### 统计代写|R代写project|Virus Protein ODE/PDE Models

R是一个用于统计计算和图形的自由软件环境。

statistics-lab™ 为您的留学生涯保驾护航 在代写R方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写R代写方面经验极为丰富，各种代写R相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|R代写project|ODE/PDE model for a single virus protein

The ODE/PDE variables are listed in Table 1.1.
Table 1.1 ODE/PDE model variables
$V_{1}(x, t)$ virus protein concentration in the cell membrane
$C_{1}(t)$ virus protein concentration in the cell interior
$x$ position within the membrane
time
The movement of the virus protein in the cell membrane is modeled with the diffusion equation
$$\frac{\partial V_{1}(x, t)}{\partial t}=D_{V 1} \frac{\partial^{2} V_{1}(x, t)}{\partial x^{2}}$$
where $D_{V 1}$ is a diffusivity.
Eq. (1.1-2) is second order in $x$ and therefore requires two boundary conditions (BCs).
$$D_{V 1} \frac{\partial V_{1}\left(x=x_{i t}, t\right)}{\partial x}=k_{1 u}\left(V_{1 s}(t)-V_{1}\left(x=x_{u}, t\right)\right)$$
BC (1.1-2) equates the rate of diffusion of the protein at the membrane outer boundary $x=x_{u},-D_{V 1} \frac{\partial V_{1}\left(x=x_{u}, t\right)}{\partial x}$ (Fick’s first law), to the rate of mass transfer at the outer boundary, $k_{1 u}\left(V_{1 s}(t)-V_{1}\left(x=x_{l}, t\right)\right.$ ), where $k_{1 u}$ is a mass transfer coefficient to be specified. $V_{1 s}(t)$ is the concentration of viral genetic material outside the cell.
$$-D_{V 1} \frac{\partial V_{1}\left(x=x_{l}, t\right)}{\partial x}=k_{1 l}\left(C_{1}(t)-V_{1}\left(x=x_{l}, t\right)\right)$$
$B C$ (1.1-3) equates the rate of diffusion of the protein at the membrane inner boundary $x=x_{l},-D_{V 1} \frac{\partial V_{1}\left(x=x_{l}, t\right)}{\partial x}$ (Fick’s first law), to the rate of mass transfer at the inner boundary, $k_{1 l}\left(C_{1}(t)-V_{1}\left(x=x_{l}, t\right)\right)$, where $k_{1 l}$ is a mass transfer coefficient to be specified.

Eq. (1.1-1) is first order in $t$ and requires one initial condition (IC)
$$V_{1}(x, t=0)=V_{10}(x)$$
where $V_{10}(x)$ is a function to be specified, and is generally taken as the zero function, that is, no virus protein initially in the cell membrane.

The concentration of the protein in the cell interior, $C_{1}(t)$, is modeled with an ODE
$$\frac{d C_{1}(t)}{d t}=-k_{1 l}\left(C_{1}(t)-V_{1}\left(x=x_{l}, t\right)\right)$$
that equates the temporal derivative $\frac{d C_{1}(t)}{d t}$ to the rate of transfer of the protein from the inner boundary of the membrane, $-k_{l l}\left(C_{1}(t)-V_{1}\left(x=x_{l}, t\right)\right)$, to the cell interior.
The IC for eq. (1.1-6) is
$$C_{1}(t=0)=C_{10}$$
where $C_{10}$ is a prescribed constant.
Eqs. (1.1) constitute the ODE/PDE model for a single virus protein. The model is next extended so that the cell interior produces a protein that then diffuses out of the cell.

## 统计代写|R代写project|ODE/PDE model for a second virus protein

The variables and parameters for the second protein are designated with subscript 2. The diffusion equation is a direct analog of eq. (1.1-1).
$$\frac{\partial V_{2}(x, t)}{\partial t}=D_{V 2} \frac{\partial^{2} V_{2}(x, t)}{\partial x^{2}}$$
The $\mathrm{BC}(1.2-2)$ at the outer boundary $x=x_{u}=1$ equates the rate of diffusion, $D_{V 2} \frac{\partial V_{2}\left(x=x_{l}, t\right)}{\partial x}$, to the mass transfer rate in response to an ambient protein concentration $V_{2 a}, k_{2 u}\left(V_{2 a}-V_{2}\left(x=x_{u}, t\right)\right)$, where $k_{2 u}$ is a mass transfer coefficient for the second protein.
$$D_{V 2} \frac{\partial V_{2}\left(x=x_{u}, t\right)}{\partial x}=k_{2 u}\left(V_{2 a}-V_{2}\left(x=x_{u}, t\right)\right)$$

