Journal of Applied Mathematics and Physics

Volume 7, Issue 4 (April 2019)

ISSN Print: 2327-4352   ISSN Online: 2327-4379

Google-based Impact Factor: 1.00  Citations  

Dynamical Analysis of a Schistosomiasis japonicum Model with Time Delay

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DOI: 10.4236/jamp.2019.74064    719 Downloads   1,577 Views  Citations

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.

Share and Cite:

Zhang, F. , Gao, S. , Cao, H. and Luo, Y. (2019) Dynamical Analysis of a Schistosomiasis japonicum Model with Time Delay. Journal of Applied Mathematics and Physics, 7, 948-967. doi: 10.4236/jamp.2019.74064.

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