Dynamical Behavior and Stability Analysis in a Hybrid Epidemiological-Economic Model with Incubation
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 commer...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/639405 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832552495931457536 |
|---|---|
| author | Chao Liu Wenquan Yue Peiyong Liu |
| author_facet | Chao Liu Wenquan Yue Peiyong Liu |
| author_sort | Chao Liu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-4b792fd3a94e4f68834c3ed3f2ccfbae |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-4b792fd3a94e4f68834c3ed3f2ccfbae2025-02-03T05:58:32ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/639405639405Dynamical Behavior and Stability Analysis in a Hybrid Epidemiological-Economic Model with IncubationChao Liu0Wenquan Yue1Peiyong Liu2Institute of Systems Science, Northeastern University, Shenyang 110004, ChinaChangli Institute of Fruit Forestry, Hebei Academy of Agricultural and Forestry Sciences, Changli 066600, ChinaState Key Laboratory of Integrated Automation of Process Industry, Northeastern University, Shenyang 110004, ChinaA 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.http://dx.doi.org/10.1155/2014/639405 |
| spellingShingle | Chao Liu Wenquan Yue Peiyong Liu Dynamical Behavior and Stability Analysis in a Hybrid Epidemiological-Economic Model with Incubation Abstract and Applied Analysis |
| title | Dynamical Behavior and Stability Analysis in a Hybrid Epidemiological-Economic Model with Incubation |
| title_full | Dynamical Behavior and Stability Analysis in a Hybrid Epidemiological-Economic Model with Incubation |
| title_fullStr | Dynamical Behavior and Stability Analysis in a Hybrid Epidemiological-Economic Model with Incubation |
| title_full_unstemmed | Dynamical Behavior and Stability Analysis in a Hybrid Epidemiological-Economic Model with Incubation |
| title_short | Dynamical Behavior and Stability Analysis in a Hybrid Epidemiological-Economic Model with Incubation |
| title_sort | dynamical behavior and stability analysis in a hybrid epidemiological economic model with incubation |
| url | http://dx.doi.org/10.1155/2014/639405 |
| work_keys_str_mv | AT chaoliu dynamicalbehaviorandstabilityanalysisinahybridepidemiologicaleconomicmodelwithincubation AT wenquanyue dynamicalbehaviorandstabilityanalysisinahybridepidemiologicaleconomicmodelwithincubation AT peiyongliu dynamicalbehaviorandstabilityanalysisinahybridepidemiologicaleconomicmodelwithincubation |