Mathematical modelling and control of echinococcus in Qinghai province, China
In this paper, two mathematical models, the baseline model and theintervention model, are proposed to study the transmission dynamicsof echinococcus. A global forward bifurcation completelycharacterizes the dynamical behavior of the baseline model. That is,when the basic reproductive number is les...
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| Format: | Article |
| Language: | English |
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AIMS Press
2012-12-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.425 |
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| author | Liumei Wu Baojun Song Wen Du Jie Lou |
| author_facet | Liumei Wu Baojun Song Wen Du Jie Lou |
| author_sort | Liumei Wu |
| collection | DOAJ |
| description | In this paper, two mathematical models, the baseline model and theintervention model, are proposed to study the transmission dynamicsof echinococcus. A global forward bifurcation completelycharacterizes the dynamical behavior of the baseline model. That is,when the basic reproductive number is less than one, thedisease-free equilibrium is asymptotically globally stable; when the number isgreater than one, the endemic equilibrium is asymptotically globally stable. Forthe intervention model, however, the basic reproduction number aloneis not enough to describe the dynamics, particularly for the casewhere the basic reproductive number is less then one. The emergenceof a backward bifurcation enriches the dynamical behavior of themodel. Applying these mathematical models to Qinghai Province,China, we found that the infection of echinococcus is in an endemicstate. Furthermore, the model appears to be supportive of humaninterventions in order to change the landscape of echinococcusinfection in this region. |
| format | Article |
| id | doaj-art-d9bab513d63240c69fae284ddfd1453d |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2012-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-d9bab513d63240c69fae284ddfd1453d2025-01-24T02:25:53ZengAIMS PressMathematical Biosciences and Engineering1551-00182012-12-0110242544410.3934/mbe.2013.10.425Mathematical modelling and control of echinococcus in Qinghai province, ChinaLiumei Wu0Baojun Song1Wen Du2Jie Lou3Department of Mathematics, Shanghai University, 99 Shangda Road, Shanghai 200444Department of Mathematics, Shanghai University, 99 Shangda Road, Shanghai 200444Department of Mathematics, Shanghai University, 99 Shangda Road, Shanghai 200444Department of Mathematics, Shanghai University, 99 Shangda Road, Shanghai 200444In this paper, two mathematical models, the baseline model and theintervention model, are proposed to study the transmission dynamicsof echinococcus. A global forward bifurcation completelycharacterizes the dynamical behavior of the baseline model. That is,when the basic reproductive number is less than one, thedisease-free equilibrium is asymptotically globally stable; when the number isgreater than one, the endemic equilibrium is asymptotically globally stable. Forthe intervention model, however, the basic reproduction number aloneis not enough to describe the dynamics, particularly for the casewhere the basic reproductive number is less then one. The emergenceof a backward bifurcation enriches the dynamical behavior of themodel. Applying these mathematical models to Qinghai Province,China, we found that the infection of echinococcus is in an endemicstate. Furthermore, the model appears to be supportive of humaninterventions in order to change the landscape of echinococcusinfection in this region.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.425backward bifurcationglobal stability.echinococcosismathematical model |
| spellingShingle | Liumei Wu Baojun Song Wen Du Jie Lou Mathematical modelling and control of echinococcus in Qinghai province, China Mathematical Biosciences and Engineering backward bifurcation global stability. echinococcosis mathematical model |
| title | Mathematical modelling and control of echinococcus in Qinghai province, China |
| title_full | Mathematical modelling and control of echinococcus in Qinghai province, China |
| title_fullStr | Mathematical modelling and control of echinococcus in Qinghai province, China |
| title_full_unstemmed | Mathematical modelling and control of echinococcus in Qinghai province, China |
| title_short | Mathematical modelling and control of echinococcus in Qinghai province, China |
| title_sort | mathematical modelling and control of echinococcus in qinghai province china |
| topic | backward bifurcation global stability. echinococcosis mathematical model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.425 |
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