Zhao Ruijun, Milner Fabio Augusto
Department of Mathematics, Purdue University, West Lafayette, IN 47907-2067, USA.
Bull Math Biol. 2008 Oct;70(7):1886-905. doi: 10.1007/s11538-008-9330-5. Epub 2008 Jul 31.
We describe and analyze a mathematical model for schistosomiasis in which infected snails are distinguished from susceptible through increased mortality and no reproduction. We based the model on the same derivation as Anderson and May (J. Anim. Ecol. 47:219-247, 1978), Feng and Milner (A New Mathematical Model of Schistosomiasis, Mathematical Models in Medical and Health Science, Nashville, TN, 1997. Innov. Appl. Math., Vanderbilt Univ. Press, Nashville, pp. 117-128, 1998), and May and Anderson (J. Anim. Ecol. 47:249-267, 1978), but used logistic growth both in human and snail hosts. We introduce a parameter r, the effective coverage of medical treatment/prevention to control the infection. We determine a reproductive number for the disease directly related to its persistence and extinction. Finally, we obtain a critical value for r that indicates the minimum treatment effort needed in order to clear out the disease from the population.
我们描述并分析了一种血吸虫病的数学模型，在该模型中，受感染的蜗牛通过死亡率增加和无繁殖能力与易感蜗牛区分开来。我们基于与安德森和梅（《动物生态学杂志》47:219 - 247，1978年）、冯和米尔纳（《血吸虫病的一种新数学模型》，《医学与健康科学中的数学模型》，田纳西州纳什维尔，1997年。《创新应用数学》，范德比尔特大学出版社，纳什维尔，第117 - 128页，1998年）以及梅和安德森（《动物生态学杂志》47:249 - 267，1978年）相同的推导，但在人类宿主和蜗牛宿主中都使用了逻辑斯蒂增长。我们引入一个参数r，即医疗治疗/预防的有效覆盖率，以控制感染。我们确定了一个与疾病持续存在和灭绝直接相关的繁殖数。最后，我们得到了r的一个临界值，该值表明为了从人群中清除疾病所需的最小治疗力度。
