A Mathematical Model with Delays for Schistosomiasis Japonicum Transmission |
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Authors: | Yu YANG and Dongmei XIAO |
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Institution: | 1. Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China 2. Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240,China |
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Abstract: | A dynamic model of schistosoma japonicum transmission is presented that incorporates effects of the prepatent periods of the
different stages of schistosoma into Barbour’s model. The model consists of four delay differential equations. Stability of
the disease free equilibrium and the existence of an endemic equilibrium for this model are stated in terms of a key threshold
parameter. The study of dynamics for the model shows that the endemic equilibrium is globally stable in an open region if
it exists and there is no delays, and for some nonzero delays the endemic equilibrium undergoes Hopf bifurcation and a periodic
orbit emerges. Some numerical results are provided to support the theoretic results in this paper. These results suggest that
prepatent periods in infection affect the prevalence of schistosomiasis, and it is an effective strategy on schistosomiasis
control to lengthen in prepatent period on infected definitive hosts by drug treatment (or lengthen in prepatent period on
infected intermediate snails by lower water temperature). |
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Keywords: | A mathematical model Schistosoma japonicum transmission Dynamics Globally stable Periodic orbits |
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