Nonlinear Physiologically Structured Population Models with Two Internal Variables
Nonlinear Physiologically Structured Population Models with Two Internal Variables
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DOI：
10.1007/s00332-020-09638-5
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发表时间：
2020-06
影响因子：
3
通讯作者：
Hao Kang;Xi Huo;S. Ruan
中科院分区：
文献类型：
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作者：
Hao Kang;Xi Huo;S. Ruan
双内变量的一阶双曲型偏微分方程已被用来模拟具有两种生理结构的生物学和流行病学问题，如流行病模型中的实足年龄和感染年龄，年龄和另一个生理特征细胞群体模型中的细胞年龄和分子含量（细胞周期蛋白含量、成熟水平、质粒拷贝、端粒长度）。本文利用积分半群理论和非稠定算子研究了具有两个内变量的非线性双生理结构种群模型。首先考虑半线性模型，然后考虑非线性模型，利用特征线方法求出无穷小生成元的预解式和常数公式的变分，应用Krasnoselskii不动点定理得到定态的存在性，并通过估计半群的本质增长界研究定态的稳定性.最后，我们推广的技术，研究了一个非线性年龄-尺寸结构模型与尺寸依赖的增长率。
First-order hyperbolic partial differential equations with two internal variables have been used to model biological and epidemiological problems with two physiological structures, such as chronological age and infection age in epidemic models, age and another physiological character (maturation, size, stage) in population models, and cell-age and molecular content (cyclin content, maturity level, plasmid copies, telomere length) in cell population models. In this paper, we study nonlinear double physiologically structured population models with two internal variables by applying integrated semigroup theory and non-densely defined operators. We consider first a semilinear model and then a nonlinear model, use the method of characteristic lines to find the resolvent of the infinitesimal generator and the variation of constant formula, apply Krasnoselskii’s fixed point theorem to obtain the existence of a steady state, and study the stability of the steady state by estimating the essential growth bound of the semigroup. Finally, we generalize the techniques to investigate a nonlinear age-size structured model with size-dependent growth rate.