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Title of Journal: Bull Math Biol

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Abbravation: Bulletin of Mathematical Biology

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Springer US

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DOI

10.1002/hlca.19420250532

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1522-9602

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The Dynamics of Growing Islets and Transmission of

Authors: Chunhua Shan Xiaonong Zhou Huaiping Zhu
Publish Date: 2014/04/24
Volume: 76, Issue: 5, Pages: 1194-1217
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Abstract

We formulate and analyze a system of ordinary differential equations for the transmission of schistosomiasis japonica on the islets in the Yangtze River China The impact of growing islets on the spread of schistosomiasis is investigated by the bifurcation analysis Using the projection technique developed by Hassard Kazarinoff and Wan the normal form of the cusp bifurcation of codimension 2 is derived to overcome the technical difficulties in studying the existence stability and bifurcation of the multiple endemic equilibria in highdimensional phase space We show that the model can also undergo transcritical bifurcations saddlenode bifurcations a pitchfork bifurcation and Hopf bifurcations The bifurcation diagrams and epidemiological interpretations are given We conclude that when the islet reaches a critical size the transmission cycle of the schistosomiasis japonica between wild rats Rattus norvegicus and snails Oncomelania hupensis could be established which serves as a possible source of schistosomiasis transmission along the Yangtze River


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