Abstract
Real networks, like the international airport network and the Internet, are composed of interconnected layers (or communities) through a small fraction of nodes that we call here 'bridge nodes'. These nodes are crucial in the spreading of epidemics because they enable the spread the disease to the entire system. In this work we study the effect of the bridge nodes on the susceptible-infected-recovered model in a two layer network with a small fraction r of these nodes. In the dynamical process, we theoretically determine that at criticality and for the limit r → 0, the time t b at which the first bridge node is infected diverges as a power-law with r, while above criticality, it appears a crossover between a logarithmic and a power-law behavior. Additionally, in the steady state at criticality, the fraction of recovered nodes scales with r as a power-law whose exponent can be understood from the finite size cluster distribution at criticality.
| Original language | English |
|---|---|
| Article number | 125003 |
| Journal | New Journal of Physics |
| Volume | 20 |
| Issue number | 12 |
| DOIs | |
| State | Published - 14 Dec 2018 |
Bibliographical note
Publisher Copyright:© 2018 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft and the Institute of Physics.
Funding
SH thanks the Israel Science Foundation, ONR, Army Research Office (ARO), the Israel Ministry of Science and Technology (MOST) with the Italy Ministry of Foreign Affairs, BSF-NSF, MOST with the Japan Science and Technology Agency, the BIU Center for Research in Applied Cryptography and Cyber Security, and DTRA (Grant no. HDTRA-1-10-1-0014) for financial support. LAB wishes to thank to UNMdP and CONICET (PIP 00443/2014) for financial support. HHAR also acknowledges the financial support from INTERNACIONAL No. 100/2018 PRPGI/IFMA; and UNIVERSAL-01429/16 FAPEMA. Work at Boston University is supported by NSF Grants PHY-1505000, CMMI1125290, and CHE-1213217, and by DTRA Grant HDTRA1-14-1-0017. HES thanks Project 71601112 by National Science Foundation of China for financial support. We thank Dr Gaogao Dong for useful discussions. SH thanks the Israel Science Foundation, ONR, Army Research Office (ARO), the Israel Ministry of Science and Technology (MOST) with the Italy Ministry of Foreign Affairs, BSF-NSF,MOSTwith the Japan Science and Technology Agency, the BIU Center for Research in Applied Cryptography and Cyber Security, and DTRA (Grant no. HDTRA-1-10-1- 0014) for financial support. LAB wishes to thank toUNMdPand CONICET (PIP 00443/2014) for financial support.HHARalso acknowledges the financial support from INTERNACIONAL No. 100/2018 PRPGI/IFMA; and UNIVERSAL-01429/16 FAPEMA. Work at Boston University is supported by NSF Grants PHY-1505000, CMMI1125290, and CHE-1213217, and by DTRAGrant HDTRA1-14-1-0017. HES thanks Project 71601112 by National Science Foundation of China for financial support.Wethank Dr Gaogao Dong for useful discussions.
| Funders | Funder number |
|---|---|
| BSF-NSF | |
| Israel Ministry of Science and Technology | |
| National Science Foundation | CMMI1125290, PHY-1505000, 71601112, HDTRA1-14-1-0017, CHE-1213217 |
| Office of Naval Research | |
| Army Research Office | |
| Defense Threat Reduction Agency | |
| National Natural Science Foundation of China | |
| Japan Science and Technology Agency | HDTRA-1-10-1-0014 |
| Consejo Nacional de Investigaciones Científicas y Técnicas | UNIVERSAL-01429/16 FAPEMA, PIP 00443/2014, 100/2018 PRPGI/IFMA |
| Ministry of Science and Technology | |
| Israel Science Foundation | |
| Ministry for Foreign Affairs | |
| Universidad Nacional de Mar del Plata | |
| National Science Foundation |
Keywords
- SIR model
- epidemic modeling
- multilayer networks
- percolation