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  • Letter
  • Open Access

Epidemic criticality in temporal networks

Chao-Ran Cai1,2,*, Yuan-Yuan Nie1, and Petter Holme3,4,†

  • 1School of Physics, Northwest University, Xi'an 710127, China
  • 2Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China
  • 3Department of Computer Science, Aalto University, Espoo 02150, Finland
  • 4Center for Computational Social Science, Kobe University, Kobe 657–8501, Japan

  • *ccr@nwu.edu.cn
  • †petter.holme@aalto.fi
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Phys. Rev. Research 6, L022017 – Published 22 April, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L022017

Abstract

Analytical studies of network epidemiology almost exclusively focus on the extreme situations where the timescales of network dynamics are well separated (longer or shorter) from that of epidemic propagation. In realistic scenarios, however, these timescales could be similar, which has profound implications for epidemic modeling (e.g., one can no longer reduce the dimensionality of epidemic models). Combining Monte Carlo simulations and mean-field theory, we analyze the critical behavior of susceptible-infected-susceptible epidemics in the vicinity of the critical threshold on the activity-driven model of temporal networks. We find that the persistence of links in the network causes the threshold to decrease as the recovery rate increases. Dynamic correlations (coming from being close to infected nodes increases the likelihood of infection) drive the threshold in the opposite direction. These two counteracting effects make epidemic criticality in temporal networks a remarkably complex phenomenon.

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References (41)

