Diekmann O, de Graaf W F, Kretzschmar M E E, Teunis P F M
Department of Mathematics, Utrecht University, Utrecht, The Netherlands.
Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, Utrecht, The Netherlands.
J Math Biol. 2018 Dec;77(6-7):2023-2048. doi: 10.1007/s00285-018-1239-5. Epub 2018 May 15.
The aim is to describe the distribution of immune status (as captured by antibody level) on the basis of a within-host submodel for continuous waning and occasional boosting. Inspired by Feller's fundamental work and the more recent delay equation formulation of models for the dynamics of physiologically structured populations, we derive, for given force of infection, a linear renewal equation. The solution is obtained by generation expansion, with the generation number corresponding to the number of times the individual became infected. Our main result provides a precise characterization of the stable distribution of immune status.
目的是基于宿主内连续衰减和偶尔增强的子模型来描述免疫状态（以抗体水平衡量）的分布。受费勒的基础工作以及生理结构种群动态模型的最新延迟方程公式的启发，对于给定的感染强度，我们推导出一个线性更新方程。通过世代展开获得解，世代数对应个体被感染的次数。我们的主要结果给出了免疫状态稳定分布的精确特征。