$B C(1.2-3)$ equates the rate of diffusion of the protein at the membrane inner boundary $x=x_{l}, D_{V 2} \frac{\partial V_{2}\left(x=x_{l}, t\right)}{\partial x}$, to the rate of mass transfer at the inner boundary, $-k_{2 l}\left(C_{2}(t)-V_{2}\left(x \stackrel{\partial x}{=} x_{l}, t\right)\right)$, where $k_{2 l}$ is a mass transfer coefficient for the second protein.
$$D_{V 2} \frac{\partial V_{2}\left(x=x_{l}, t\right)}{\partial x}=-k_{2 l}\left(C_{2}(t)-V_{2}\left(x=x_{l}, t\right)\right)$$
The initial condition for $V_{2}(x, t)$ is
$$V_{2}(x, t=0)=V_{20}(x)$$
where $V_{20}(x)$ is a function to be specified (usually taken as the zero function).
The concentration of the second protein in the cell interior is modeled with an ODE
$$\frac{d C_{2}(t)}{d t}=-k_{2 l}\left(C_{2}(t)-V_{2}\left(x=x_{l}, t\right)\right)+k_{r 2} C_{1}^{n_{2}}$$
that equates the temporal derivative $\frac{d C_{2}(t)}{d t}$ to the sum of (1) the rate of transfer of the second protein from the cell interior to the membrane inner boundary, $-k_{2 l}\left(C_{2}(t)-V_{2}\left(x=x_{l}, t\right)\right)$, and (2) the rate of production of the second protein from the first protein, $+k_{r 2} C_{1}^{n_{2}}$. For (2), an $n_{2}^{t h}$ order reaction is assumed, but this rate can be modified to reflect another rate of production of the second protein.
The IC for eq. $(1.2-5)$ is
$$C_{2}(t=0)=C_{20}$$
where $C_{10}$ is a prescribed constant.
Eqs. (1.1), (1.2) constitute the ODE/PDE models implemented in the R routines discussed in Chapter $2 .$

## 统计代写|R代写project|R routines for the ODE/PDE models

• $21 t$ output points as the first dimension of the solution matrix out from lsodes as programmed in the main program of Listing $2.1$ (with nout=21).
• The solution matrix out returned by lsodes has 23 elements as a second dimension. The first element is the value of $t$. Elements 2 to 23 are $V_{1}(x, t), C_{1}(t)$ from eqs. (1.1) (for each of the 21 output points).
16
2 Implementation of the ODE/PDE Models
• The solution is displayed for $t=0,240 \star 4 / 20=48, \ldots, 240$ as programmed in Listing $2.1$ (every fourth value of $t$ is displayed as explained previously).
• ICs (1.1-4, 1.1-6) are confirmed ( $t=0)$.
• $V_{1}\left(x=x_{u}=1, t\right)$ tracks $V_{1}(s)$ according to $\mathrm{BC}$ (1.1-2).
• $C_{1}(t)$ tracks the solution $V_{1}\left(x=x_{l}=0, t\right)$ as defined by $\mathrm{BC}(1.1-3)$ (at $x=0$ ) and the RHS of eq. (1.1-5).
• The computational effort as indicated by ncall $=235$ is modest so that sodes computed the solution to eqs. (1.1) efficiently.
The graphical output is in Figs. 2.1.

## 统计代写|R代写project|ODE/PDE model for a single virus protein

ODE/PDE 变量列于表 1.1。

C1(吨)细胞内部的病毒蛋白浓度
X在膜

∂在1(X,吨)∂吨=D在1∂2在1(X,吨)∂X2

D在1∂在1(X=X一世吨,吨)∂X=ķ1在(在1s(吨)−在1(X=X在,吨))
BC (1.1-2) 等于蛋白质在膜外边界的扩散速率X=X在,−D在1∂在1(X=X在,吨)∂X（菲克第一定律），外边界的质量传递速率，ķ1在(在1s(吨)−在1(X=Xl,吨)）， 在哪里ķ1在是要指定的传质系数。在1s(吨)是细胞外病毒遗传物质的浓度。
−D在1∂在1(X=Xl,吨)∂X=ķ1l(C1(吨)−在1(X=Xl,吨))

dC1(吨)d吨=−ķ1l(C1(吨)−在1(X=Xl,吨))

C1(吨=0)=C10

## 统计代写|R代写project|ODE/PDE model for a second virus protein

∂在2(X,吨)∂吨=D在2∂2在2(X,吨)∂X2

D在2∂在2(X=X在,吨)∂X=ķ2在(在2一种−在2(X=X在,吨))

D在2∂在2(X=Xl,吨)∂X=−ķ2l(C2(吨)−在2(X=Xl,吨))

dC2(吨)d吨=−ķ2l(C2(吨)−在2(X=Xl,吨))+ķr2C1n2

C2(吨=0)=C20

## 统计代写|R代写project|R routines for the ODE/PDE models

• 21吨输出点作为解矩阵的第一维从 lsodes 输出，如清单的主程序中编程的那样2.1（与nout = 21）。
• lsodes 返回的解矩阵 out 有 23 个元素作为第二维。第一个元素是值吨. 元素 2 到 23 是在1(X,吨),C1(吨)从等式。(1.1)（对于 21 个输出点中的每一个）。
16
2 ODE/PDE 模型的实现
• 解决方案显示为吨=0,240⋆4/20=48,…,240如清单中所编程2.1（每四个值吨显示如前所述）。
• IC（1.1-4、1.1-6）已确认（吨=0).
• 在1(X=X在=1,吨)轨道在1(s)根据乙C (1.1-2).
• C1(吨)跟踪解决方案在1(X=Xl=0,吨)定义为乙C(1.1−3)（在X=0) 和等式的 RHS。(1.1-5)。
• ncall 表示的计算量=235是适度的，因此 sodes 计算出 eqs 的解。(1.1) 有效。
图形输出如图。2.1。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。