Mathematical modelling of the host response to inhaled anthrax across different scales

炭疽病因其高度的稳定性、传染性和致命性，在20世纪被许多州开发并用作生物战剂(BWA)。在这个项目中，将开发一个新的多尺度机制的数学和计算模型，以模拟吸入后炭疽感染的细胞内和宿主内的进展。(2011)《理论生物学杂志》；Pantha等人。(2016)《生物系统杂志》；Pantha等人。(2018)数学生物科学)，但将纳入一些重要的增加，以代表宿主内感染的动态。特别是，我们的目标是在这里适应和推广利兹和Dstl(Gillard等人)团队最近开发的多尺度方法学--用于图拉氏方济各菌感染。(2014)细胞和感染微生物学的前沿；Carruthers等人。(2018)微生物学前沿)。这一一般框架使人们能够解释发生在不同尺度上的感染动态：从细胞内，到宿主内和种群水平。此外，我们将考虑随机方法，以表示在这些系统中出现的自然随机事件，例如吞噬细胞破裂，在淋巴结内释放随机数量的繁殖菌。本项目的主要目标是：(1)开发一个数学机制模型来解释炭疽菌细胞内的随机感染动力学，包括孢子萌发、细菌复制和吞噬细胞破裂。借助于概要统计(随机描述符)(例如破裂大小分布)来分析该系统，该概要统计然后可用于将细胞内感染动态与宿主内感染动态联系起来，从而允许对吸入后炭疽感染的进展进行真实的随机表示。(O2)通过考虑非指数等待时间(例如孢子萌发或吞噬细胞破裂)来改进(O1)中所开发的数学模型，并开发用于分析这些非马尔科夫系统的新方法。(O3)利用贝叶斯推断方法来校准(O1)-(O2)中的数学/计算模型，应用和好处：我们的目标是开发一种数学和计算工具，可以在项目期间测试和验证，供DSTL使用，为英国政府的决策者提供定量建议。数学、理论和方法新颖性：在这个项目中，我们将开发分析多维随机过程的新方法。特别是，新的敏感性分析方法(扩展了Gomez-Corral&Lopez-Garcia(2018)数值线性代数中的方法及其应用)将使人们能够阐明不同的模型参数(例如，吞噬细胞破裂的速度，或孢子萌发的速度)对特定模型输出的影响，例如，单个个体在暴露后出现症状的概率。最近开发的技术(Castro等人将延长(2018)科学报告)，以便将这些系统中自然产生的非指数等待时间纳入模型。与EPSRC职权范围一致：该项目属于全球不确定性主题的范围，其中核心要素之一是恐怖主义和BWAS。我们的项目既属于数学生物学，也属于统计和应用概率EPSRC研究领域。在数学生物学领域，EPSRC认为“为严重威胁开发更好的解决方案：网络、国防、金融和健康”是一个有弹性的抱负。韧性国家和健康国家都是EPSRC愿景和战略优先事项中确定的四个主要目标中的两个。

The disease anthrax was developed and used as a biological warfare agent (BWA) during the 20th century by a number of states, due to its high stability, infectivity and lethality. In this project, a novel multi-scale mechanistic mathematical and computational model will be developed to simulate the intra-cellular and within-host progression of anthrax infection after inhalation.The work will be built upon existing work by Judy Day and collaborators (Day et al. (2011) Journal of Theoretical Biology; Pantha et al. (2016) Journal of Biological Systems; Pantha et al. (2018) Mathematical Biosciences), but will incorporate a number of important additions to represent the within-host infection dynamics. In particular, we aim to adapt and extend here for anthrax infection the recently-developed multi-scale methodology - for Francisella tularensis infection - by the teams at Leeds and Dstl (Gillard et al. (2014) Frontiers in Cellular and Infection Microbiology; Carruthers et al. (2018) Frontiers in Microbiology). This general framework allows one to account for the infection dynamics occurring across scales: from the intra-cellular, to the within-host and population levels. Furthermore, we will consider stochastic methodologies in order to represent naturally random events arising in these systems e.g., rupture of a phagocyte releasing a random number of vegetative bacteria in the lymph nodes.The main objectives of this project are:(O1) to develop a mathematical mechanistic model to account for the stochastic intra-cellular infection dynamics of anthrax, including spore germination, bacterial replication and phagocyte rupture. To analyse this system by means of summary statistics (stochastic descriptors) e.g., rupture size distribution, which can be then used to link intra-cellular with within-host infection dynamics, allowing for a realistic stochastic representation of the progression of anthrax infection after inhalation.(O2) to improve the developed mathematical models in (O1) by accounting for non-exponential waiting times e.g., spore germination or phagocyte rupture, and to develop novel methodologies for analysing these non-Markovian systems.(O3) to calibrate the mathematical/computational models in (O1)-(O2) making use of Bayesian inference methods, with existing -and potentially to be generated at Dstl during the course of the project- experimental data.Applications and benefits: We aim to develop a mathematical and computational tool, which can be tested and validated, during the project, to be used by Dstl to provide quantitative advice to decision-makers in UK Government.Mathematical, theoretical and methodological novelty: Within this project we will develop new methodologies for the analysis of multi-dimensional stochastic processes. In particular, novel sensitivity analysis methods (extending those in Gomez-Corral & Lopez-Garcia (2018) Numerical Linear Algebra with Applications) will allow one to shed light on the impact that different model parameters (e.g., the rate at which phagocytes rupture, or at which spores germinate) have on particular model outputs e.g., the probability of a single individual developing symptoms after exposure. Recently-developed techniques (Castro et al. (2018) Scientific Reports) will be extended so that non-exponential waiting times naturally arising in these systems can be incorporated into the models.Alignment with EPSRC remit: This project falls in the remit of the Global Uncertainties theme, where one of the core elements is terrorism and BWAs. Our project belongs both to the Mathematical Biology and to the Statistics and Applied Probability EPSRC research areas. Within the Mathematical Biology area, EPSRC considers "developing better solutions to acute threats: cyber, defence, financial and health" as a resilient ambition. Both Resilient nation and Healthy nation are two of the four main goals identified in the EPSRC vision and strategic priorities.