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Abstract and Applied Analysis
Volume 2014, Article ID 639405, 22 pages
Research Article

Dynamical Behavior and Stability Analysis in a Hybrid Epidemiological-Economic Model with Incubation

1Institute of Systems Science, Northeastern University, Shenyang 110004, China
2State Key Laboratory of Integrated Automation of Process Industry, Northeastern University, Shenyang 110004, China
3Changli Institute of Fruit Forestry, Hebei Academy of Agricultural and Forestry Sciences, Changli 066600, China
4Institute of Biotechnology, College of Life and Health Sciences, Northeastern University, Shenyang 110004, China

Received 12 January 2014; Accepted 15 April 2014; Published 12 May 2014

Academic Editor: Weiming Wang

Copyright © 2014 Chao Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.