DIFFERENTIAL-EQUATION MODELS OF SOME PARASITIC INFECTIONS - METHODS FOR THE STUDY OF ASYMPTOTIC-BEHAVIOR
DIFFERENTIAL-EQUATION MODELS OF SOME PARASITIC INFECTIONS - METHODS FOR THE STUDY OF ASYMPTOTIC-BEHAVIOR
复制标题
DOI：
10.1002/cpa.3160380607
复制
发表时间：
1985-01-01
影响因子：
3
通讯作者：
GABRIEL, JP
中科院分区：
文献类型：
--
作者：
HIRSCH, WM;HANISCH, H;GABRIEL, JP
本文讨论了在寄生虫感染传播研究中出现的一类二维常微分方程自治系统解的渐近行为。本主题的现象学方面已在bbb中描述。在目前的工作中，我们将强调数学方法，因此我们在这里只给出寄生虫学背景的味道。在[7]，[8]中，Nhsell和Hirsch提出了两种寄生虫传播的数学模型，雌雄异株（两性）和雌雄同体（单性）。这两种蠕虫的生命周期相似。有一种脊椎动物宿主，它产生并排泄第一种幼虫形式。这感染了一个软体动物宿主，它产生并排泄第二种幼虫。反过来，这又感染脊椎动物宿主，完成生命周期。因此，传播的动态可以概括为从脊椎动物到软体动物种群的流动，然后再返回。
We discuss in this paper the asymptotic behavior of solutions of certain two-dimensional autonomous systems of ordinary differential equations which arise in the study of the transmission of parasitic infections. The phenomenological aspects of the subject have been described in [2]. In the present work we shall emphasize mathematical methods, and therefore we give here only the flavor of the parasitological background., In [7],[8], Nhsell and Hirsch pr ‘oposed mathematical models of the transmission of two types of parasitic worms, dioecious (two sexes) and hermaphroditic (single sex). Both types of worms have similar life-cycles. There is a vertebrate host which produces and excretes a first larval form. This infects a molluscan host, which produces and excretes a second larval form. In turn, this infects a vertebrate host, completing the life-cycte. Thus the dynamics of transmission can be epitomized as a flow from the vertebrate to the molluscan population and back again.