Department of Mathematics and Statistics, University of Central Oklahoma, Edmond, OK 73034, USA.
Math Biosci. 2010 May;225(1):59-67. doi: 10.1016/j.mbs.2010.02.001. Epub 2010 Feb 12.
A mathematical model of erythropoiesis subject to malaria infection is developed by combining ideas from previous models that addressed only one of the two phenomena. The nature of the model allows one to account for suppression of erythropoiesis by the toxin hemozoin, which is a by-product of digested hemoglobin. Following the derivation of the model, numerical simulations are performed and show that the number of parasites produced per bursting erythrocyte has the most significant effect of erythropoiesis. It is also shown that removing hemozoin may be an effective method for aiding the recovery of the erythrocyte population, but is not effective in maintaining a healthy population in the early stages of infection. The second half of the paper introduces an implicit finite difference scheme that was used to perform the simulations previously mentioned. An existence-uniqueness result is then provided via the numerical method.
建立了一个受疟疾感染影响的红细胞生成的数学模型，该模型结合了之前仅解决两种现象之一的模型的思路。该模型的性质使得人们可以考虑到由血红蛋白消化产生的毒素——血影蛋白对红细胞生成的抑制作用。在模型的推导之后，进行了数值模拟，结果表明每个爆裂红细胞产生的寄生虫数量对红细胞生成的影响最大。结果还表明，去除血影蛋白可能是一种有效辅助红细胞恢复的方法，但在感染早期对维持健康的种群并不有效。本文的后半部分介绍了之前提到的用于进行模拟的隐式有限差分方案。然后通过数值方法提供了存在唯一性结果。
