Vaccination Campaigns on Random and Scale-Free Networks
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Abstract
The spreading of person-to-person infectious diseases (such as influenza) depends significantly on the contact network of the community. Any successful vaccination plan demands a complete understanding of how the disease can possibly propagate on this network. For this purpose, we examined vaccination actions on two specific community networks: scale-free networks and random networks. We applied a “random” vaccination plan and a “strategic” vaccination plan on both networks. The former corresponds to vaccine interventions regardless of the community structure, while the latter corresponds to preferential interventions according to the individual’s degree of connectivity. The “random” vaccination shows to be capable of reducing the infection peak, but the overall performance varies significantly if applied on a scale-free or random network. The “strategic” plan, on the contrary, prioritized vaccination actions on highly connected individuals. It showed more effective results since it slowed down the disease propagation while providing more time for immunization. We further applied the “strategic” plan to families instead of individuals alone. The plan appeared to perform nicely but not as effectively as vaccinating highly connected individuals.
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References
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 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).
12 D. Brockmann, L. Hufnagel, T. Geisel, The scaling laws of human travel., Nature 439, 462-465 (2006).
13 M. González, C. Hidalgo, A. Barabási, Understanding individual human mobility patterns, Nature 453, 779-782 (2008).
14 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).
15 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).
16 L. Valdez, L. Braunstein, S. Havlin, Epidemic spreading on modular networks: The fear to declare a pandemic., Phys. Rev. E. 101 032309 (2020).
17 M. Kuperman, G. Abramson, Small world effect in an epidemiological model., Phys. Rev. Lett. 86, 2909 (2001).
18 H. Wearing, M. P. Rohani, Appropriate models for the management of infectious diseases., PloS Medicine 2(7) 0621–0627 (2005).
19 K. A. Kabir, K. Kuga, J. Tanimoto, The impact of information spreading on epidemic vaccination game dynamics in a heterogeneous complex network, Chaos, Solitons and Fractals 132 109548 (2020).
20 M. Shahzamal, B. Mans, F. d. Hoog, D. Paini, R. Jurdak, Vaccination strategies on dynamic networks with indirect transmission links and limited contact information, PLOS ONE 15 (11) 1–24 (2020).
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 R. M. Anderson, R. M. May, Infectious diseases of humans, (Oxford University Press, Oxford, 1991) (1992).
31 W. O. Kermack, A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. R. Soc. Lond. A 115 (1927).
32 D. H. Barmak, C. O. Dorso, M. Otero, H. G. Solari, Dengue epidemics and human mobility, Phys. Rev. E 84 (2011) 011901.
33 F. Cornes, G. Frank, C. Dorso, Estrategia cı́clica de aislamiento y actividad económica durante la pandemia covid-19., Anales AFA 31(4) (2021).
34 H. Benı́tez, F. Cornes, C. Dorso, G. Frank, Disease spreading through complex small world networks, Medical Research Archives 12 (8) (2024).
35 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).
36 E. Bokányi, E. Heemskerk, F. Takes, The anatomy of a population-scale social network, Sci Rep 13 (9209) (2023).