The epidemiology of pandemics is classically viewed using geographical and political borders; however, these artificial divisions can result in a misunderstanding of the current epidemiological state within a given region. To improve upon current methods, we propose a clustering algorithm which is capable of recasting regions into well-mixed clusters such that they have a high level of interconnection while minimizing the external flow of the population towards other clusters. Moreover, we analyze and identify so-called core clusters, clusters that retain their features over time (temporally stable) and independent of the presence or absence of policy measures. In order to demonstrate the capabilities of this algorithm, we use USA county-level cellular mobility data to divide the country into such clusters. Herein, we show a more granular spread of SARS-CoV-2 throughout the first weeks of the pandemic. Moreover, we are able to identify areas (groups of counties) that were experiencing above average levels of transmission within a state, as well as pan-state areas (clusters overlapping more than one state) with very similar disease spread. Therefore, our method enables policymakers to make more informed decisions on the use of public health interventions within their jurisdiction, as well as guide collaboration with surrounding regions to benefit the general population in controlling the spread of communicable diseases.
Citation: David Lyver, Mihai Nica, Corentin Cot, Giacomo Cacciapaglia, Zahra Mohammadi, Edward W. Thommes, Monica-Gabriela Cojocaru. Population mobility, well-mixed clustering and disease spread: a look at COVID-19 Spread in the United States and preventive policy insights[J]. Mathematical Biosciences and Engineering, 2024, 21(4): 5604-5633. doi: 10.3934/mbe.2024247
The epidemiology of pandemics is classically viewed using geographical and political borders; however, these artificial divisions can result in a misunderstanding of the current epidemiological state within a given region. To improve upon current methods, we propose a clustering algorithm which is capable of recasting regions into well-mixed clusters such that they have a high level of interconnection while minimizing the external flow of the population towards other clusters. Moreover, we analyze and identify so-called core clusters, clusters that retain their features over time (temporally stable) and independent of the presence or absence of policy measures. In order to demonstrate the capabilities of this algorithm, we use USA county-level cellular mobility data to divide the country into such clusters. Herein, we show a more granular spread of SARS-CoV-2 throughout the first weeks of the pandemic. Moreover, we are able to identify areas (groups of counties) that were experiencing above average levels of transmission within a state, as well as pan-state areas (clusters overlapping more than one state) with very similar disease spread. Therefore, our method enables policymakers to make more informed decisions on the use of public health interventions within their jurisdiction, as well as guide collaboration with surrounding regions to benefit the general population in controlling the spread of communicable diseases.
| [1] |
W. O. Kermack, A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. R. Soc. Lond. A, 115 (1927), 700–721. https://doi.org/10.1098/rspa.1927.0118 doi: 10.1098/rspa.1927.0118
|
| [2] |
J. Arino, P. van den Driessche, A multi-city epidemic model, Math. Popul. Stud., 10 (2003), 175–193. https://doi.org/10.1080/08898480306720 doi: 10.1080/08898480306720
|
| [3] | J. Arino, P. van den Driessche, The basic reproduction number in a multi-city compartmental epidemic model, in Positive Systems: Proceedings of the First Multidisciplinary International Symposium on Positive Systems: Theory and Applications (POSTA 2003), Rome, Italy, 294 (2004), 135–142. https://doi.org/10.1007/978-3-540-44928-7_19 |
