Dynamical Analysis of a <i>Schistosomiasis japonicum</i> Model with Time Delay

Abstract

In this paper, a Schistosomiasis japonicum model incorporating time delay is proposed which represents the developmental time from cercaria penetration through skins of human hosts to egg laying. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equations, the local stability of the equilibria is investigated. And it proves that Hopf bifurcations occur when the time delay passes through a sequence of critical value. Furthermore, the explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions are derived by using techniques from the normal form theory and Center Manifold Theorem. Some numerical simulations which support our theoretical analysis are also conducted.