Dadi Zohreh, Alizade Samira
Department of Mathematics, University of Bojnord, Bojnord, Islamic Republic of Iran.
Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran.
Springerplus. 2016 Feb 1;5:106. doi: 10.1186/s40064-016-1737-0. eCollection 2016.
One of the important medical problems is infectious diseases such as HIV and hepatitis which annually causes the death of many people. So it is important to study infectious diseases parametric models. In this paper, we investigate differential equations system of HIV and hepatitis (with delay and without delay) from the stability and codimension-one bifurcation point of view. We show that their dynamical behaviour will change when the parameters vary. We prove that this model has a saddle-node bifurcation and transcritical bifurcation when the delay parameter is absent. Also by using the center manifold theory, we show that the delay model has a saddle-node bifurcation.
重要的医学问题之一是诸如艾滋病毒和肝炎等传染病，这些传染病每年导致许多人死亡。因此，研究传染病参数模型很重要。在本文中，我们从稳定性和余维一分岔点的角度研究艾滋病毒和肝炎的微分方程组（有延迟和无延迟）。我们表明，当参数变化时，它们的动力学行为会发生变化。我们证明，当不存在延迟参数时，该模型具有鞍结分岔和跨临界分岔。此外，通过使用中心流形理论，我们表明延迟模型具有鞍结分岔。
