation to crucial network structures. Numerical results show the dynamical weight reduction and reveal the role of the network structure and the epidemic model in reducing the infection size in the presence of indiscernible infected nodes.