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

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.