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Author: Molkenthin, Nora × Type: Article ×

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    Moving the epidemic tipping point through topologically targeted social distancing
    (Berlin ; Heidelberg : Springer, 2021) Ansari, Sara; Anvari, Mehrnaz; Pfeffer, Oskar; Molkenthin, Nora; Moosavi, Mohammad R.; Hellmann, Frank; Heitzig, Jobst; Kurths, Jürgen
    The epidemic threshold of a social system is the ratio of infection and recovery rate above which a disease spreading in it becomes an epidemic. In the absence of pharmaceutical interventions (i.e. vaccines), the only way to control a given disease is to move this threshold by non-pharmaceutical interventions like social distancing, past the epidemic threshold corresponding to the disease, thereby tipping the system from epidemic into a non-epidemic regime. Modeling the disease as a spreading process on a social graph, social distancing can be modeled by removing some of the graphs links. It has been conjectured that the largest eigenvalue of the adjacency matrix of the resulting graph corresponds to the systems epidemic threshold. Here we use a Markov chain Monte Carlo (MCMC) method to study those link removals that do well at reducing the largest eigenvalue of the adjacency matrix. The MCMC method generates samples from the relative canonical network ensemble with a defined expectation value of λmax . We call this the "well-controlling network ensemble" (WCNE) and compare its structure to randomly thinned networks with the same link density. We observe that networks in the WCNE tend to be more homogeneous in the degree distribution and use this insight to define two ad-hoc removal strategies, which also substantially reduce the largest eigenvalue. A targeted removal of 80% of links can be as effective as a random removal of 90%, leaving individuals with twice as many contacts. Finally, by simulating epidemic spreading via either an SIS or an SIR model on network ensembles created with different link removal strategies (random, WCNE, or degree-homogenizing), we show that tipping from an epidemic to a non-epidemic state happens at a larger critical ratio between infection rate and recovery rate for WCNE and degree-homogenized networks than for those obtained by random removals.
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    Ensemble analysis of complex network properties—an MCMC approach
    ([London] : IOP, 2022) Pfeffer, Oskar; Molkenthin, Nora; Hellmann, Frank
    What do generic networks that have certain properties look like? We use relative canonical network ensembles as the ensembles that realize a property R while being as indistinguishable as possible from a background network ensemble. This allows us to study the most generic features of the networks giving rise to the property under investigation. To test the approach we apply it to study properties thought to characterize ‘small-world networks’. We consider two different defining properties, the ‘small-world-ness’ of Humphries and Gurney, as well as a geometric variant. Studying them in the context of Erdős-Rényi and Watts-Strogatz ensembles we find that all ensembles studied exhibit phase transitions to systems with large hubs and in some cases cliques. Such features are not present in common examples of small-world networks, indicating that these properties do not robustly capture the notion of small-world networks. We expect the overall approach to have wide applicability for understanding network properties of real world interest, such as optimal ride-sharing designs, the vulnerability of networks to cascades, the performance of communication topologies in coordinating fluctuation response or the ability of social distancing measures to suppress disease spreading.
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    Scaling Laws of Collective Ride-Sharing Dynamics
    (College Park, Md. : APS, 2020) Molkenthin, Nora; Schröder, Malte; Timme, Marc
    Ride-sharing services may substantially contribute to future sustainable mobility. Their collective dynamics intricately depend on the topology of the underlying street network, the spatiotemporal demand distribution, and the dispatching algorithm. The efficiency of ride-sharing fleets is thus hard to quantify and compare in a unified way. Here, we derive an efficiency observable from the collective nonlinear dynamics and show that it exhibits a universal scaling law. For any given dispatcher, we find a common scaling that yields data collapse across qualitatively different topologies of model networks and empirical street networks from cities, islands, and rural areas. A mean-field analysis confirms this view and reveals a single scaling parameter that jointly captures the influence of network topology and demand distribution. These results further our conceptual understanding of the collective dynamics of ride-sharing fleets and support the evaluation of ride-sharing services and their transfer to previously unserviced regions or unprecedented demand patterns.