Receptor-mediated endocytosis modeling of antibody-drug conjugates to the released payload within the intracellular space considering target antigen expression levels

An antibody-drug conjugate (ADC) is one of the effective treatment modalities designed as a targeted therapy for treating tumors. Certain ADCs such as brentuximab vedotin are known to kill negative tumor cells indirectly via membrane permeability and bystander-killing effect and to kill positive tumor cells directly. In this study, we propose a mathematical model to describe the ADC-receptor endocytosis mechanism and to predict payloads over a time profile more accurately, while considering target antigen-positive (Ag+)/negative (Ag--) cells. We discuss how the target-antigen expression levels derived using a ratio of Ag+ to Ag-- cells determine the payload release in the intracellular space. The model is aimed at capturing the amount of the payloads based on the target expression levels with the total number of cells fixed. The results indicate that (i) the profile of the total payloads over a time within the intracellular space is less influenced by the target expression levels after a time period, but the slope at the growth phase in which the payload increases is determined by the target expression levels, (ii) the change in the area under the curve of the total intracellularly released payload with a change in the ratio of Ag+ to Ag-- cells is more significant due to the initial ADC injection, (iii) the fluctuations in the released payloads within the Ag+ cells increase as the target expression levels decrease, unlike in the case of Ag-- cells or extracellular space. In addition, the time $t_{max}$ that corresponds to the maximum payload concentration $C_{max}$ is shifted towards the right as the target-antigen levels decrease, and it is strengthened by an increase in the initial free ADCs. The proposed model may reduce the discrepancy between the experiment and the model in the prediction of payloads over time profile.     

Continuum-Mechanical Analysis of Human Brain Tissue

The effective treatment of brain diseases, such as malignant brain tumours, is generally constricted by the controlled contribution of therapeutic agents. Novel brain tumour therapy proceeds from a direct infusion of the drug into the extra-vascular space of the nervous brain tissue (convection-enhanced delivery). This is carried out using catheter to bypass the blood-brain barrier, which effectively separates brain tissue from the intra-vascular space and hence hamper drug delivery through the bloodstream. The dilation of the target tissue, as response to the local pressure increase, initiates interstitial fluid flow and, thus, the distribution of the chemical agents. An adequate constitutive model of the complex tissue aggregate in the framework of the Theory of Porous Media is essential in order to assist modern clinical application via numerical simulations. The presented model consists of an elastically deformable solid skeleton, provided by the tissue cells, permeated by two viscous, materially incompressible pore-liquid phases, interstitial fluid and blood plasma. Both liquids are mobile within the solid skeleton and separated from each other. With regard to simulate a drug infusion process in the extra-vascular space, the interstitial fluid is treated as a solution of a liquid solvent and a dissolved therapeutic solute. The constitutive assumptions for the involved constituents are adjusted in order to describe the physical behaviour of human brain tissue. The presented numerical examples illustrate the fundamental effects during an infusion process. Therefore, the resulting set of coupled partial differential equations is spatially discretised using hexahedral mixed finite elements with an implicit (backward) Euler time integration scheme to solve the considered problem in a monolithic manner for the primary variables. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical approximation of a stochastic age-structured population model in a polluted environment with Markovian switching

In this paper, a stochastic age-structured population model with Markovian switching is investigated in a polluted environment. Both the stochastic disturbance of environment and the Markovian switching are incorporated into the model. By Itô formula and several assumptions, the boundedness in the qth moment of exact solutions of model are proved. Furthermore, making use of truncated Euler–Maruyama (EM) method, the strong convergence criterion of numerical approximation in the qth moment is established, and the rate of convergence is estimated. Numerical simulations are carried out to illustrate the theoretical results. Our results indicate that the truncated EM method can be used for stochastic age-structured population system in a polluted environment.     

Dynamics of individual specialization and global diversification in communities

We discuss a model of an economic community consisting of N interacting agents. The state of each agent at any time is characterized, in general, by a mixed strategy profile drawn from a space of s pure strategies. The community evolves as agents update their strategy profiles in response to payoffs received from other agents. The evolution equation is a generalization of the replicator equation. We argue that when N is sufficiently large and the payoff matrix elements satisfy suitable inequalities, the community evolves to retain the full diversity of available strategies even as individual agents specialize to pure strategies. © 1998 John Wiley & Sons, Inc.     

分布式配送系统在运输时间均匀分布条件下的性能分析

本文在运输时间不确定的前提下，对分布式配送系统在两个部件和最终产品早到无限制的情形下建立了随机优化模型。我们在极小化库存费用的同时以满足定时送货要求为目标，讨论了如何确定运输提前期，并给出了敏感性分析结果。     

与年龄相关的模糊随机种群扩散系统的均方散逸性

讨论了一类与年龄相关的模糊随机种群扩散系统,该系统受随机和模糊两种不确定性因素的影响.在有界的条件(弱于线性增长条件)和Lipschitz条件下,利用It公式和Bellman-Gronwall-Type引理,建立了均方意义下与年龄相关的模糊随机种群扩散系统均方散逸性的判定准则.并通过数值例子对所给出的结论进行了验证.     

与年龄相关的模糊随机种群扩散系统的指数稳定性

讨论了一类与年龄相关的模糊随机种群扩散系统,系统受两种不确定性因素的影响,即随机和模糊.在有界和Lipschitz条件下,利用Ito公式和Gronwall引理,建立了均方意义下与年龄相关的模糊随机种群扩散系统指数稳定性的判定准则并通过数值例子对所给出的结论进行了验证.     

