Dynamical behavior and stability analysis in a hybrid epidemiological-economic model with incubation
type: Item
instance of: scholarly article
title: Dynamical behavior and stability analysis in a hybrid epidemiological-economic model with incubation
zbMATH Open document ID: 1406.92594
DOI: 10.1155/2014/639405
author: Chao Liu
author: Wenquan Yue
author: Peiyong Liu
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: A hybrid SIR vector disease model with incubation is established, where susceptible host population satisfies the logistic equation and the recovered host individuals are commercially harvested. It is utilized to discuss the transmission mechanism of infectious disease and dynamical effect of commercial harvest on population dynamics. Positivity and permanence of solutions are analytically investigated. By choosing economic interest of commercial harvesting as a parameter, dynamical behavior and local stability of model system without time delay are studied. It reveals that there is a phenomenon of singularity induced bifurcation as well as local stability switch around interior equilibrium when economic interest increases through zero. State feedback controllers are designed to stabilize model system around the desired interior equilibria in the case of zero economic interest and positive economic interest, respectively. By analyzing corresponding characteristic equation of model system with time delay, local stability analysis around interior equilibrium is discussed due to variation of time delay. Hopf bifurcation occurs at the critical value of time delay and corresponding limit cycle is also observed. Furthermore, directions of Hopf bifurcation and stability of the bifurcating periodic solutions are studied. Numerical simulations are carried out to show consistency with theoretical analysis.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 91B76
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 7022800
zbMATH Keywords: hybrid epidemiological-economic model
zbMATH Keywords: stability
zbMATH Keywords: harvesting
Wikidata QID: Q59040269
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/639405
OpenAlex ID: W2046614337
cites work: The mathematics of infectious diseases
cites work: Stability analysis for a vector disease model
cites work: Dynamical behavior of epidemiological models with nonlinear incidence rates
cites work: Global asymptotic properties of a delay SIR epidemic model with finite incubation times
cites work: Global asymptotic stability of an \(SIR\) epidemic model with distributed time delay.
cites work: Global stability of an SIR epidemic model with delay and general nonlinear incidence
cites work: STABILITY AND HOPF BIFURCATION OF A DELAY ECO‐EPIDEMIOLOGICAL MODEL WITH NONLINEAR INCIDENCE RATE
cites work: Analysis of an SIR model with bilinear incidence rate
cites work: Stability analysis of delayed SIR epidemic models with a class of nonlinear incidence rates
cites work: Dynamical behavior of an epidemic model with a nonlinear incidence rate
cites work: Global stability of an SIR epidemic model with time delay.
cites work: Global stability of a SIR epidemic model with nonlinear incidence rate and time delay
cites work: Q3997210
cites work: Harvesting as a disease control measure in an eco-epidemiological system -- a theoretical study
cites work: Dynamics of a ratio-dependent eco-epidemiological system with prey harvesting
cites work: On an eco-epidemiological model with prey harvesting and predator switching: local and global perspectives
cites work: The dynamics of an eco-epidemic model with distributed time delay and impulsive control strategy
cites work: BIFURCATION AND CONTROL IN A DIFFERENTIAL-ALGEBRAIC HARVESTED PREY-PREDATOR MODEL WITH STAGE STRUCTURE FOR PREDATOR
cites work: Dynamical behavior in a stage-structured differential-algebraic prey-predator model with discrete time delay and harvesting
cites work: Bifurcations of a singular prey-predator economic model with time delay and stage structure
cites work: Hopf bifurcation for a differential-algebraic biological economic system with time delay
cites work: Bifurcation and control of a bioeconomic model of a prey-predator system with a time delay
cites work: Dynamical analysis and control in a delayed differential-algebraic bio-economic model with stage structure and diffusion
cites work: Q3852479
cites work: Looking for nonnegative solutions of a Leontief dynamic model.
cites work: Computation of Singular and Singularity Induced Bifurcation Points of Differential-Algebraic Power System Model
cites work: Singular Dynamic Leontief Systems
cites work: Permanence and positive periodic solution for a single-species nonautonomous delay diffusive models
cites work: Q4420178
cites work: Introduction to functional differential equations
cites work: Delay differential equations: with applications in population dynamics
cites work: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
cites work: Local bifurcations and feasibility regions in differential-algebraic systems
cites work: Elements of Mathematical Ecology
cites work: Singularity induced bifurcation and the van der Pol oscillator
cites work: The singularity-induced bifurcation and its Kronecker normal form
cites work: An improved version of the singularity-induced bifurcation theorem
cites work: Singular control systems
cites work: The trade-off between mutual interference and time lags in predator-prey systems
cites work: Q3930015
description: scientific article; zbMATH DE number 7022800