  1. N. H. Fefferman and K. L. Ng, How disease models in static networks can fail to approximate disease in dynamic networks, Phys. Rev. E 76, 031919 (2007).
  2. S. Bansal, J. Read, B. Pourbohloul, and L. A. Meyers, The dynamic nature of contact networks in infectious disease epidemiology, J. Biol. Dyn. 4, 478 (2010).
  3. N. Masuda and P. Holme, Predicting and controlling infectious disease epidemics using temporal networks, F1000Prime Rep. 5, 6 (2013).
  4. N. Masuda and P. Holme, Introduction to temporal network epidemiology, in Temporal Network Epidemiology (Springer, Singapore, 2017), pp. 1–16.
  5. D. Soriano-Paños, G. Ghoshal, A. Arenas, and J. Gómez-Gardeñes, Impact of temporal scales and recurrent mobility patterns on the unfolding of epidemics, J. Stat. Mech. (2020) 024006.
  6. P. Holme, Temporal network structures controlling disease spreading, Phys. Rev. E 94, 022305 (2016).
  7. P. de Castro, F. Urbina, A. Norambuena, and F. Guzmán-Lastra, Sequential epidemic-like spread between agglomerates of self-propelled agents in one dimension, Phys. Rev. E 108, 044104 (2023).
  8. T. Gross, C. J. D. D'Lima, and B. Blasius, Epidemic dynamics on an adaptive network, Phys. Rev. Lett. 96, 208701 (2006).
  9. P. C. Ventura, A. Aleta, F. A. Rodrigues, and Y. Moreno, Epidemic spreading in populations of mobile agents with adaptive behavioral response, Chaos Soliton. Fract. 156, 111849 (2022).
  10. M. Hasler, V. Belykh, and I. Belykh, Dynamics of stochastically blinking systems. Part I: Finite time properties, SIAM J. Appl. Dyn. Syst. 12, 1007 (2013).
  11. N. Perra, B. Gonçalves, R. Pastor-Satorras, and A. Vespignani, Activity driven modeling of time varying networks, Sci. Rep. 2, 469 (2012).
  12. S. Liu, N. Perra, M. Karsai, and A. Vespignani, Controlling contagion processes in activity driven networks, Phys. Rev. Lett. 112, 118702 (2014).
  13. B. Ribeiro, N. Perra, and A. Baronchelli, Quantifying the effect of temporal resolution on time-varying networks, Sci. Rep. 3, 3006 (2013).
  14. A. Moinet, M. Starnini, and R. Pastor-Satorras, Random walks in non-Poissoinan activity driven temporal networks, New J. Phys. 21, 093032 (2019).
  15. M. Starnini and R. Pastor-Satorras, Topological properties of a time-integrated activity-driven network, Phys. Rev. E 87, 062807 (2013).
  16. M. Karsai, N. Perra, and A. Vespignani, Time varying networks and the weakness of strong ties, Sci. Rep. 4, 4001 (2014).
  17. A. Rizzo, M. Frasca, and M. Porfiri, Effect of individual behavior on epidemic spreading in activity-driven networks, Phys. Rev. E 90, 042801 (2014).
  18. E. Valdano, L. Ferreri, C. Poletto, and V. Colizza, Analytical computation of the epidemic threshold on temporal networks, Phys. Rev. X 5, 021005 (2015).
  19. K. Sun, A. Baronchelli, and N. Perra, Contrasting effects of strong ties on SIR and SIS processes in temporal networks, Eur. Phys. J. B 88, 326 (2015).
  20. L. Zino, A. Rizzo, and M. Porfiri, Continuous-time discrete-distribution theory for activity-driven networks, Phys. Rev. Lett. 117, 228302 (2016).
  21. A. Rizzo, B. Pedalino, and M. Porfiri, A network model for Ebola spreading, J. Theor. Biol. 394, 212 (2016).
  22. E. Ubaldi, N. Perra, M. Karsai, A. Vezzani, R. Burioni, and A. Vespignani, Asymptotic theory of time-varying social networks with heterogeneous activity and tie allocation, Sci. Rep. 6, 35724 (2016).
  23. I. Pozzana, K. Sun, and N. Perra, Epidemic spreading on activity-driven networks with attractiveness, Phys. Rev. E 96, 042310 (2017).
  24. M. Tizzani, S. Lenti, E. Ubaldi, A. Vezzani, C. Castellano, and R. Burioni, Epidemic spreading and aging in temporal networks with memory, Phys. Rev. E 98, 062315 (2018).
  25. L. Zino, A. Rizzo, and M. Porfiri, Modeling memory effects in activity-driven networks, SIAM J. Appl. Dyn. Syst. 17, 2830 (2018).
  26. P. Hu, L. Ding, and X. An, Epidemic spreading with awareness diffusion on activity-driven networks, Phys. Rev. E 98, 062322 (2018).
  27. A. Moinet, R. Pastor-Satorras, and A. Barrat, Effect of risk perception on epidemic spreading in temporal networks, Phys. Rev. E 97, 012313 (2018).
  28. M. Nadini, A. Rizzo, and M. Porfiri, Epidemic spreading in temporal and adaptive networks with static backbone, IEEE Trans. Netw. Sci. Eng. 7, 549 (2020).
  29. F. Parino, L. Zino, M. Porfiri, and A. Rizzo, Modelling and predicting the effect of social distancing and travel restrictions on COVID-19 spreading, J. R. Soc. Interface 18, 20200875 (2021).
  30. N. Gozzi, M. Scudeler, D. Paolotti, A. Baronchelli, and N. Perra, Self-initiated behavioral change and disease resurgence on activity-driven networks, Phys. Rev. E 104, 014307 (2021).
  31. B. Wang, Z. Xie, and Y. Han, Impact of individual behavioral changes on epidemic spreading in time-varying networks, Phys. Rev. E 104, 044307 (2021).
  32. C.-R. Cai, Z.-X. Wu, M. Z. Q. Chen, P. Holme, and J.-Y. Guan, Solving the dynamic correlation problem of the susceptible-infected-susceptible model on networks, Phys. Rev. Lett. 116, 258301 (2016).
  33. K. Y. Leung and O. Diekmann, Dangerous connections: On binding site models of infectious disease dynamics, J. Math. Biol. 74, 619 (2017).
  34. J. P. Rodríguez, M. Paoluzzi, D. Levis, and M. Starnini, Epidemic processes on self-propelled particles: Continuum and agent-based modeling, Phys. Rev. Res. 4, 043160 (2022).
  35. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L022017 for a representative code.
  36. M. Boguñá, C. Castellano, and R. Pastor-Satorras, Nature of the epidemic threshold for the susceptible-infected-susceptible dynamics in networks, Phys. Rev. Lett. 111, 068701 (2013).
  37. S. N. Chowdhury, S. Majhi, M. Ozer, D. Ghosh, and M. Perc, Synchronization to extreme events in moving agents, New J. Phys. 21, 073048 (2019).
  38. S. N. Chowdhury, S. Majhi, and D. Ghosh, Distance dependent competitive interactions in a frustrated network of mobile agents, IEEE Trans. Netw. Sci. Eng. 7, 3159 (2020).
  39. G. Mikaberidze, S. N. Chowdhury, A. Hastings, and R. M. D'Souza, Consensus formation among mobile agents in networks of heterogeneous interaction venues, Chaos Soliton. Fract. 178, 114298 (2024).
  40. A. Badie-Modiri, A. K. Rizi, M. Karsai, and M. Kivelä, Directed percolation in temporal networks, Phys. Rev. Res. 4, L022047 (2022).
  41. A. Badie-Modiri, A. K. Rizi, M. Karsai, and M. Kivelä, Directed percolation in random temporal network models with heterogeneities, Phys. Rev. E 105, 054313 (2022).

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Phys. Rev. Research 6, L022017– Published 22 April, 2024
  • Received 21 November 2023
  • Accepted 21 February 2024
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