In this letter, we propose an epidemic model over temporal networks that explicitly encapsulates two different control actions. We develop our model within the theoretical framework of activity driven networks (ADNs), which have emerged as a valuable tool to capture the complexity of dynamical processes on networks, coevolving at a comparable time scale to the temporal network formation. Specifically, we complement a susceptible–infected–susceptible epidemic model with features that are typical of nonpharmaceutical interventions in public health policies: i) actions to promote awareness, which induce people to adopt self-protective behaviors, and ii) confinement policies to reduce the social activity of infected individuals. In the thermodynamic limit of large-scale populations, we use a mean-field approach to analytically derive the epidemic threshold, which offers viable insight to devise containment actions at the early stages of the outbreak. Through the proposed model, it is possible to devise an optimal epidemic control policy as the combination of the two strategies, arising from the solution of an optimization problem. Finally, the analytical computation of the epidemic prevalence in endemic diseases on homogeneous ADNs is used to optimally calibrate control actions toward mitigating an endemic disease. Simulations are provided to support our theoretical results.
This content will become publicly available on January 1, 2023
Depth-Separation with Multilayer Mean-Field Networks
Mean-field limit has been successfully applied to neural networks, leading to many results in optimizing overparametrized networks. However, existing works often focus on two-layer networks and/or require large number of neurons. We give a new framework for extending the mean-field limit to multilayer network, and show that a polynomial-size three-layer network in our framework can learn the function constructed by Safran et al. (2019) – which is known to be not approximable by any two-layer networks
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