A Decision - Support Modelling Toolset for Anthrax Infection and Treatment

The disease anthrax was developed and weaponised 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, existing and adapted versions of mathematical models for Anthrax infection in the literature (Day et al. (2011) Journal of Theoretical Biology; Pantha et al. (2016) Journal of Biological Systems; Pantha et al. (2018) Mathematical Biosciences), as well as multi-scale mechanistic models being currently developed by our team at Leeds, will be extended to evaluate the efficacy of different available medical treatment strategies following pathogen exposure.

A number of existing antibiotics and antitoxin treatments will be considered. The leverage of a mechanistic model for anthrax infection will allow us to quantify the efficacy of each treatment strategy. Both stochastic and deterministic methodologies will be considered for these systems. Furthermore, simplified versions of the mechanistic models by Day et al., as well as those being developed at Leeds, will be considered in a pharmacokinetic-pharmacodynamic (PK-PD) modelling framework (Nielsen et al. (2013) Pharmacological Reviews). The advantage of this PK-PD approach is that it will allow us to better understand the efficacy of each treatment without having to parametrise the complex mechanistic models, which is a challenging task that requires large amounts of experimental data.

The main objectives are:

(O1) to consider simplified versions of existing mechanistic models for anthrax infection, in terms of a PK-PD framework. To include into this framework the effect of different treatments, and to evaluate their efficacy against different pathogen exposure doses and for different intervention times or dosing strategies.

(O2) to incorporate the treatments considered in (O1) into adapted versions of the novel multi-scale models being developed at Leeds for anthrax infection. To use these extended models to get a better understanding of the treatments and efficacies studied in (O1).

(O3) to parametrise and calibrate models in (O1)-(O2), making use of Bayesian inference methods and of existing experimental data sets related to the efficacy of these treatments for dealing with anthrax infection.

Applications and benefits: We aim to develop a mathematical/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: We will develop new mathematical and statistical methodologies for the analysis of multi-dimensional stochastic processes within a PK-PD framework. Sensitivity analysis methods (Gomez-Corral & Lopez-Garcia (2018) Numerical Linear Algebra with Applications) will be adapted for these PK-PD systems, which will allow us to shed light on the impact that different model parameters -e.g., the rate at which the levels of a given antibiotic decay within the body- have on particular model outputs -e.g., the probability of an individual recovering after pathogen exposure and treatment provided-. In the same way, recent methodological techniques for the analysis of within-host infection dynamics (Carruthers et al. (2018) Frontiers in Microbiology; de la Higuera et al. (2019) Frontiers in Immunology) will be adapted and extended for our PK-PD systems.

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.