Su Ying, Ruan Shigui, Wei Junjie
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, People's Republic of China.
J Math Biol. 2011 Sep;63(3):557-74. doi: 10.1007/s00285-010-0381-5. Epub 2010 Nov 16.
Malaria fever is highly periodic and is associated with the parasite replication cycles in red blood cells. The existence of periodicity in malaria infection demonstrates that parasite replication in different red blood cells is synchronized. In this article, rigorous mathematical analysis of an age-structured human malaria model of infected red blood cells (Rouzine and McKenzie, Proc Natl Acad Sci USA 100:3473-3478, 2003) is provided and the synchronization of Plasmodium falciparum erythrocytic stages is investigated. By using the replication rate as the bifurcation parameter, the existence of Hopf bifurcation in the age-structured malaria infection model is obtained. Numerical simulations indicate that synchronization with regular periodic oscillations (of period 48 h) occurs when the replication rate increases. Therefore, Kwiatkowski and Nowak's observation (Proc Natl Acad Sci USA 88:5111-5113, 1991) that synchronization could be generated at modest replication rates is confirmed.
疟疾热具有高度周期性，且与疟原虫在红细胞中的复制周期相关。疟疾感染中周期性的存在表明不同红细胞中的疟原虫复制是同步的。本文对一个关于受感染红细胞的年龄结构人类疟疾模型（Rouzine和McKenzie，《美国国家科学院院刊》100:3473 - 3478，2003）进行了严格的数学分析，并研究了恶性疟原虫红细胞阶段的同步性。通过将复制率作为分岔参数，得出了年龄结构疟疾感染模型中霍普夫分岔的存在。数值模拟表明，当复制率增加时会出现与规则周期性振荡（周期为48小时）的同步。因此，证实了Kwiatkowski和Nowak的观察结果（《美国国家科学院院刊》88:5111 - 5113，1991），即在适度复制率下可以产生同步。
