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Mathematical Biosciences and Engineering

2016, Volume 13, Issue 1: 43-65. doi: 10.3934/mbe.2016.13.43
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Modelling the spatial-temporal progression of the 2009 A/H1N1 influenza pandemic in Chile

  • 1.
    CI2MA and Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160-C, Concepción
  • 2.
    School of Public Health, Georgia State University, Atlanta, Georgia
  • 3.
    Departament de Matemàtica Aplicada, Universitat de València, Av. Dr. Moliner 50, E-46100 Burjassot
  • 4.
    GIMNAP-Departamento de Matemáticas, Universidad del Bío-Bío, Casilla 5-C, Concepción
  • Received: 01 July 2014 Accepted: 29 June 2018 Published: 01 October 2015

  • MSC : Primary: 92D30; Secondary: 97M60.

  • A spatial-temporal transmission model of 2009 A/H1N1 pandemic influenza across Chile,a country that spans a large latitudinal range, is developed to characterize the spatial variation in peak timingof that pandemic as a function of local transmission rates, spatial connectivity assumptions for Chilean regions, andthe putative location of introduction of the novel virus into the country. Specifically, ametapopulation SEIR (susceptible-exposed-infected-removed) compartmental model that tracks the transmissiondynamics of influenza in 15 Chilean regions is calibrated. The model incorporates population mobility among neighboringregions and indirect mobility to and from other regions via themetropolitan central region (``hub region''). The stability of the disease-freeequilibrium of this model is analyzed and compared with thecorresponding stability in each region, concluding that stability mayoccur even with some regions having basic reproduction numbersabove 1.The transmission model is used along with epidemiological data to explorepotential factors that could have driventhe spatial-temporal progression of the pandemic. Simulations and sensitivity analyses indicate that thisrelatively simple model is sufficient to characterize the south-north gradient in peak timing observed during the pandemic, and suggest that south Chile observed the initial spread of the pandemic virus, which is in line with a retrospective epidemiological study. The ``hub region'' in our model significantly enhanced population mixing in a short time scale.

    Citation: Raimund Bürger, Gerardo Chowell, Pep Mulet, Luis M. Villada. Modelling the spatial-temporal progression of the 2009 A/H1N1 influenza pandemic in Chile[J]. Mathematical Biosciences and Engineering, 2016, 13(1): 43-65. doi: 10.3934/mbe.2016.13.43

    Related Papers:

  • A spatial-temporal transmission model of 2009 A/H1N1 pandemic influenza across Chile,a country that spans a large latitudinal range, is developed to characterize the spatial variation in peak timingof that pandemic as a function of local transmission rates, spatial connectivity assumptions for Chilean regions, andthe putative location of introduction of the novel virus into the country. Specifically, ametapopulation SEIR (susceptible-exposed-infected-removed) compartmental model that tracks the transmissiondynamics of influenza in 15 Chilean regions is calibrated. The model incorporates population mobility among neighboringregions and indirect mobility to and from other regions via themetropolitan central region (``hub region''). The stability of the disease-freeequilibrium of this model is analyzed and compared with thecorresponding stability in each region, concluding that stability mayoccur even with some regions having basic reproduction numbersabove 1.The transmission model is used along with epidemiological data to explorepotential factors that could have driventhe spatial-temporal progression of the pandemic. Simulations and sensitivity analyses indicate that thisrelatively simple model is sufficient to characterize the south-north gradient in peak timing observed during the pandemic, and suggest that south Chile observed the initial spread of the pandemic virus, which is in line with a retrospective epidemiological study. The ``hub region'' in our model significantly enhanced population mixing in a short time scale.


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    [1] SIAM J. Appl. Math., 67 (2007), 1283-1309.
    [2] Amer. J. Epidemiol., 165 (2007), 1434-1442.
    [3] Oxford Science Publications, 1991.
    [4] Modeling and Dynamics of Infectious Diseases, Higher Education Press, Beijing, 11 (2009), 64-122.
    [5] Mathematical Medicine and Biology, 22 (2005), 129-142.
    [6] Math. Popul. Studies, 10 (2003), 175-193.
    [7] BMC Med., 7 (2009), p45 (12pp).
    [8] Second Ed., Springer, New York, 2012.
    [9] Lancet Infect. Dis., 9 (2009), 473-481.
    [10] PLoS One, 7 (2012), e41069 (10pp).
    [11] PloS Med., 8 (2011), e1000436 (13pp).
    [12] BMC Infect. Dis., 12 (2012), p298 (12pp).
    [13] PLoS One, 6 (2011), e21287 (10pp).
    [14] Proc. Biol. Sci., 277 (2010), 1857-1866.
    [15] PLoS Med., 4 (2007), e13 (16pp).
    [16] Princeton Series in Theoretical and Computational Biology, Princeton University Press, 2013.
    [17] J. Math. Biol., 28 (1990), 365-382.
    [18] In F. Brauer, P. van den Driessche and J. Wu (Eds.), Mathematical Epidemiology, Springer-Verlag, Berlin, 1945 (2008), 147-157.
    [19] Mathematical Epidemiology, Springer-Verlag, Berlin, 1945 (2008), 179-189.
    [20] Math. Biosci., 228 (2010), 71-77.
    [21] Math. Biosci., 180 (2002), 29-48.
    [22] Math. Biosci., 246 (2013), 164-175.
    [23] PLoS Comput. Biol., 10 (2014), e1003635 (11pp).
    [24] Math. Biosci. Eng., 8 (2011), 21-48.
    [25] Available from: http://www.ine.cl/canales/chile_estadistico/demografia_y_vitales/demo_y_vita.php
    [26] BMJ open, 3 (2) (2013), e002149 (10pp).
    [27] Cochrane Database Syst. Rev., April 10, 2014 (560pp).
    [28] Proc. Roy. Soc. A, 115 (1927), 700-721.
    [29] New Engl. J. Med., 361 (2009), 212-214.
    [30] Nonlin. Anal. Real World Appl., 14 (2013), 1135-1143.
    [31] Math. Biosci. Eng., 11 (2014), 1375-1393.
    [32] Canad. Appl. Math. Quart., 17 (2009), 175-187.
    [33] PLoS Pathog., 3 (2007), 1470-1476.
    [34] J. Virol.., 82 (2008), 5650-5652.
    [35] J. Infect. Dis., 199 (2009), 858-865.
    [36] PLoS Pathog. 7 (2011), e1002225 (10pp).
    [37] Eurosurveillance 15 (2010), 19456 (9pp).
    [38] Math. Biosci., 246 (2013), 47-54.
    [39] Princeton University Press, 2009.
    [40] Math. Biosci., 128 (1995), 71-91.
    [41] PLoS One, 6 (2011), e21471 (8pp).
    [42] PLoS One, 7 (2012), e41918 (10pp).
    [43] Proc. Natl. Acad. Sci. USA, 106 (2009), 3243-3248.
    [44] PLoS Biol., 8 (2010), e1000316 (13pp).
    [45] PLoS Med., 10 (2013), e1001558 (17pp).
    [46] J. Virol., 85 (2011), 1400-1402.
    [47] Comput. Math. Applic., 60 (2010), 2286-2291.
    [48] Environ. Health Perspect., 119 (2011), 439-445.
    [49] Science, 312 (2006), 447-451.
    [50] Oxford University Press, 2010.
    [51] PLoS One, 5 (2010), e10187 (11pp).
    [52] Emerg. Infect. Dis., 18 (2012), 758-766.
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  • © 2016 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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