Dynamics of a delay Schistosomiasis model in snail infections
In this paper we modify and study a system of delay differential equations model proposed by Nåsell and Hirsch (1973) for the transmission dynamics of schistosomiasis. The modified stochastic version of MacDonald’s model takes into account the time delay for the transmission of infection. We carry o...
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| Format: | Article |
| Language: | English |
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AIMS Press
2011-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.1099 |
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| _version_ | 1832590184691007488 |
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| author | Chunhua Shan Hongjun Gao Huaiping Zhu |
| author_facet | Chunhua Shan Hongjun Gao Huaiping Zhu |
| author_sort | Chunhua Shan |
| collection | DOAJ |
| description | In this paper we modify and study a system of delay differential equations model proposed by Nåsell and Hirsch (1973) for the transmission dynamics of schistosomiasis. The modified stochastic version of MacDonald’s model takes into account the time delay for the transmission of infection. We carry out bifurcation studies of the model. The saddle-node bifurcation of the model suggests that the transmission and spread of schistosomiasis is initial size dependent. The existence of a Hopf bifurcation due to the delay indicates that the transmission can be periodic. |
| format | Article |
| id | doaj-art-581858c61f6042da97430cf91b860588 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2011-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-581858c61f6042da97430cf91b8605882025-01-24T02:02:16ZengAIMS PressMathematical Biosciences and Engineering1551-00182011-07-01841099111510.3934/mbe.2011.8.1099Dynamics of a delay Schistosomiasis model in snail infectionsChunhua Shan0Hongjun Gao1Huaiping Zhu2Department of Mathematics and Statistics, LAMPS and CDM, York University, Toronto, ON, M3J 1P3Department of Mathematics and Statistics, LAMPS and CDM, York University, Toronto, ON, M3J 1P3Department of Mathematics and Statistics, LAMPS and CDM, York University, Toronto, ON, M3J 1P3In this paper we modify and study a system of delay differential equations model proposed by Nåsell and Hirsch (1973) for the transmission dynamics of schistosomiasis. The modified stochastic version of MacDonald’s model takes into account the time delay for the transmission of infection. We carry out bifurcation studies of the model. The saddle-node bifurcation of the model suggests that the transmission and spread of schistosomiasis is initial size dependent. The existence of a Hopf bifurcation due to the delay indicates that the transmission can be periodic.https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.1099time delaystabilityhopf bifurcation.saddle-node bifurcationschistosomiasis |
| spellingShingle | Chunhua Shan Hongjun Gao Huaiping Zhu Dynamics of a delay Schistosomiasis model in snail infections Mathematical Biosciences and Engineering time delay stability hopf bifurcation. saddle-node bifurcation schistosomiasis |
| title | Dynamics of a delay Schistosomiasis model in snail infections |
| title_full | Dynamics of a delay Schistosomiasis model in snail infections |
| title_fullStr | Dynamics of a delay Schistosomiasis model in snail infections |
| title_full_unstemmed | Dynamics of a delay Schistosomiasis model in snail infections |
| title_short | Dynamics of a delay Schistosomiasis model in snail infections |
| title_sort | dynamics of a delay schistosomiasis model in snail infections |
| topic | time delay stability hopf bifurcation. saddle-node bifurcation schistosomiasis |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.1099 |
| work_keys_str_mv | AT chunhuashan dynamicsofadelayschistosomiasismodelinsnailinfections AT hongjungao dynamicsofadelayschistosomiasismodelinsnailinfections AT huaipingzhu dynamicsofadelayschistosomiasismodelinsnailinfections |