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

由于炭疽的高稳定性、传染性和致死率，许多国家在20世纪开发并使用了炭疽作为生物战剂。在这个项目中，将建立一个新的多尺度机械数学和计算模型来模拟吸入后炭疽感染的细胞内和宿主内的进展。这项工作将建立在Judy Day和合作者(Day et al. (2011) Journal of Theoretical Biology；Pantha et al. (2016) Journal of Biological Systems；Pantha等人（2018）数学生物科学)，但将纳入一些重要的补充来代表宿主内感染动态。特别是，我们的目标是适应和扩展炭疽感染最近开发的多尺度方法-土拉菌感染-由利兹和Dstl的团队(Gillard等人（2014）细胞和感染微生物学前沿；Carruthers et al.（2018）微生物学前沿)。这一总体框架允许人们解释跨尺度发生的感染动态：从细胞内到宿主内和种群水平。此外，我们将考虑随机方法，以表示这些系统中出现的自然随机事件，例如，吞噬细胞破裂释放淋巴结中随机数量的营养细菌。本项目的主要目标是：(1)建立一个数学机制模型来解释炭疽随机细胞内感染动力学，包括孢子萌发，细菌复制和吞噬细胞破裂。通过汇总统计（随机描述符）分析该系统，例如，破裂大小分布，然后可用于连接细胞内与宿主内感染动态，允许吸入后炭疽感染进展的现实随机表示。(2)通过计算非指数等待时间（如孢子萌发或吞噬细胞破裂）来改进(1)中开发的数学模型，并开发分析这些非马尔可夫系统的新方法。（O3）利用贝叶斯推理方法校准(O1)-(O2)中的数学/计算模型，并使用Dstl在项目过程中可能生成的现有实验数据。应用和好处：我们的目标是开发一种数学和计算工具，可以在项目期间进行测试和验证，供Dstl使用，为英国政府的决策者提供定量建议。数学，理论和方法的新颖性：在这个项目中，我们将开发新的方法来分析多维随机过程。特别是，新的敏感性分析方法（扩展了Gomez-Corral & Lopez-Garcia（2018）的数值线性代数应用）将使人们能够阐明不同模型参数（例如，吞噬细胞破裂的速度或孢子发芽的速度）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 et al. (2018) Scientific Reports）将得到扩展，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的职责一致：该项目属于全球不确定性主题的职责范围，其中一个核心要素是恐怖主义和bwa。我们的项目既属于数学生物学，也属于EPSRC的统计和应用概率研究领域。在数学生物学领域，EPSRC认为“为网络、国防、金融和健康等严重威胁开发更好的解决方案”是一个有弹性的目标。韧性国家和健康国家是EPSRC愿景和战略重点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.