Chan M S, Isham V S
Wellcome Trust Centre for the Epidemiology of Infectious Disease, University of Oxford, UK.
Math Biosci. 1998 Aug 1;151(2):179-98. doi: 10.1016/s0025-5564(98)10014-7.
Schistosomiasis is a helminth (worm) infection with approximately 200 million people infected worldwide. There is still controversy on whether differing worm burdens between individuals is a result of differing contact rates or of acquired immunity. In this paper, we present a stochastic modelling framework to address these issues. By using appropriate approximations for the higher moments of the joint distributions, differential equations for the means, variances and co-variances of infection and immunity can be obtained. Numerical solutions of these equations to obtain age profiles of the above properties were compared with Monte Carlo simulations of the stochastic process. Simulations showed that the results depended on whether between host heterogeneity was generated by differing contact rates or differing immune responses. Heterogeneity in contact rates produced a highly aggregated distribution of parasites with a large variance/mean ratio. Heterogeneity in the immune response had very little effect on the overall dynamics. This agrees with the predominant field evidence which would suggest that infection is mainly determined by ecology with a smaller contribution of immunity.
血吸虫病是一种由蠕虫引起的感染，全球约有2亿人感染。个体之间不同的虫负荷是由于不同的接触率还是获得性免疫导致的，目前仍存在争议。在本文中，我们提出了一个随机建模框架来解决这些问题。通过对联合分布的高阶矩使用适当的近似，可以得到感染和免疫的均值、方差和协方差的微分方程。将这些方程的数值解以获得上述属性的年龄分布与随机过程的蒙特卡罗模拟进行了比较。模拟结果表明，结果取决于宿主间的异质性是由不同的接触率还是不同的免疫反应产生的。接触率的异质性产生了寄生虫高度聚集的分布，方差/均值比很大。免疫反应的异质性对整体动态影响很小。这与主要的现场证据一致，表明感染主要由生态学决定，免疫的作用较小。
