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

作　　者：Fumin Zhang Shujing Gao Huahua Cao Youquan Luo 

机构地区：[1]Key Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques, Gannan Normal University, Ganzhou, China

出　　处：《Journal of Applied Mathematics and Physics》2019年第4期948-967,共20页应用数学与应用物理（英文）

摘　　要：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.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.

关 键 词：SCHISTOSOMIASIS JAPONICUM Time Delay Stability HOPF BIFURCATION 

分 类 号：O1[理学—数学]