Epidemiology of Dengue Fever: A Model with Temporary Cross-Immunity and Possible Secondary Infection Shows Bifurcations and Chaotic Behaviour in Wide Parameter Regions

Aguiar, Maíra, Kooi, Bob, and Stollenwerk, Nico. "Epidemiology of Dengue Fever: A Model with Temporary Cross-Immunity and Possible Secondary Infection Shows Bifurcations and Chaotic Behaviour in Wide Parameter Regions." Mathematical Modelling of Natural Phenomena 3.4 (2008): 48-70. <http://eudml.org/doc/222374>.

@article{Aguiar2008,
abstract = { Basic models suitable to explain the epidemiology of dengue fever have previously shown the possibility of deterministically chaotic attractors, which might explain the observed fluctuations found in empiric outbreak data. However, the region of bifurcations and chaos require strong enhanced infectivity on secondary infection, motivated by experimental findings of antibody-dependent-enhancement. Including temporary cross-immunity in such models, which is common knowledge among field researchers in dengue, we find bifurcations up to chaotic attractors in much wider and also unexpected parameter regions of reduced infectivity on secondary infection, realistically describing more likely hospitalization on secondary infection when the viral load becomes high. The model shows Hopf bifurcations, symmetry breaking bifurcations of limit cycles, coexisting isolas, and two different possible routes to chaos, via the Feigenbaum period doubling and via torus bifurcations. },
author = {Aguiar, Maíra, Kooi, Bob, Stollenwerk, Nico},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {temporary cross-immunity; antibody-dependent-enhancement (ADE); Lyapunov exponents; torus bifurcation; isolas; antibody-dependent-enhancement; torus bifurcation},
language = {eng},
month = {12},
number = {4},
pages = {48-70},
publisher = {EDP Sciences},
title = {Epidemiology of Dengue Fever: A Model with Temporary Cross-Immunity and Possible Secondary Infection Shows Bifurcations and Chaotic Behaviour in Wide Parameter Regions},
url = {http://eudml.org/doc/222374},
volume = {3},
year = {2008},
}

TY - JOUR
AU - Aguiar, Maíra
AU - Kooi, Bob
AU - Stollenwerk, Nico
TI - Epidemiology of Dengue Fever: A Model with Temporary Cross-Immunity and Possible Secondary Infection Shows Bifurcations and Chaotic Behaviour in Wide Parameter Regions
JO - Mathematical Modelling of Natural Phenomena
DA - 2008/12//
PB - EDP Sciences
VL - 3
IS - 4
SP - 48
EP - 70
AB - Basic models suitable to explain the epidemiology of dengue fever have previously shown the possibility of deterministically chaotic attractors, which might explain the observed fluctuations found in empiric outbreak data. However, the region of bifurcations and chaos require strong enhanced infectivity on secondary infection, motivated by experimental findings of antibody-dependent-enhancement. Including temporary cross-immunity in such models, which is common knowledge among field researchers in dengue, we find bifurcations up to chaotic attractors in much wider and also unexpected parameter regions of reduced infectivity on secondary infection, realistically describing more likely hospitalization on secondary infection when the viral load becomes high. The model shows Hopf bifurcations, symmetry breaking bifurcations of limit cycles, coexisting isolas, and two different possible routes to chaos, via the Feigenbaum period doubling and via torus bifurcations.
LA - eng
KW - temporary cross-immunity; antibody-dependent-enhancement (ADE); Lyapunov exponents; torus bifurcation; isolas; antibody-dependent-enhancement; torus bifurcation
UR - http://eudml.org/doc/222374
ER -