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Immunization strategies in directed networks

Department of Mathematics, Shanghai University, Shanghai 200444, China

Special Issues: Multiscale dynamics of infectious diseases, immune responses and therapeutics

Many complex systems can be modeled as directed networks, which can be regarded as a generalization of undirected networks. In this paper, epidemic dynamics and immunization strategies in directed networks are studied. First, a Susceptible-Infected-Susceptible (SIS) model on a directed network is established employing the mean-field method, and its dynamics and epidemic threshold of the network are studied. Then based on the continuous degree technique, namely, considering the degree of a node as a continuous variable, we propose a method to calculate the epidemic threshold of the immunized network. Besides, some immunization strategies, including optimal immunization, random immunization, combined targeted immunization, and combined acquaintance immunization, and three special networks are considered. Finally, through numerical analysis, all immunization strategies are simulated and compared on different types of networks. We find that the nodes with the largest product of in-degree and out-degree are the most worthy of being immunized.
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Keywords directed network; optimal immunization; random immunization; combined targeted immunization; combined acquaintance immunization

Citation: Junbo Jia, Wei Shi, Pan Yang, Xinchu Fu. Immunization strategies in directed networks. Mathematical Biosciences and Engineering, 2020, 17(4): 3925-3952. doi: 10.3934/mbe.2020218

References

  • 1. M. Newman, Networks, Oxford University Press, 2018.
  • 2. M. Faloutsos, P. Faloutsos, C. Faloutsos, On power-law relationships of the internet topology, Comput. Commun. Rev., 29 (1999), 251-262.
  • 3. G. Kossinets, D. J. Watts, Empirical analysis of an evolving social network, Science, 311 (1999), 88-90.
  • 4. D. J. Watts, S. H. Strogatz, Collective dynamics of small-world networks, Nature, 393 (1998), 440-442.
  • 5. J. Scott, Social network analysis, Sociology, 22 (1988), 109-127.
  • 6. E. H. Davidson, D. H. Erwin, Gene regulatory networks and the evolution of animal body plans, Science, 311 (2006), 796-800.
  • 7. P. Erdős, A. Rényi, On the evolution of random graphs, Publ. Math. Inst. Hung. Acad. Sci., 5 (1960), 17-60.
  • 8. A. L. Barabási, R. Albert, Emergence of scaling in random networks, Science, 286 (1999), 509- 512.
  • 9. M. E. J. Newman, M. Girvan, Finding and evaluating community structure in networks, Phys. Rev. E, 69 (2004), 026113.
  • 10. A. Clauset, M. E. J. Newman, C. Moore, Finding community structure in very large networks, Phys. Rev. E, 70 (2004), 066111.
  • 11. S. Fortunato, Community detection in graphs, Phys. Rep., 486 (2010), 75-174.
  • 12. H. Cherifi, G. Palla, B. K. Szymanski, X. Lu, On community structure in complex networks: Challenges and opportunities, Appl. Network Sci., 4 (2019), 1-35.
  • 13. A. Clauset, C. Moore, M. E. J. Newman, Hierarchical structure and the prediction of missing links in networks, Nature, 453 (2008), 98-101.
  • 14. R. Pastor-Satorras, A. Vespignani, Epidemic spreading in scale-free networks, Phys. Rev. Lett., 86 (2001), 3200.
  • 15. X. Fu, M. Small, G. Chen, Propagation Dynamics on Complex Networks: Models, Methods and Stability Analysis, John Wiley and Sons, 2013.
  • 16. M. Jalili, M. Perc, Information cascades in complex networks, J. Complex Networks, 5 (2017), 665-693.
  • 17. M. Nadini, K. Sun, E. Ubaldi, M. Starnini, A. Rizzo, N. Perra, Epidemic spreading in modular time-varying networks, Sci. Rep., 8 (2018), 1-11.
  • 18. J. Jia, Z. Jin, X. Fu, Epidemic spread in directed interconnected networks, Commun. Nonlinear Sci. Numeri. Simul., 75 (2019), 1-13.
  • 19. C. Pizzuti, A. Socievole, Epidemic spreading curing strategy over directed networks, in International Conference on Numerical Computations: Theory and Algorithms, Springer, Cham, (2020), 182-194.
  • 20. L. Meyers, M. Newman, B. Pourbohloul, Predicting epidemics on directed contact networks, J. Theor. Biol., 240 (2006), 400-418.
  • 21. X. Zhang, G. Sun, Y. Zhu, J. Ma, Z. Jin, Epidemic dynamics on semi-directed complex networks, Math. Biosci., 246 (2013), 242-251.
  • 22. M. Moslonka-Lefebvre, T. Harwood, M. J. Jeger, M. Pautasso, SIS along a continuum (SISc) epidemiological modelling and control of diseases on directed trade networks, Math. Biosci., 236 (2012), 44-52.
  • 23. D. H. Zanette, M. Kuperman, Effects of immunization in small-world epidemics, Phys. A: Stat. Mech. Appl., 309 (2002), 445-452.
  • 24. R. Pastor-Satorras, A. Vespignani, Immunization of complex networks, Phys. Rev. E, 65 (2002), 036104.
  • 25. N. Madar, T. Kalisky, R. Cohen, D. Ben-avraham, S. Havlin, Immunization and epidemic dynamics in complex networks, Eur. Phys. J. B, 38 (2004), 269-276.
  • 26. R. Cohen, S. Havlin, D. Ben-Avraham, Efficient immunization strategies for computer networks and populations, Phys. Rev. Lett., 91 (2003), 247901.
  • 27. D. Chakraborty, A. Singh, H. Cherifi, Immunization strategies based on the overlapping nodes in networks with community structure, in International Conference on Computational Social Networks, Springer, Cham, (2016), 62-73.
  • 28. X. Fu, M. Small, D. M. Walker, H. Zhang, Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization, Phys. Rev. E, 77 (2008), 036113.
  • 29. Y. Yang, A. McKhann, S. Chen, G. Harling, J. P. Onnela, Efficient vaccination strategies for epidemic control using network information, Epidemics, 27 (2019), 115-122.
  • 30. J. Jia, Z. Jin, L. Chang, X. Fu, Structural calculations and propagation modeling of growing networks based on continuous degree, Math. Biosci. Eng., 14 (2017), 1215-1232.
  • 31. J. Joo, J. L. Lebowitz, Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation, Phys. Rev. E, 69 (2004), 066105.
  • 32. T. Zhou, J. Liu, W. Bai, G. Chen, B. Wang, Behaviors of susceptible-infected epidemics on scalefree networks with identical infectivity, Phys. Rev. E, 74 (2006), 056109.
  • 33. C. Nowzari, V. M. Preciado, G. J. Pappas, Analysis and control of epidemics: A survey of spreading processes on complex networks, IEEE Control Syst. Mag., 36 (2016), 26-46.
  • 34. R. Noldus, P. Van Mieghem, Assortativity in complex networks, J. Complex Networks, 3 (2015), 507-542.
  • 35. N. Gupta, A. Singh, H. Cherifi, Community-based immunization strategies for epidemic control, in 2015 7th International Conference on Communication Systems and Networks (COMSNETS), IEEE, 2015.

 

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