Inaba Hisashi
Department of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro-ku, Tokyo 153-8914, Japan.
Math Biosci. 2006 May;201(1-2):15-47. doi: 10.1016/j.mbs.2005.12.017. Epub 2006 Feb 8.
In this paper we consider an age-duration-structured population model for HIV infection in a homosexual community. First we investigate the invasion problem to establish the basic reproduction ratio R(0) for the HIV/AIDS epidemic by which we can state the threshold criteria: The disease can invade into the completely susceptible population if R(0)>1, whereas it cannot if R(0)<1. Subsequently, we examine existence and uniqueness of endemic steady states. We will show sufficient conditions for a backward or a forward bifurcation to occur when the basic reproduction ratio crosses unity. That is, in contrast with classical epidemic models, for our HIV model there could exist multiple endemic steady states even if R(0) is less than one. Finally, we show sufficient conditions for the local stability of the endemic steady states.
在本文中，我们考虑了一个关于同性恋群体中HIV感染的年龄-病程结构的人口模型。首先，我们研究入侵问题，以建立HIV/AIDS流行的基本再生数(R(0))，据此我们可以陈述阈值标准：如果(R(0)>1)，疾病可以侵入完全易感人群，而如果(R(0)<1)，则不能侵入。随后，我们研究地方病稳态的存在性和唯一性。我们将展示当基本再生数超过1时发生向后或向前分岔的充分条件。也就是说，与经典的流行病模型不同，对于我们的HIV模型，即使(R(0))小于1，也可能存在多个地方病稳态。最后，我们展示地方病稳态局部稳定性的充分条件。