| [4] | E. W. Thommes, M. G. Cojocaru, S. Athar, Absenteeism impact on local economy during a pandemic via hybrid SIR dynamics, in Dynamics of Disasters—Key Concepts, Models, Algorithms, and Insights, Kalamata, Greece, 185 (2016), 309–328. |
| [5] |
R. M. Anderson, R. M. May, Population biology of infectious diseases: Part Ⅰ, Nature, 280 (1979), 361–367. https://doi.org/10.1038/280361a0 doi: 10.1038/280361a0
|
| [6] | A. G. Hevesi, Outdated municipal structures, Office N. Y. State Comptroller, 2006. |
| [7] | L. Makra, Z. Sümeghy, Objective analysis and ranking of Hungarian cities, with different classification techniques, part 2: Analysis, Acta Climatologica Et Chorologica, (2007), 91–100. |
| [8] |
I. Ben-Gal, S. Weinstock, G. Singer, N. Bambos, Clustering users by their mobility behavioral patterns, ACM Trans. Knowl. Discovery Data, 13 (2019), 1556–4681. https://doi.org/10.1145/3322126 doi: 10.1145/3322126
|
| [9] |
E. Thuillier, L. Moalic, S. Lamrous, A. Caminada, Clustering weekly patterns of human mobility through mobile phone data, IEEE Trans. Mob. Comput., 17 (2017), 817–830. https://10.1109/TMC.2017.2742953 doi: 10.1109/TMC.2017.2742953
|
| [10] | S. Liu, Y. Liu, L. M. Ni, J. Fan, M. Li, Towards mobility-based clustering, in Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Washington, DC, USA, (2010), 910–928. https://doi.org/10.1145/1835804.1835920 |
| [11] |
S. Chang, E. Pierson, P. W. Koh, J. Gerardin, B. Redbird, D. Grusky, et al., Mobility network models of COVID-19 explain inequities and inform reopening, Nature, 589 (2021), 82–87. https://doi.org/10.1038/s41586-020-2923-3 doi: 10.1038/s41586-020-2923-3
|
| [12] |
R. Fields, L. Humphrey, D. Flynn-Primrose, Z. Mohammadi, M. Nahirniak, E. W. Thommes, et al., Age-stratified transmission model of COVID-19 in Ontario with human mobility during pandemic's first wave, Heliyon, 7 (2021), e07905. https://doi.org/10.1016/j.heliyon.2021.e07905 doi: 10.1016/j.heliyon.2021.e07905
|
| [13] |
Z. Mohammadi, M. G. Cojocaru, E. W. Thommes, Human behaviour, NPI and mobility reduction effects on COVID-19 transmission in different countries of the world, BMC Public Health, 1594 (2022), 1–19. https://doi.org/10.1186/s12889-022-13921-3 doi: 10.1186/s12889-022-13921-3
|
| [14] |
G. Cacciapaglia, C. Cot, F. Sannino, Second wave COVID-19 pandemics in Europe: A temporal playbook, Sci. Rep., 10 (2020), 15514. https://doi.org/10.1038/s41598-020-72611-5 doi: 10.1038/s41598-020-72611-5
|
| [15] |
G. Cacciapaglia, C. Cot, A. S. Islind, M. Óskarsdóttir, F. Sannino, Impact of US vaccination strategy on COVID-19 wave dynamics, Sci. Rep., 11 (2021), 10960. https://doi.org/10.1038/s41598-021-90539-2 doi: 10.1038/s41598-021-90539-2
|
| [16] | G. Fung, A comprehensive overview of basic clustering algorithms, 2001. |
| [17] |
M. Z. Rodriguez, C. H. Comin, D. Casanova, O. M. Bruno, D. R. Amancio, L. F. Costa, et al., Clustering algorithms: A comparative approach, PloS One, 14 (2019), e0210236. https://doi.org/10.1371/journal.pone.0210236 doi: 10.1371/journal.pone.0210236
|
| [18] |
D. Xu, Y. Tian, A comprehensive survey of clustering algorithms, Ann. Data Sci., 2 (2015), 165–193. https://doi.org/10.1007/s40745-015-0040-1 doi: 10.1007/s40745-015-0040-1
|
| [19] | New York Times, COVID-19-data, 2023. Available from: https://github.com/nytimes/covid-19-data. |
| [20] | Google, COVID-19 community mobility reports, 2022. Available from: https://www.google.com/covid19/mobility/. |
| [21] | Statistics Canada, Commuting flow from geography of residence to geography of work - census divisions: Sex (3) for the employed labour force aged 15 years and over having a usual place of work, in private households, 2016 Census - 25% sample data, 2018. Available from: https://www150.statcan.gc.ca/n1/en/catalogue/98-400-X2016391. |
| [22] | L. A. Cauchy, Méthode générale pour la résolution des systèmes d'équations simultanées, Comp. Rend. Sci. Paris, 25 (1847), 536–538. |
| [23] | S. Ruder, An overview of gradient descent optimization algorithms, preprint, arXiv: 1609.04747. https://doi.org/10.48550/arXiv.1609.04747 |
| [24] | I. Goodfellow, Y. Bengio, A. Courville, Deep Learning, MIT Press, 2016. |