具扩散的年龄结构脉冲随机时滞种群方程的均方稳定性(英文)

本文考虑一类具扩散的年龄结构脉冲随机时滞种群方程.主要目的是研究具扩散的年龄结构脉冲随机时滞种群平凡解的均方稳定性,给定两个使平凡解均方稳定的充分条件.     

Lp空间中随机过程泛函的某些收敛性

随机变量之和的收敛性问题已有许多人在研究,并取得很多很好的结果.本文则进一步讨论了随机过程之和在Lp空间中依联合测度收敛的情况.     

Convergence of numerical solutions to stochastic age-structured system of three species

In general, most of stochastic age-structured system of three species do not have explicit solutions, thus numerical approximation schemes are invaluable tools for exploring their properties. The aim of this paper is to investigate the convergence of numerical approximation solution to the true solution for stochastic age-structured system of three species.     

具有年龄结构的传染病SIR流行病模型的研究

给出美国流感监测网络统计的2008年10月至2009年9月流感症状患者数在四个年龄段的分布,结合当前H1N1新型流感发病的特点,提出一年龄结构型的流感传播模型,讨论了这个模型的应用和优点.     

Stochastic classical solutions for space–time fractional evolution equations on a bounded domain

Space–time fractional evolution equations are a powerful tool to model diffusion displaying space–time heterogeneity. We prove existence, uniqueness and stochastic representation of classical solutions for an extension of Caputo evolution equations featuring time-nonlocal initial conditions. We discuss the interpretation of the new stochastic representation. As part of the proof a new result about inhomogeneous Caputo evolution equations is proven.     

OU models based on positive and negative subordinate processes applying in SHIBOR time series analysis and derivative pricing – through discrete differential method

ABSTRACT

On account of that the OU models based on Gaussian process cannot describe the characteristics of peak, bias and asymmetric thick tail in SHIBOR time series, this paper replaces the Gaussian process in OU model with Levy process which can be decomposed into positive and negative subordinate processes, constructs OU model based on positive and negative subordinate processes. Methods parameter estimation and stochastic simulation were carried out by making discrete the stochastic differential equations into stochastic difference equations. The result shows that non-Gaussian OU process based on positive and negative subordinate processes not only fits the time series but also has better economic interpretation. The innovation of our research is to build a model of Non-Gaussian OU process based on positive and negative subordinate processes with less stochastic terms, and it provides an efficient tool for forecasting SHIBOR time series.     

Minimax and risk averse multistage stochastic programming

In this paper we study relations between the minimax, risk averse and nested formulations of multistage stochastic programming problems. In particular, we discuss conditions for time consistency of such formulations of stochastic problems. We also describe a connection between law invariant coherent risk measures and the corresponding sets of probability measures in their dual representation. Finally, we discuss a minimax approach with moment constraints to the classical inventory model.     

An Age-structured Mathematical Model for the Within Host Dynamics of Malaria and the Immune System

In the paper, we use a mathematical model to study the population dyna mics of replicating malaria parasites and their interaction with the immune cells within a human host. The model is formulated as a system of age-structured partial differential equations that are then integrated over age to obtain a system of nonlinear delay differential equations. Our model incorporates an intracellular time delay between the infection of the red blood cells by the merozoites that grow and replicate within the infected cells to produce new merozoites. The infected red blood cells burst approximately every 48 h releasing daughter parasites to renew the cycle. The dynamical processes of the parasites within the human host are subjected to pressures exerted by the human immunological responses. The system is then solved using a first-order, finite difference method to give a discrete system. Numerical simulations carried out to illustrate stability of the system reveal that the populations undergo damped oscillations that stabilise to steady states.      

巴拿哈空间中随机年龄结构种群方程的数值分析

本文研究年龄结构随机种群方程的离散误差,在空间离散中用到Galerkin公式,时间离散中用到显式欧拉公式.     

Global asymptotic stability for an age-structured model of hematopoietic stem cell dynamics

We investigate a system of two nonlinear age-structured partial differential equations describing the dynamics of proliferating and quiescent hematopoietic stem cell (HSC) populations. The method of characteristics reduces the age-structured model to a system of coupled delay differential and renewal difference equations with continuous time and distributed delay. By constructing a Lyapunov–Krasovskii functional, we give a necessary and sufficient condition for the global asymptotic stability of the trivial steady state, which describes the population dying out. We also give sufficient conditions for the existence of unbounded solutions, which describe the uncontrolled proliferation of HSC population. This study may be helpful in understanding the behavior of hematopoietic cells in some hematological disorders.     

随机环境下风险模型的破产问题

本文研究了在随机环境下风险模型的破产问题.利用递归方法,获得了破产前盈余的分布和描述破产严重性的预警区的分布, 推广了已有结果.     

Banach空间中带Poisson跳的随机种群方程的数值分析

本文研究Banach空间中带Poisson跳的随机种群方程,通过离散使之成为随机微分方程,进而运用显式Euler公式来分析其数值解与解析解的误差.     

Optimal harvesting in age-structured populations

In this paper, we discuss the optimal harvesting in age-structured populations. We characterize the optimal controls for finite-horizon problems and describe a scheme to approximate them. We also give an analysis of the infinite-horizon problem as a function of a bifurcation parameter.This research was supported by NSF Grant R11-89-05084.