Disease Spreading through Complex Small World Networks

Main Article Content

H. E. Benítez F. E. Cornes C. O. Dorso G.A. Frank

Abstract

The end of the COVID-19 pandemic allows an analysis in retrospect of the spread and early containment scenarios of the disease. Today we can weigh the diversity of results imposed by highly heterogeneous urban landscapes (both geographical and social). In this research, we address scenarios of one or more communities (neighborhoods) formed by small structures with strong connectivity among themselves (families). Special attention was paid to the early containment of the epidemic. After simulating many scenarios, it was observed that early isolation of the infected individuals is more efficient than the isolation of their entire family. But we also noted that the containment of the disease loses effectiveness if the clinical tests for its detection are reported late (from 1 to 4 days). On the other hand, the existence of neighborhoods (with high population density) complicates the disease containment strategies, since (a) the disease spreads faster due to the highly dense environment, and (b) these act as “hubs of contagion”, even if the disease itself is of low contagiousness.

Keywords: complex networks, small world, COVID-19

Article Details

How to Cite
BENÍTEZ, H. E. et al. Disease Spreading through Complex Small World Networks. Medical Research Archives, [S.l.], v. 12, n. 8, aug. 2024. ISSN 2375-1924. Available at: <https://esmed.org/MRA/mra/article/view/5706>. Date accessed: 06 sep. 2024. doi: https://doi.org/10.18103/mra.v12i8.5706.
Section
Research Articles

References

1. C. Heine, K. O’Keeffe, P. Santi, Travel distance, frequency of return, and the spread of disease, Sci Rep. 13, 14064 (2023).
2. A. Medus, C. Dorso, Diseases spreading through individual based models with realistic mobility patterns., arXiv:1104.4913 [q-bio.PE] (2011).
3. S. E. Eikenberry, M. Mancuso, E. Iboi, T. Phan, K. Eikenberry, Y. Kuang, E. Kostelich, A. B. Gumel, To mask or not to mask: Modeling the potential for face mask use by the general public to curtail the covid-19 pandemic, Infectious Disease Modelling 5, 293-308 (2020).
4. X. Zhang, Y. Song, H. Wanga, G.-P. Jiang, Epidemic spreading combined with age and region in complex networks, Hindawi Mathematical Problems in Engineering 5 (2020).
5. D. Barmak, C. Dorso, M. Otero, Modelling dengue epidemic with human mobility, Physica A 47 129-140 (2016).
6. F. Cornes, G. Frank, C. Dorso, Covid-19 spreading under containment actions, Physica A: Statistical Mechanics and its Applications 588, 126566 (2022).
7. F. Cornes, G. Frank, C. Dorso, Estrategia cíclica de aislamiento y actividad económica durante la pandemia covid-19., Anales AFA 31(4) (2021).
8. Y. M. Bar-On, A. Flamholz, R. Phillips, R. Milo, Science forum: Sars-cov-2 (covid-19) by the numbers, eLife 9, e57309 (2020).
9. R. Li, S. Pei, B. Chen, Y. Song, T. Zhang,W. Yang, J. Shaman, Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (covid-19), medRxiv (2020).
10. J. Read, J. Bridgen, D. Cummings, A. Ho, C. Jewell, Novel coronavirus 2019-ncov: early estimation of epidemiological parameters and epidemic predictions, Philosophical Transactions of the Royal Society b: Biological Sciences 376, 376 (2021).
11. A. J. Kucharski, T. W. Russell, C. Diamond, Y. Liu, C. nCoV working group, J. Edmunds, S. Funk, R. M. Eggo, Early dynamics of transmission and control of covid-19: a mathematical modelling study, medRxiv (2020).
12. X.-Y. Yan, C. Zhao, Y. Fan, Z. Di, W.-X. Wang, Universal predictability of mobility patterns in cities, Journal of The Royal Society Interface 11 (2013).
13. D. Brockmann, L. Hufnagel, T. Geisel, The scaling laws of human travel., Nature 439, 462-465 (2006).
14. M. González, C. Hidalgo, A. Barabási, Understanding individual human mobility patterns, Nature 453, 779-782 (2008).
15. I. Rhee, M. Shin, S. Hong, K. Lee, S. Chong, On the levy-walk nature of human mobility., IEEE INFOCOM 2008 - The 27th Conference on Computer Communications, Phoenix, AZ, USA. 924-932 (2008).
16. M. Ahsanullah, V. Nevzorov, Some inferenceson the levy distribution., Journal of Statistical Theory and Applications 13(3) 205-211 (2014).
17. I. A. Perez, M. A. Di Muro, C. E. La Rocca, L. A. Braunstein, Disease spreading with social distancing: A prevention strategy in disordered multiplex networks, Phys. Rev. E 102 022310 (2020).
18. L. Valdez, L. Braunstein, S. Havlin, Epidemic spreading on modular networks: The fear to declare a pandemic., Phys. Rev. E. 101 032309 (2020).
19. M. Kuperman, G. Abramson, Small world effect in an epidemiological model., Phys. Rev. Lett. 86, 2909 (2001).
20. H. Wearing, M. P. Rohani, Appropriate models for the management of infectious diseases., PloS Medicine 2(7) 0621–0627 (2005).
21. P. Erdôs, A. Rényi, On random graphs, Publ. Math. Debrecen 6 290-297 (1959).
22. A.-L. Barabási, R. Albert., Emergence of scaling in random networks., Science 286 509-512 (1999).
23. Albert, L. Barabási, Network Science 1st Edition, Cambridge University Press, (2016).
24. A.-L. Barabási, E. Bonabeau, Scale-free networks., Scientific American 208(5) 60-69 (2003).
25. M. Newman, Fast algorithm for detecting community structure in networks, Phys. Rev. E. 69, 066133 (2004).
26. M. van den Heuvel, O. Sporns, Network hubs in the human brain., Trends in Cognitive Sciences 12(12) 683-696 (2013).
27. M. Saberi, R. Khosrowabadi, A. Khatibi, B. Misic, G. Jafari, Topological impact of negative links on the stability of resting-state brain network, Scientific Reports 11(1) 269-271 (2021).
28. S. Perera, M. Bell, M. Bliemer, Network science approach to modelling the topology and robustness of supply chain networks: a review and perspective, Applied Network Science 2, 33 (2017).
29. D. Watts, S. Strogatz, A social network model based on caveman network, Nature 393(6684) 440-442 (1998).
30. A. Medus, C. Dorso, Alternative approach to community detection in networks., Phys. Rev. E. 79(6) 066111 (2009).
31. M. Girvan, M.E.J.Newman, Community structure in social and biological networks., Proc. Natl. Acad. Sci. USA. 99 7821–7826 (2002).
32. Y. Wu, L. Kang, Z. Guo, J. Liu, M. Liu, W. Liang, Incubation period of covid-19 caused by unique sars-cov-2 strains: A systematic review and meta-analysis., JAMA Netw Open 5(8) e2228008 (2022).