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Dynamical Analysis of a Schistosomiasis japonicum Model with Time Delay

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Document pages: 20 pages

Abstract: In this paper, a Schistosomiasis japonicum modelincorporating time delay is proposed which represents the developmental timefrom cercaria penetration through skins of human hosts to egg laying. Bylinearizing the system at the positive equilibrium and analyzing the associatedcharacteristic equations, the local stability of the equilibria isinvestigated. And it proves that Hopf bifurcations occur when the time delaypasses through a sequence of critical value. Furthermore, the explicit formulae for determining the stability and thedirection of the Hopf bifurcation periodic solutions are derived by usingtechniques from the normal form theory and Center Manifold Theorem. Somenumerical simulations which support our theoretical analysis are alsoconducted.

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