Global analysis of a simple parasite-host model withhomoclinic orbits
In this paper, a simple parasite-host model proposed by Ebert etal.(2000) is reconsidered. The basic epidemiological reproductionnumber of parasite infection ($R_0$) and the basic demographicreproduction number of infected hosts ($R_1$) are given. The globaldynamics of the model is completely inves...
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AIMS Press
2012-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.767 |
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| author | Jianquan Li Yanni Xiao Yali Yang |
| author_facet | Jianquan Li Yanni Xiao Yali Yang |
| author_sort | Jianquan Li |
| collection | DOAJ |
| description | In this paper, a simple parasite-host model proposed by Ebert etal.(2000) is reconsidered. The basic epidemiological reproductionnumber of parasite infection ($R_0$) and the basic demographicreproduction number of infected hosts ($R_1$) are given. The globaldynamics of the model is completely investigated, and the existenceof heteroclinic and homoclinic orbits is theoretically proved,which implies that the outbreak of parasite infection may happen.The thresholds determining the host extinction in the presence ofparasite infection and variation in the equilibrium level of theinfected hosts with $R_0$ are found. The effects of $R_0$ and $R_1$on dynamics of the model are considered and we show that theequilibrium level of the infected host may not be monotone withrespect to $R_0$. In particular, it is found that full loss offecundity of infected hosts may lead to appearance of the singularcase. |
| format | Article |
| id | doaj-art-839345fc28074c268884bd99bfc89984 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2012-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-839345fc28074c268884bd99bfc899842025-01-24T02:07:06ZengAIMS PressMathematical Biosciences and Engineering1551-00182012-09-019476778410.3934/mbe.2012.9.767Global analysis of a simple parasite-host model withhomoclinic orbitsJianquan Li0Yanni Xiao1Yali Yang2Faculty of Science, Air Force Engineering University, Xi'an 710051Faculty of Science, Air Force Engineering University, Xi'an 710051Faculty of Science, Air Force Engineering University, Xi'an 710051In this paper, a simple parasite-host model proposed by Ebert etal.(2000) is reconsidered. The basic epidemiological reproductionnumber of parasite infection ($R_0$) and the basic demographicreproduction number of infected hosts ($R_1$) are given. The globaldynamics of the model is completely investigated, and the existenceof heteroclinic and homoclinic orbits is theoretically proved,which implies that the outbreak of parasite infection may happen.The thresholds determining the host extinction in the presence ofparasite infection and variation in the equilibrium level of theinfected hosts with $R_0$ are found. The effects of $R_0$ and $R_1$on dynamics of the model are considered and we show that theequilibrium level of the infected host may not be monotone withrespect to $R_0$. In particular, it is found that full loss offecundity of infected hosts may lead to appearance of the singularcase.https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.767homoclinicorbitparasite-host modelglobal dynamicsreproduction number. |
| spellingShingle | Jianquan Li Yanni Xiao Yali Yang Global analysis of a simple parasite-host model withhomoclinic orbits Mathematical Biosciences and Engineering homoclinicorbit parasite-host model global dynamics reproduction number. |
| title | Global analysis of a simple parasite-host model withhomoclinic orbits |
| title_full | Global analysis of a simple parasite-host model withhomoclinic orbits |
| title_fullStr | Global analysis of a simple parasite-host model withhomoclinic orbits |
| title_full_unstemmed | Global analysis of a simple parasite-host model withhomoclinic orbits |
| title_short | Global analysis of a simple parasite-host model withhomoclinic orbits |
| title_sort | global analysis of a simple parasite host model withhomoclinic orbits |
| topic | homoclinicorbit parasite-host model global dynamics reproduction number. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.767 |
| work_keys_str_mv | AT jianquanli globalanalysisofasimpleparasitehostmodelwithhomoclinicorbits AT yannixiao globalanalysisofasimpleparasitehostmodelwithhomoclinicorbits AT yaliyang globalanalysisofasimpleparasitehostmodelwithhomoclinicorbits |