Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Quantitative Biology > Populations and Evolution

arXiv:0806.4576 (q-bio)
[Submitted on 27 Jun 2008]

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

Authors:Maira Aguiar, Nico Stollenwerk, Bob W. Kooi
View PDF
Abstract: We analyse an epidemiological model of competing strains of pathogens and hence differences in transmission for first versus secondary infection due to interaction of the strains with previously aquired immunities, as has been described for dengue fever (in dengue known as antibody dependent enhancement, ADE). Such models show a rich variety of dynamics through bifurcations up to deterministic chaos. Including temporary cross-immunity even enlarges the parameter range of such chaotic attractors, and also gives rise to various coexisting attractors, which are difficult to identify by standard numerical bifurcation programs using continuation methods. A combination of techniques, including classical bifurcation plots and Lyapunov exponent spectra has to be applied in comparison to get further insight into such dynamical structures. Here we present for the first time multi-parameter studies in a range of biologically plausible values for dengue. The multi-strain interaction with the immune system is expected to also have implications for the epidemiology of other diseases.
Comments: 13 pages, 4 fugures; proceedings of CMMSE 2008, ISBN 978-84-612-1982-7
Subjects: Populations and Evolution (q-bio.PE); Quantitative Methods (q-bio.QM)
Cite as: arXiv:0806.4576 [q-bio.PE]
  (or arXiv:0806.4576v1 [q-bio.PE] for this version)
  https://doi.org/10.48550/arXiv.0806.4576

Submission history

From: Nico Stollenwerk [view email]
[v1] Fri, 27 Jun 2008 18:40:23 UTC (60 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
q-bio.PE
< prev   |   next >
new | recent | 2008-06
Change to browse by:
q-bio
q-bio.QM

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)