Time-scale separation and centre manifold analysis describing vector-borne disease dynamics

References

• M. Aguiar and N. Stollenwerk, A new chaotic attractor in a basic multi-strain epidemiological model with temporary cross-immunity, 2007. arXiv:0704.3174v1 [nlin.CD]. Available at http://arxive.org.
   Google Scholar
• 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) doi: 10.1051/mmnp:2008070
   Web of Science ®Google Scholar
• M. Aguiar, N. Stollenwerk, and B. W. Kooi, Torus bifurcations, isolas and chaotic attractors in a simple dengue model with ADE and temporary cross immunity, Int. J. Comput. Math. 86 (2009), pp. 1867–1877, (doi:10.1080/00207160902783532) doi: 10.1080/00207160902783532
   Web of Science ®Google Scholar
• 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) doi: 10.1016/j.jtbi.2011.08.043
   PubMed Web of Science ®Google Scholar
• D. K. Arrowsmith, and C. M. PlaceAn Introduction to Dynamical Systems, Cambridge University Press, Cambridge, (1990)
   Google Scholar
• P. Auger, S. Charles, M. Viala, and J.-C. Poggiale, Aggregation and emergence in ecological modelling: Integration of ecological levels, Ecol. Model. 127 (2000), pp. 11–20, (doi:10.1016/S0304-3800(99)00201-X) doi: 10.1016/S0304-3800(99)00201-X
   Web of Science ®Google Scholar
• R. EngbertChance and Chaos in Seasonally Driven Epidemics, Research Center Jülich, Juelich, Germany, (1993), Jül-Report 2826
   Google Scholar
• Y. Eynaud, D. Nerini, M. Baklouti, and J.-C. Poggiale, Towards a simplification of models using regression trees, J. R. Soc. Interface. 10 (2012), pp. 20120613, (doi:10.1098/rsif.2012.0613) doi: 10.1098/rsif.2012.0613
   Web of Science ®Google Scholar
• 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
   Web of Science ®Google Scholar
• E. Forgosten, L. Billings, and I. Schwartz, Accurate noise projection for reduced stochastic epidemic models, Chaos 19 (2009), pp. 043110-1–043110-15
   Web of Science ®Google Scholar
• J. Guckenheimer, and Ph. HolmesNonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer-Verlag, Heidelberg, New York, (1983)
   Google Scholar
• H. HeuserLehrbuch der Analysis, Teubner, Stuttgart, (1980)
   Google Scholar
• C. C. Jansen, and N. W. Beebe, The dengue vector Aedes aegypti: What comes next, Microbes Infect. 29 (2011), pp. 7221–7228
   Google Scholar
• A. Morozov, and J.-C. Poggiale, From spatially explicit ecological models to mean-field dynamics: The state of the art and perspectives, Ecol. Complex. 10 (2012), pp. 1–11, (doi:10.1016/j.ecocom.2012.04.001) doi: 10.1016/j.ecocom.2012.04.001
   Web of Science ®Google Scholar
• V. N. Mose, T. Nguyen-uu, P. Auger, and D. Western, Modelling herbivore population dynamics in the Amboseli National Park, Kenya: Application of spatial aggregation of variables to derive a master model, Ecol. Complex. 10 (2012), pp. 42–51, (doi:10.1016/j.ecocom.2012.02.002) doi: 10.1016/j.ecocom.2012.02.002
   Web of Science ®Google Scholar
• J.-C. Poggiale, and P. Auger, Fast oscillating migrations in a predator–prey model, Math. Models Methods Appl. Sci. 2 (1996), pp. 217–226, (doi:10.1142/S0218202596000559) doi: 10.1142/S0218202596000559
   Web of Science ®Google Scholar
• M.O. Souza, Multiscale analysis for a vector-borne epidemic model, preprint (2011), to appear in J. Math. Biol. Available at arXiv, 1108.1999v1 [q-bio.PE].
   Google Scholar
• N. Stollenwerk, and V. JansenPopulation Biology and Criticality, Imperial College Press, London, (2011)
   Google Scholar
• J. Whitehorn, and C. P. Simmons, The pathogenesis of dengue, Vaccine 29 (2011), pp. 7221–7228, (doi:10.1016/j.vaccine.2011.07.022) doi: 10.1016/j.vaccine.2011.07.022
   PubMed Web of Science ®Google Scholar
• WHO – World Health Organization, Dengue/dengue Haemorrhagic Fever, (2012), Available at http://www.who.int/csr/disease/dengue/en/.
   Google Scholar
• H. M. Yang, M. Macoris, K. Galvani, and M. Andrighetti, Follow up estimation of Aedes aegypti entomological parameters and mathematical modellings, Biosystems 103 (2011), pp. 360–371, (doi:10.1016/j.biosystems.2010.11.002) doi: 10.1016/j.biosystems.2010.11.002
   PubMed Web of Science ®Google Scholar