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| A Mathematical Model with Delays for Schistosomiasis Japonicum Transmission |
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Citation： |
Yu YANG,Dongmei XIAO.A Mathematical Model with Delays for Schistosomiasis Japonicum Transmission[J].Chinese Annals of Mathematics B,2010,31(4):433~446 |
| Page view： 1921
Net amount： 1121 |
Authors： |
Yu YANG; Dongmei XIAO; |
Foundation： |
the National Natural Science Foundation of China (Nos. 10831003, 10925102)
and the Program of Shanghai Subject Chief Scientist (No. 10XD1406200). |
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| Abstract： |
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). |
Keywords： |
A mathematical model, Schistosoma japonicum transmission, Dynamics,
Globally stable, Periodic orbits |
Classification： |
34C25, 92D25, 58F14 |
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