Dynamical Behavior and Stability Analysis in a Hybrid Epidemiological-Economic Model with Incubation
文献类型： 外文期刊
作者： Liu, Chao 1 ; Yue, Wenquan 3 ; Liu, Peiyong 2 ;
作者机构： 1.Northeastern Univ, Inst Syst Sci, Shenyang 110004, Peoples R China
2.Northeastern Univ, State Key Lab Integrated Automat Proc Ind, Shenyang 110004, Peoples R China
3.Hebei Acad Agr & Forestry Sci, Changli Inst Fruit Forestry, Changli 066600, Peoples R China
4.Northeastern Univ, Coll Life & Hlth Sci, Inst Biotechnol, Shenyang 110004, Peoples R China
期刊名称：ABSTRACT AND APPLIED ANALYSIS （ 影响因子：1.274； 五年影响因子：1.288 ）
ISSN： 1085-3375
年卷期： 2014 年
页码：
收录情况： SCI
摘要： 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.
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