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Original Articles

Understanding dengue fever dynamics: a study of seasonality in vector-borne disease models

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Pages 1405-1422 | Received 07 Jan 2014, Accepted 23 Apr 2015, Published online: 18 Jun 2015

References

  • L. Acedo, G. González-Parra, and A.J. Arenas, An exact global solution for the classical sirs epidemic model, Nonlinear Anal., Real World Appl. 11(3) (2010), pp. 1819–1825. doi: 10.1016/j.nonrwa.2009.04.007
  • L. Acedo, G. González-Parra, and A.J. Arenas, Modal series solution for an epidemic model, Phys. A 389(5) (2010), pp. 1151–1157. doi: 10.1016/j.physa.2009.11.003
  • M. Aguiar, B.W. Kooi, and N. Stollenwerk, Epidemiology of dengue fever: A model with temporary cross-immunity and possible secondary infection shows bifurcations and chaotic behaviour in wide parameter regions, Math. Model. Nat. Phenom. 3 (2008), pp. 48–70. doi: 10.1051/mmnp:2008070
  • M. Aguiar, S. Ballesteros, B.W. Kooi, and N. Stollenwerk, The role of seasonality and import in a minimalistic multi-strain dengue model capturing differences between primary and secondary infections: Complex dynamics and its implications for data analysis, J. Theoret. Biol. 289 (2011), pp. 181–196. doi: 10.1016/j.jtbi.2011.08.043
  • M. Aguiar, B.W. Kooi, F. Rocha, P. Ghaffari, and N. Stollenwerk, How much complexity is needed to describe the fluctuations observed in dengue hemorrhagic fever incidence data? Ecol. Complex. 16 (2013), pp. 31–40. doi: 10.1016/j.ecocom.2012.09.001
  • M. Aguiar, B.W. Kooi, J. Martins, and N. Stollenwerk, Scaling of stochasticity in dengue hemorrhagic fever epidemics, Math. Model. Nat. Phenom. 7(3) (2012), pp. 181–196. doi: 10.1051/mmnp/20127301
  • E. Augeraud-Véron and N. Sari, Seasonal dynamics in an SIR epidemic system, J. Math. Biol. 68(3) (2014), pp. 701–725. doi: 10.1007/s00285-013-0645-y
  • N. Bacaër, Approximation of the basic reproduction number R0 for vector-borne diseases with a periodic vector population, Bull. Math. Biol. 69(3) (2007), pp. 1067–1091. doi: 10.1007/s11538-006-9166-9
  • N. Bacaër and S. Guernaoui, The epidemic threshold of vector-borne diseases with seasonality, J. Math. Biol. 53(3) (2006), pp. 421–436. doi: 10.1007/s00285-006-0015-0
  • N. Bacaër and R. Ouifki, Growth rate and basic reproduction number for population models with a simple periodic factor, Math. Biosci. 210(2) (2007), pp. 647–658. doi: 10.1016/j.mbs.2007.07.005
  • Z. Bai and Y. Zhou, Existence of two periodic solutions for a non-autonomous SIR epidemic model, Appl. Math. Model. 35(1) (2011), pp. 382–391. doi: 10.1016/j.apm.2010.07.002
  • Z. Feng and J.X. Velasco-Hernandez, Competitive exclusion in a vector–host model for the dengue fever, J. Math. Biol. 35(5) (1997), pp. 523–544. doi: 10.1007/s002850050064
  • D.B. Fischer and S.B. Halstead, Observations related to pathogenesis of dengue hemorrhagic fever. V. Examination of age specific sequential infection rates using a mathematical model, J. Biol. Med. 42 (1970), pp. 329–349.
  • I. Grattan-Guinness, Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, Taylor & Francis Books Ltd, London, 2003.
  • Z. Grossman, Oscillatory phenomena in a model of infectious diseases, Theor. Popul. Biol. 18(2) (1980), pp. 204–243. doi: 10.1016/0040-5809(80)90050-7
  • H.W. Hethcote, Asymptotic behavior in a deterministic epidemic model, Bull. Math. Biol. 35 (1973), pp. 607–614. doi: 10.1007/BF02458365
  • H.W. Hethcote, The mathematics of infectious diseases, SIAM Rev. 42(4) (2000), pp. 599–653. doi: 10.1137/S0036144500371907
  • H.W. Hethcote and S.A. Levin, Periodicity in epidemiological models, in Applied Mathematical Ecology, S.A. Levin, T. Hallam and L. Gross, eds., Springer, Berlin, Heidelberg, 1989, pp. 193–211.
  • Information System of Disease Information (SINAN) of Brazilian Ministry of Health. Available at http://dtr2004.saude.gov.br/sinanweb/.
  • C.C. Jansen and N.W. Beebe, The dengue vector Aedes aegypti: What comes next, Microbes Infect. 29 (2011), pp. 7221–7228.
  • M. Kamo and A. Sasaki, The effect of cross-immunity and seasonal forcing in a multi-strain epidemic model, Phys. D., Nonlinear Phenom. 165(3) (2002), pp. 228–241. doi: 10.1016/S0167-2789(02)00389-5
  • T. Kuniya and H. Inaba, Endemic threshold results for an age-structured SIS epidemic model with periodic parameters, J. Math. Anal. Appl. 402(2) (2013), pp. 477–492. doi: 10.1016/j.jmaa.2013.01.044
  • Y.A. Kuznetsov and C. Piccardi, Bifurcation analysis of periodic SEIR and SIR epidemic models, J. Math. Biol. 32(2) (1994), pp. 109–121. doi: 10.1007/BF00163027
  • M. Langlais and S. Busenberg, Global behaviour in age structured sis models with seasonal periodicities and vertical transmission, J. Math. Anal. Appl. 213(2) (1997), pp. 511–533. doi: 10.1006/jmaa.1997.5554
  • Y. Nakata and T. Kuniya, Global dynamics of a class of SEIRS epidemic models in a periodic environment, J. Math. Anal. Appl. 363(1) (2010), pp. 230–237. doi: 10.1016/j.jmaa.2009.08.027
  • M. Otero and H.G. Solari, Stochastic eco-epidemiological model of dengue disease transmission by Aedes aegypti mosquito, Math. Biosci. 223(1) (2010), pp. 32–46. doi: 10.1016/j.mbs.2009.10.005
  • A. Pandey, A. Mubayi, and J. Medlock, Comparing vector–host and SIR models for dengue transmission, Math. Biosci. 246(2) (2013), pp. 252–259. doi: 10.1016/j.mbs.2013.10.007
  • C. Rebelo, A. Margheri, and N. Bacaër, Persistence in seasonally forced epidemiological models, J. Math. Biol. 64(6) (2012), pp. 933–949. doi: 10.1007/s00285-011-0440-6
  • F. Rocha, M. Aguiar, M. Souza, and N. Stollenwerk, Time-scale separation and center manifold analysis describing vector-borne disease dynamics, Int. J. Comput. Math. 90(10) (2013), pp. 2105–2125. doi: 10.1080/00207160.2013.783208
  • H.L. Smith, Multiple stable subharmonics for a periodic epidemic model, J. Math. Biol. 17(2) (1983), pp. 179–190. doi: 10.1007/BF00305758
  • M.O. Souza, Multiscale analysis for a vector-borne epidemic model, Math. Biol. 68 (2014), pp. 1269–1293. doi: 10.1007/s00285-013-0666-6
  • J. Whitehorn and C.P. Simmons, The pathogenesis of dengue, Vaccine 29 (2011), pp. 7221–7228. doi: 10.1016/j.vaccine.2011.07.022

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