Complex dynamics of discrete SEIS models with simple demography
type: Item
instance of: scholarly article
title: Complex dynamics of discrete SEIS models with simple demography
zbMATH Open document ID: 1233.92066
DOI: 10.1155/2011/653937
author: Hui Cao
author: Yicang Zhou
author: Baojun Song
published in: Discrete Dynamics in Nature and Society
publication date: 2012-03-13T00:00:00Z
review text: Summary: We investigate bifurcations and dynamical behaviors of discrete SEIS models with exogenous reinfections and a variety of treatment strategies. Bifurcations identified from the models include period doubling, backward, forward-backward, and multiple backward bifurcations. Multiple attractors, such as bistability and tristability, are observed. We also estimate the ultimate boundary of the infected regardless of initial status. Our rigorous mathematical analysis together with numerical simulations show that epidemiological factors alone can generate complex dynamics, though demographic factors only support simple equilibrium dynamics. Our model analysis supports and urges to treat a fixed percentage of exposed individuals.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 39A60
Mathematics Subject Classification ID: 39A28
Mathematics Subject Classification ID: 65C20
Mathematics Subject Classification ID: 37N25
zbMATH DE Number: 6014513
Wikidata QID: Q58655528
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/653937
OpenAlex ID: W2158425472
cites work: Simple mathematical models with very complicated dynamics
cites work: Discrete-time S-I-S models with complex dynamics.
cites work: Dispersal, disease and life-history evolution
cites work: Backwards bifurcations and catastrophe in simple models of fatal diseases
cites work: Bifurcation Analysis of a Predator-Prey System with Nonmonotonic Functional Response
cites work: Saturation recovery leads to multiple endemic equilibria and backward bifurcation
cites work: Backward bifurcation in epidemic control
cites work: A simple SIS epidemic model with a backward bifurcation
cites work: Analysis of an epidemic model with bistable equilibria using the Poincaré index.
cites work: Backward bifurcation of an epidemic model with treatment
cites work: Dynamics of infection with nonlinear incidence in a simple vaccination model
cites work: Stability and bifurcation of an SIR epidemic model with nonlinear incidence and treatment
cites work: Some discrete-time SI, SIR, and SIS epidemic models
cites work: Comparison of deterministic and stochastic SIS and SIR models in discrete time
cites work: Discrete-time deterministic and stochastic models for the spread of rabies
cites work: Q4407480
cites work: Discrete-Time SIS EpidemicModel in a Seasonal Environment
cites work: Dynamics of a discrete age-structured SIS models
cites work: Global stability of a class of discrete age-structured SIS models with immigration
cites work: Q5416659
cites work: Uniform persistence and permanence for non-autonomous semiflows in population biology
cites work: Persistence under Relaxed Point-Dissipativity (with Application to an Endemic Model)
cites work: Persistence in dynamical systems
cites work: Q3975200
cites work: A model for tuberculosis with exogenous reinfection
cites work: Dynamical models of tuberculosis and their applications
cites work: The basic reproduction number in some discrete-time epidemic models
cites work: Q4336515
cites work: Q4700332
description: scientific article; zbMATH DE number 6014513