| [25] |
I. Kouretas, V. Paliouras, Hardware implementation of a softmax-like function for deep learning, Technologies, 8 (2020), 46. https://doi.org/10.3390/technologies8030046 doi: 10.3390/technologies8030046
|
| [26] | Zoooook, CoronvirusTimelapse, 2020. Available from: https://github.com/Zoooook/CoronavirusTimelapse/blob/master/static/population.json. |
| [27] |
A. Moreland, C. Herlihy, M. A. Tynan, G. Sunshine, R. F. McCord, C. Hilton, et al., Timing of state and territorial COVID-19 stay-at-home orders and changes in population movement—United States, March 1–May 31, 2020, MMWR Morb. Mortal. Wkly. Rep., 69 (2020), 1198–1203. https://doi.org/10.15585/mmwr.mm6935a2 doi: 10.15585/mmwr.mm6935a2
|
| [28] | S. A. Golding, R. L. Winkler, Tracking urbanization and exurbs: Migration across the rural–urban continuum, 1990–2016, Popul. Res. Policy Rev., 39 (2020), 835–959. |
| [29] | Z. Mohammadi, M. Cojocaru, J. Arino, A. Hurford, Importation models for travel-related SARS-CoV-2 cases reported in Newfoundland and Labrador during the COVID-19 pandemic, preprint, medRxiv. https://doi.org/10.1101/2023.06.08.23291136 |
| [30] | U.S. Department of transportation, Enplanements at the Top 50 U.S. Airports: 2015, 2016. Available from: https://www.bts.gov/enplanements-top-50-us-airports-2015. |
| [31] |
J. L. Ma, Estimating epidemic exponential growth rate and basic reproduction number, Infect. Dis. Modell., 5 (2020), 129–141. https://doi.org/10.1016/j.idm.2019.12.009 doi: 10.1016/j.idm.2019.12.009
|
| [32] | R. Machne, P. F. Stadler, dpseg: Piecewise linear segmentation by dynamic programming, 2020. Available from: https://CRAN.R-project.org/package = dpseg. |
| [33] |
L. Humphrey, E. W. Thommes, R. Fields, L. Coudeville, N. Hakim, A. Chit, et al., Large-scale frequent testing and tracing to supplement control of COVID-19 and vaccination rollout constrained by supply, Infect. Dis. Modell., 6 (2021), 955–974. https://doi.org/10.1016/j.idm.2021.06.008 doi: 10.1016/j.idm.2021.06.008
|
| [34] |
D. Hsiehchen, M. Espinoza, P. Slovic, Political partisanship and mobility restriction during the COVID-19 pandemic, Public Health, 187 (2020), 111–114. https://doi.org/10.1016/j.puhe.2020.08.009 doi: 10.1016/j.puhe.2020.08.009
|
| [35] | Rockport Analytics, Travel & tourism makes a convincing recovery from the COVID-19 pandemic, 2021. Available from: https://www.visitflorida.org/media/30679/florida-visitor-economic-impact-study.pdf. |
| [36] |
C. Cot, G. Cacciapaglia, F. Sannino, Mining Google and Apple mobility data: Temporal anatomy for COVID-19 social distancing, Sci. Rep., 11 (2021), 4150. https://doi.org/10.1038/s41598-021-83441-4 doi: 10.1038/s41598-021-83441-4
|
| [37] | R. Fields, L. Humphrey, E. W. Thommes, M. G. Cojocaru, COVID-19 in ontario: Modelling the pandemic by age groups incorporating preventative rapid-testing, in Mathematics of Public Health: Proceedings of the Seminar on the Mathematical Modelling of COVID-19, (eds. V.K. Murty and J. Wu), Springer, Cham, 85 (2021), 67–83. https://doi.org/10.1007/978-3-030-85053-1_4 |
| [38] | S. Smook, Adapting a Time-Dependent Vaccination Game to Mask Compliance, Ph.D thesis, University of Guelph in Guelph, 2022. |
| [39] | Association of Local Public Health Agencies, Public Health Units, 2024. Available from: https://www.alphaweb.org/page/PHU. |
| [40] |
G. Cacciapaglia, F. Sannino, Interplay of social distancing and border restrictions for pandemics (COVID-19) via the epidemic Renormalisation Group framework, Sci. Rep., 10 (2020). https://doi.org/10.1038/s41598-020-72175-4 doi: 10.1038/s41598-020-72175-4
|
Figures(18) / Tables(2)
David Lyver, Mihai Nica, Corentin Cot, Giacomo Cacciapaglia, Zahra Mohammadi, Edward W. Thommes, Monica-Gabriela Cojocaru. Population mobility, well-mixed clustering and disease spread: a look at COVID-19 Spread in the United States and preventive policy insights[J]. Mathematical Biosciences and Engineering, 2024, 21(4): 5604-5633. doi: 10.3934/mbe.2024247
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