Geodesic
Scaling of Stochasticity in Dengue Hemorrhagic Fever Epidemics
M. Aguiar1, 2 ; B.W. Kooi3 ; J. Martins4 ; N. Stollenwerk1
1 Centro de Matemática e Aplicações Fundamentais da Universidade de Lisboa Avenida Professor Gama Pinto 2, 1649-003 Lisboa, Portugal
2 Fundação Ezequiel Dias, Serviço de Virologia e Riquetisioses, Laboratório de dengue e febre amarela Rua Conde Pereira Carneiro 80, 30510-010 Belo Horizonte-MG, Brazil
3 Faculty of Earth and Life Sciences, Department of Theoretical Biology, Vrije Universiteit, De Boelelaan 1087, NL 1081 HV Amsterdam, The Netherlands
4 Department of Mathematics, School of Technology and Management, Polytechnic Institute of Leiria Campus 2, Morro do Lena, Alto do Vieiro, 2411-901 Leiria, Portugal
Mathematical modelling of natural phenomena, Tome 7 (2012) no. 3, pp. 1-11.

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In this paper we analyze the stochastic version of a minimalistic multi-strain model, which captures essential differences between primary and secondary infections in dengue fever epidemiology, and investigate the interplay between stochasticity, seasonality and import. The introduction of stochasticity is needed to explain the fluctuations observed in some of the available data sets, revealing a scenario where noise and complex deterministic skeleton strongly interact. For large enough population size, the stochastic system can be well described by the deterministic skeleton gaining insight on the relevant parameter values purely on topological information of the dynamics, rather than classical parameter estimation of which application is in general restricted to fairly simple dynamical scenarios.
DOI : 10.1051/mmnp/20127301

M. Aguiar 1, 2 ; B.W. Kooi 3 ; J. Martins 4 ; N. Stollenwerk 1

1 Centro de Matemática e Aplicações Fundamentais da Universidade de Lisboa Avenida Professor Gama Pinto 2, 1649-003 Lisboa, Portugal
2 Fundação Ezequiel Dias, Serviço de Virologia e Riquetisioses, Laboratório de dengue e febre amarela Rua Conde Pereira Carneiro 80, 30510-010 Belo Horizonte-MG, Brazil
3 Faculty of Earth and Life Sciences, Department of Theoretical Biology, Vrije Universiteit, De Boelelaan 1087, NL 1081 HV Amsterdam, The Netherlands
4 Department of Mathematics, School of Technology and Management, Polytechnic Institute of Leiria Campus 2, Morro do Lena, Alto do Vieiro, 2411-901 Leiria, Portugal 
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M. Aguiar; B.W. Kooi; J. Martins; N. Stollenwerk. Scaling of Stochasticity in Dengue Hemorrhagic Fever Epidemics. Mathematical modelling of natural phenomena, Tome 7 (2012) no. 3, pp. 1-11. doi : 10.1051/mmnp/20127301. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20127301/

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