Torus bifurcations, isolas and chaotic attractors in a simple dengue fever model with ADE and temporary cross immunity

DOI10.1080/00207160902783532zbMath1173.92023arXiv0806.4576OpenAlexW2148427710WikidataQ57635139 ScholiaQ57635139MaRDI QIDQ3643172

Maíra Aguiar, Nico Stollenwerk, Bob W. Kooi

Publication date: 10 November 2009

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.4576

zbMATH Keywords

Lyapunov exponentsepidemiologynumerical bifurcation analysisantibody dependent enhancement (ADE)\(\mathbb Z_2\) symmetry

Mathematics Subject Classification ID

Epidemiology (92D30) Dynamical systems in biology (37N25) Bifurcation theory for ordinary differential equations (34C23) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Dynamical aspects of attractors and their bifurcations (37G35) Numerical bifurcation problems (65P30) Medical epidemiology (92C60)

Related Items (9)

Transmission dynamics of multi-strain dengue virus with cross-immunity ⋮ Prediction and Predictability in Population Biology: Noise and Chaos ⋮ Modeling secondary infections with temporary immunity and disease enhancement factor: mechanisms for complex dynamics in simple epidemiological models ⋮ Temporary cross-immunity as a plausible driver of asynchronous cycles of dengue serotypes ⋮ Analysis of an asymmetric two-strain dengue model ⋮ Bifurcation analysis of a family of multi-strain epidemiology models ⋮ Time-scale separation and centre manifold analysis describing vector-borne disease dynamics ⋮ Stochastic models in population biology: from dynamic noise to Bayesian description and model comparison for given data sets ⋮ 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

Uses Software

• AUTO

Cites Work

• Routes to chaos in high-dimensional dynamical systems: a qualitative numerical study
• Singularities and groups in bifurcation theory. Volume I
• Homoclinic and heteroclinic orbits to a cycle in a tri-trophic food chain
• Practical bifurcation and stability analysis: from equilibrium to chaos.
• Evolution towards criticality in an epidemiological model for meningococcal disease
• Consequences of symbiosis for food web dynamics
• Scale-free network of a dengue epidemic
• Epidemiology of Dengue Fever: A Model with Temporary Cross-Immunity and Possible Secondary Infection Shows Bifurcations and Chaotic Behaviour in Wide Parameter Regions
• IDENTIFICATION OF TRUE AND SPURIOUS LYAPUNOV EXPONENTS FROM TIME SERIES
• Chaos in Dynamical Systems
• Multiple attractors and boundary crises in a tri-trophic food chain

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