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We develop some basic principles for the design and robustness analysis of a continuous-time bilinear dynamical network, where an attacker can manipulate the strength of the interconnections/edges between some of the agents/nodes. We formulate the edge protection optimization problem of picking a limited number of attack-free edges and minimizing the impact of the attack over the bilinear dynamical network. In particular, the H2-norm of bilinear systems is known to capture robustness and performance properties analogous to its linear counterpart and provides valuable insights for identifying which edges are most sensitive to attacks. The exact optimization problem is combinatorial in the number of edges, and brute-force approaches show poor scalability. However, we show that the H2-norm as a cost function is supermodular and, therefore, allows for efficient greedy approximations of the optimal solution. We illustrate and compare the effectiveness of our theoretical findings via numerical simulation
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Continuous-Time Simulation of Epidemic Processes on Dynamic Interaction Networks
Contagious processes on networks, such as spread of disease through physical proximity or information diffusion over social media, are continuous-time processes that depend upon the pattern of interactions between the individuals in the network. Continuous-time stochastic epidemic models are a natural fit for modeling the dynamics of such processes. However, prior work on such continuous-time models doesn’t consider the dynamics of the underlying interaction network which involves addition and removal of edges over time. Instead, researchers have typically simulated these processes using discrete-time approximations, in which one has to trade off between high simulation accuracy and short computation time. In this paper, we incorporate continuous-time network dynamics (addition and removal of edges) into continuous-time epidemic simulations. We propose a rejection-sampling based approach coupled with the well-known Gillespie algorithm that enables exact simulation of the continuous-time epidemic process. Our proposed approach gives exact results, and the computation time required for simulation is reduced as compared to discrete-time approximations of comparable accuracy.
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- Award ID(s):
- 1755824
- PAR ID:
- 10099274
- Date Published:
- Journal Name:
- Proceedings of the International Conference on Social Computing, Behavioral-Cultural Modeling and Prediction and Behavior Representation in Modeling and Simulation
- Page Range / eLocation ID:
- 143 - 152
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1007/978-3-030-21741-9_15
