[2210.17156] Bifurcation analysis of the Microscopic Markov Chain Approach to contact-based epidemic spreading in networks
Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Physics > Physics and Society

arXiv:2210.17156 (physics)
COVID-19 e-print

Important: e-prints posted on arXiv are not peer-reviewed by arXiv; they should not be relied upon without context to guide clinical practice or health-related behavior and should not be reported in news media as established information without consulting multiple experts in the field.

[Submitted on 31 Oct 2022]

Title:Bifurcation analysis of the Microscopic Markov Chain Approach to contact-based epidemic spreading in networks

Authors:Alex Arenas, Antonio Garijo, Sergio Gómez, Jordi Villadelprat
View PDF
Abstract:The dynamics of many epidemic compartmental models for infectious diseases that spread in a single host population present a second-order phase transition. This transition occurs as a function of the infectivity parameter, from the absence of infected individuals to an endemic state. Here, we study this transition, from the perspective of dynamical systems, for a discrete-time compartmental epidemic model known as Microscopic Markov Chain Approach, whose applicability for forecasting future scenarios of epidemic spreading has been proved very useful during the COVID-19 pandemic. We show that there is an endemic state which is stable and a global attractor and that its existence is a consequence of a transcritical bifurcation. This mathematical analysis grounds the results of the model in practical applications.
Comments: 15 pages, 3 figures
Subjects: Physics and Society (physics.soc-ph); Statistical Mechanics (cond-mat.stat-mech); Social and Information Networks (cs.SI); Dynamical Systems (math.DS)
Cite as: arXiv:2210.17156 [physics.soc-ph]
  (or arXiv:2210.17156v1 [physics.soc-ph] for this version)
  https://doi.org/10.48550/arXiv.2210.17156
Journal reference: Chaos, Solitons & Fractals 166 (2023) 112921
Related DOI: https://doi.org/10.1016/j.chaos.2022.112921

Submission history

From: Sergio Gómez [view email]
[v1] Mon, 31 Oct 2022 09:09:03 UTC (37 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
physics.soc-ph
< prev   |   next >
new | recent | 2022-10
Change to browse by:
cond-mat
cond-mat.stat-mech
cs
cs.SI
math
math.DS
physics

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?)