Individual-based optimal weight adaptation for heterogeneous epidemic spreading networks

We study epidemic spreading on arbitrary weighted, directed, and heterogeneous complex networks. We propose an individual-based weight adaptation mechanism in which individuals' contact strength is adaptable depending on the level of contagion spreading over the network. An optimal control formulation is presented to address the trade-off between the global infection level and the local weight adaptation cost corresponding to the topology of the underlying contact network. We prove the existence of a solution to the optimal control problem and obtain its explicit expression from a rigorous mathematical analysis. Additionally, we derive an approximation to the optimal solution and analyze its uniqueness with a specific cost function. In a series of numerical experiments, the forward-backward sweep method is adopted to verify the obtained theoretical results. Our findings uncover novel insights into the relationship between epidemic spreading on heterogeneous complex networks, the resulting dynamics of behavioral responses, and the associated control strategy costs, with important consequences for the future development of adaptive public health policies.