血吸虫病模型翻译修订.doc

1.IntroductionIn modeling our environment one of the most difficult choices we haveto make is the amount of detail we are willing to put into the model or,rather, the amount of detail we are capable of modeling due to our limited ability to gather information. This decision is especially crucial when trying to describe biotic interactions, and it requires a delicate balancebetween the need for enough detail to resolve important characteristicsof the dynamics of the interactions and our ability to obtain data insufficient detail to use the model.When modeling any ecosystem in some detail, one should begin with asimple model. If this model captures the essential features of theinteractions being modeled, simulations should reflect those aspects of reallife behavior. Hopefully, a simple model can be thoroughly analyzed and then built upon to derive increasingly more complex models. At eachstage these require the same type of validation concerning the new features being added and the extent to which the numbers predicted by themodel compare with real data.Several studies have addressed the dynamics of schistosomiasis andother helminth infection of humans 14,9,10,1315,18,19,25,26 usingsystems similar to the one we are interested in. We shall consider hereSchistosoma mansoni, a human blood fluke which causes schistosomiasis.The freshwater snail Biomphalaria glabrata serves as the main interme-diate host. Anderson and May1 introduced models for macroparasite- host interactions when the parasites have direct lifecycles involving only a single host population and one stage of parasites. In 19 a free-living stage of the parasite was considered in the model. Interactions between schistosome infection and molluscan intermedia- te hosts (snails) were studied in 2. Multiple stages of parasites and two host populations were considered in 10 which, however, assumes a constant population size of the human host and no density dependence and age of infection in the snail population. Campaigns against S.manso- ni frequently focus on treatment of infected humans with Praziquantal or other drugs that kill the parasites in the treated humans. Mathemati- cal models hve been used to assess community chemotherapy programs for schistosomiasis through simulations 6,7. These models also do not include explicit snail dynamics. We shall introduce in this paper models with more features describing the dynamics of schistosomes, snails, and humans; we shall study their qualitative and quantitative mathematical properties and deduce biologi-cal and ecological consequences. In particular, we shall model treatment of humans and establish an explicit treatment rate threshold above which parasites will die out or the infection in the population will remain below a certain level. We shall also study the sensitivity of the mean parasite load per human host to the changes in the two transmission rates: the mansnail transmission rate and the snailman transmission rate. We shall introduce an age structure in the class of infected snails,since their cercarial production seems to be periodic in time and there is a prepatent period after initial infection (see Fig. 1, 21). The manschistosome interaction is modeled as a macroparasite infection and we assume a negative binomial distribution for the parasite distribution among the human hosts as in 1. The population sizes of both human and snail hosts are variable by allowing disease-induced mortality. We shall also compare the prediction of the new models with that of a simpler model proposed earlier by other authors 25,26, to which ourmodel reduces if we assume no parasiteinduced additional mortality inhumans as well as constant cercarial production by infected snails. We shall show that this mean parasite load does not depend linearly on the transmission rate from snail to human as the simpler model predicts, but rather on the square root of this transmission rate. We shall also show(numerically) that the new model may produce a bifurcation at which the unique endemic equilibrium changes its stability and stable periodic solutions exist.Fig. 1. This graph shows how the number of cercariae released by a snail changes with time since infection. The prepatent period is about 35 days after initial infection. After that the number fluctuates with a period of about 30 days until the snail dies.1.引言在模拟环境中，我们不得不做出的一个最艰难的抉择之一是，由于我们收集数据的能力有限，我们将投入大量细节到模型中，或者相反，我们只能掌握我们力所能及的模型。当试图描述生物间相互作用的时候，这个抉择就显得尤为重要了，它需要有一个微妙的平衡，即对于尽力解决相互作用间动力主要特征的需要同我们为了使用模型而尽可能获取数据能力之间的平衡。当我们在某些细节上模拟任何生态系统时，起初都应该从一个简单的模型开始。如果这个模型捕捉到了模拟过的相互作用的基本功能，模拟就应该反映现实生活习惯中的那些方面。我们希望，一个简单的模型能够用来深入分析，然后建立在提取更加复杂的模型之上。在每一阶段，这些都需要被添加新的功能的相同类型的验证，以及同真实数据相比，用模型得出的数据预测的真实程度。有几项研究利用我们感兴趣的这个系统解决了血吸虫病和其他人体蠕虫感染的动力学原理。在这里。我们将考虑曼氏血吸虫，这是一个侥幸造成血吸虫病的人的血液。淡水蜗牛光滑双脐螺作为主要的中间宿主。安德森.和梅.作者用英文介绍了几种宏观寄生虫宿主相互作用的模型，当寄生虫仅仅涉及单一宿主人口及寄生虫的一个阶段时，它们往往有一个直接的生命周期。在19中，寄生虫的一个自由生存阶段被考虑在模型之内。2研究了血吸虫感染同软体动物中间宿主（钉螺）之间的相互作用。然而，10中则考虑了寄生虫和两个宿主数目的多个阶段，它假设了人体宿主的一个连续的数目规模，钉螺数目中的感染时间以及无密度依赖。对抗曼氏血吸虫的平凡运动将重点放在利用Praziquantal或其他人体治疗中杀死寄生虫的药物对已感人群的治疗上。数学模型已经通过模拟6,7，被用来评估社会血吸虫病化疗方案。这些模式也没有包括明确的蜗牛动力。我们将在本文中介绍几个模型，它们用更多特征描述血吸虫、蜗牛和人类的动力学原理；我们会研究它们的定性的和定量的数学性质，并推断生物和生态结果。 特别地，我们将对人体治疗进行建模，并且建立一个明确的治疗率阈值，在此阈值以上，寄生虫将会消亡，或者人口感染将保持在一个固定水平以下。我们也将研究每个人体宿主负载的寄生虫在两个传输速率变化中的敏感度：人-蜗牛传输速率和蜗牛-人传输速率。 我们将介绍受感染的螺类年龄结构，因为他们的尾蚴生产看起来是及时定期的，并且在感染初期有一个潜伏期（见图1，21） 人和血吸虫之间的相互作用建模为一个宏观的寄生虫感染，我们假设一个负二项分布作为人体宿主寄生虫分布，如1所示。在允许疾病死亡率的前提下，人体和蜗牛