TITLE:
Dynamical Analysis of a Schistosomiasis japonicum Model with Time Delay
AUTHORS:
Fumin Zhang, Shujing Gao, Huahua Cao, Youquan Luo
KEYWORDS:
Schistosomiasis japonicum, Time Delay, Stability, Hopf Bifurcation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.4,
April
29,
2019
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.