本次统计代写主要是R语言进行感染模型数据分析,生物信息bio相关

STA365 Assignment 1

这是一项使用实际数据和真实数学模型的作业。因此,您应该为模型做好准备,使其可能无法很好地适应数据。在预热阶段,您很可能还会在Stan代码中收到一些警告。没关系,不用担心!在采样阶段可能偶尔会出现警告,并且随着该阶段警告数量的增加,您应该越来越担心!

模拟衣原体感染的动力学

沙眼衣原体是一种专性的细胞内细菌病原体,可感染人类的​​生殖器和眼粘膜,引起性传播疾病和沙眼,是人类最常见的细菌性传播疾病。妇女面临着最严重的感染后果,包括慢性疼痛,输卵管因素不孕,异位妊娠和生殖道感染导致的盆腔炎。在大多数情况下,这种感染是无症状的,并且可能持续数月至数年而没有得到治疗或诊断。这样的结果促使沙眼衣原体被定位为除艾滋病毒/艾滋病之外成本最高的性传播感染,仅在美国,医疗费用每年就增加到至少20亿美元。

沙眼衣原体是一种细胞内病原体,可通过独特的双相发育周期进行复制,该周期涉及真核细胞和两种不同形式的细菌:基本体(EB),是细胞外的,代谢惰性的感染性形式;以及网状体(RB),它是细胞内的复制结构。在这个发育周期中(见图),直径约0.3μm的具有传染性但无代谢活性的基本体被真核细胞内吞,并位于胞质内。在包含物中,EB转变为非传染性但代谢活跃且较大(直径约1μm)的网状体。 RB通过二元裂变的重复循环进行复制,然后再分化回传染性EB形式。然后,EBs在细胞裂解后释放到细胞外部1。

1用较少的技术语言,EB入侵了细胞并在其中生活。然后,它转变为一个RB,这些RB繁殖,然后又变成EB并爆炸出细胞(在裂解事件中)。这大约是电影《外星人》的情节。

1个

图1:衣原体生命周期的示意图。取自Mallett等人,Bull Math Biol(2013)75:2257-2270。

数据

我们的数据已从Rank等人的图1中以数字方式提取。 (2003)2,该方法测量了一段时间内雌性豚鼠生殖道中的EB数量。感染后每3天测量一次该数据

(第3-30天)。在所有情况下,感染均在21天内完全清除。

来自Rank等的数据。 (2003年)分两次收集。首先,雌性豚鼠被已知数量的EB人工感染(范围为10-10000)。然后每天测量其生殖道中的EB数量,结果报告所有接受相同剂量的豚鼠的平均数量。这将是任务2中使用的数据

在第二波数据中,雄性豚鼠被感染,并且感染性传播给雌性豚鼠。该研究的目的之一是了解通过性交传递了多少EB。这将是任务3中使用的数据。

在这两种情况下,数据的单位均为“ 104 EB”。也就是说,C(t)= 1的度量意味着在时间t处有104个EB。

数学模型

这是一种复杂的感染,但是可以使用一组三个普通的微分方程来模拟它的动力学,这三个方程取自Wilson(2004)3。该模型是基于数学和生物学考虑独立于数据而提出的。此模型可能不是很好!

2 Rank,R.G.,Bowlin,A.K.,Reed,R.L。和Tarville,T。(2003)。从雄性到雌性豚鼠的性传播导致衣原体生殖器感染的特征和感染剂量的确定。感染。免疫,71(11),6148-6154。

3D。 P. Wilson衣原体的数学建模,ANZIAM J. 45(E)ppC201–214,2004年。

This is an assignment that uses real data and a real mathematical model. As such, you should be prepared for the model to possibly be a poor fit for the data. You will also most likely get some warnings in your Stan code during the warmup phase. This is ok and don’t worry about them! There may be very occasional warnings during the sampling phase, and you should become increasingly concerned as the number of warnings in this phase increases!

Modelling the dynamics of a Chalmydia infection

Chlamydia trachomatis, an obligate intracellular bacterial pathogen that infects the genital and ocular mucosa of humans causing sexually transmitted disease and trachoma, is the most common bacterial sexually transmitted disease in humans. Women face the most serious consequences of the infection including chronic pain, tubal factor infertility, ectopic pregnancy, and pelvic inflammatory disease resulting from genital tract infections. In a majority of cases, the infections are asymptomatic and may persist for months to years without treatment or diagnosis. Such outcomes contribute to C. trachomatis being positioned as the most costly sexually transmitted infection besides HIV/AIDS with the health care costs in the United States alone rising to at least $2 billion per year.

C. trachomatis is an intracellular pathogen that replicates via a unique biphasic developmental cycle involving eukaryotic cells and two distinctive forms of the bacteria: the Elementary Body (EB), which is the extracellular, metabolically inert, infectious form; and the Reticulate Body (RB), which is the intracellular, replicating structure. In this developmental cycle (see the diagram), the infectious but metabolically inactive elementary body, approximately 0.3 μm in diameter, is endocytosed by eukaryotic cells and resides within a cytoplasmic inclusion. Within the inclusion, the EBs transform into the non-infectious, but metabolically active and larger (approximately 1 μm in diameter) reticulate body. The RBs replicate via repeated cycles of binary fission, before differentiating back to the infectious EB form. The EBs are then released to the cell exterior upon cell lysis1.

1In less technical language, the EB invades the cell and lives within it. It then transfroms to an RB and these RBs reproduce, before turning back into EBs and exploding out of the cell (in the lysis event). This is approximately the plot of the film Alien.

1

Figure 1: A diagramatic representation of the life-cycle of Chlamydia. Taken from Mallett et al., Bull Math Biol (2013) 75:2257–2270.

The data

Our data has been digitally extracted from Figure 1 in Rank et al. (2003)2, which measures the number of EBs in a female guinea pig’s genital tract over time. This data is measured once every 3 days after infection

(days 3–30). In all cases, the infections had completely cleared within 21 days.

The data from Rank et al. (2003) was collected in two waves. Firstly, the female guinea pigs were artificially infected with a known number of EBs (ranging from 10–10000). The number of EBs in their genital tract was then measured every day and the results report the average number across all infected guinea pigs that received the same dose. This will be the data used in Task 2

In the second wave of data, male guinea pigs were infected and the infection was passed sexually to female guinea pigs. One of the aims of the study was to understand how many EBs are passed through sexual intercourse. This will be the data used in Task 3.

In both cases the units of the data are “104 EBs”. That is a measurement of C(t) = 1 means there are 104 EBs at time t.

The mathematical model

This is a complex infection, but the dynamics of it can be modelled using a set of three ordinary differential equations, taken from Wilson (2004)3. This model was proposed independently of the data based on mathematical and biological considerations. It is possible that this model may not be very good!

2Rank, R. G., Bowlin, A. K., Reed, R. L., & Darville, T. (2003). Characterization of chlamydial genital infection resulting from sexual transmission from male to female guinea pigs and determination of infectious dose. Infect. Immun., 71(11), 6148–6154.


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