A mathematical model with delays for schistosomiasis japonicum transmission

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).

Keywords

A mathematical model / Schistosoma japonicum transmission / Dynamics / Globally stable / Periodic orbits

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