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Dynamical Behavior and Stability Analysis in a Hybrid Epidemiological-Economic Model with Incubation
Joint Authors
Liu, Chao
Yue, Wenquan
Liu, Peiyong
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-22, 22 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-05-12
Country of Publication
Egypt
No. of Pages
22
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Liu, Chao& Yue, Wenquan& Liu, Peiyong. 2014. Dynamical Behavior and Stability Analysis in a Hybrid Epidemiological-Economic Model with Incubation. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-22.
https://search.emarefa.net/detail/BIM-1014416
Modern Language Association (MLA)
Liu, Chao…[et al.]. Dynamical Behavior and Stability Analysis in a Hybrid Epidemiological-Economic Model with Incubation. Abstract and Applied Analysis No. 2014 (2014), pp.1-22.
https://search.emarefa.net/detail/BIM-1014416
American Medical Association (AMA)
Liu, Chao& Yue, Wenquan& Liu, Peiyong. Dynamical Behavior and Stability Analysis in a Hybrid Epidemiological-Economic Model with Incubation. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-22.
https://search.emarefa.net/detail/BIM-1014416
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1014416