Analytical Computation of the Epidemic Threshold on Temporal Networks
The time variation of contacts in a networked system may fundamentally alter the properties of spreading processes and affect the condition for large-scale propagation, as encoded in the epidemic threshold. Despite the great interest in the problem for the physics, applied mathematics, computer scie...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2015-04-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/PhysRevX.5.021005 |
| _version_ | 1819010945592066048 |
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| author | Eugenio Valdano Luca Ferreri Chiara Poletto Vittoria Colizza |
| author_facet | Eugenio Valdano Luca Ferreri Chiara Poletto Vittoria Colizza |
| author_sort | Eugenio Valdano |
| collection | DOAJ |
| description | The time variation of contacts in a networked system may fundamentally alter the properties of spreading processes and affect the condition for large-scale propagation, as encoded in the epidemic threshold. Despite the great interest in the problem for the physics, applied mathematics, computer science, and epidemiology communities, a full theoretical understanding is still missing and currently limited to the cases where the time-scale separation holds between spreading and network dynamics or to specific temporal network models. We consider a Markov chain description of the susceptible-infectious-susceptible process on an arbitrary temporal network. By adopting a multilayer perspective, we develop a general analytical derivation of the epidemic threshold in terms of the spectral radius of a matrix that encodes both network structure and disease dynamics. The accuracy of the approach is confirmed on a set of temporal models and empirical networks and against numerical results. In addition, we explore how the threshold changes when varying the overall time of observation of the temporal network, so as to provide insights on the optimal time window for data collection of empirical temporal networked systems. Our framework is of both fundamental and practical interest, as it offers novel understanding of the interplay between temporal networks and spreading dynamics. |
| first_indexed | 2024-12-21T01:20:20Z |
| format | Article |
| id | doaj.art-3012201ae71f404292c757b98a614862 |
| institution | Directory Open Access Journal |
| issn | 2160-3308 |
| language | English |
| last_indexed | 2024-12-21T01:20:20Z |
| publishDate | 2015-04-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj.art-3012201ae71f404292c757b98a6148622022-12-21T19:20:40ZengAmerican Physical SocietyPhysical Review X2160-33082015-04-015202100510.1103/PhysRevX.5.021005Analytical Computation of the Epidemic Threshold on Temporal NetworksEugenio ValdanoLuca FerreriChiara PolettoVittoria ColizzaThe time variation of contacts in a networked system may fundamentally alter the properties of spreading processes and affect the condition for large-scale propagation, as encoded in the epidemic threshold. Despite the great interest in the problem for the physics, applied mathematics, computer science, and epidemiology communities, a full theoretical understanding is still missing and currently limited to the cases where the time-scale separation holds between spreading and network dynamics or to specific temporal network models. We consider a Markov chain description of the susceptible-infectious-susceptible process on an arbitrary temporal network. By adopting a multilayer perspective, we develop a general analytical derivation of the epidemic threshold in terms of the spectral radius of a matrix that encodes both network structure and disease dynamics. The accuracy of the approach is confirmed on a set of temporal models and empirical networks and against numerical results. In addition, we explore how the threshold changes when varying the overall time of observation of the temporal network, so as to provide insights on the optimal time window for data collection of empirical temporal networked systems. Our framework is of both fundamental and practical interest, as it offers novel understanding of the interplay between temporal networks and spreading dynamics.http://doi.org/10.1103/PhysRevX.5.021005 |
| spellingShingle | Eugenio Valdano Luca Ferreri Chiara Poletto Vittoria Colizza Analytical Computation of the Epidemic Threshold on Temporal Networks Physical Review X |
| title | Analytical Computation of the Epidemic Threshold on Temporal Networks |
| title_full | Analytical Computation of the Epidemic Threshold on Temporal Networks |
| title_fullStr | Analytical Computation of the Epidemic Threshold on Temporal Networks |
| title_full_unstemmed | Analytical Computation of the Epidemic Threshold on Temporal Networks |
| title_short | Analytical Computation of the Epidemic Threshold on Temporal Networks |
| title_sort | analytical computation of the epidemic threshold on temporal networks |
| url | http://doi.org/10.1103/PhysRevX.5.021005 |
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