Filling in the gaps: estimating numbers of chlamydia tests and diagnoses by age group and sex before and during the implementation of the English National Screening Programme, 2000 to 2012.

To inform mathematical modelling of the impact of chlamydia screening in England since 2000, a complete picture of chlamydia testing is needed. Monitoring and surveillance systems evolved between 2000 and 2012. Since 2012, data on publicly funded chlamydia tests and diagnoses have been collected nationally. However, gaps exist for earlier years. We collated available data on chlamydia testing and diagnosis rates among 15-44-year-olds by sex and age group for 2000-2012. Where data were unavailable, we applied data- and evidence-based assumptions to construct plausible minimum and maximum estimates and set bounds on uncertainty. There was a large range between estimates in years when datasets were less comprehensive (2000-2008); smaller ranges were seen hereafter. In 15-19-year-old women in 2000, the estimated diagnosis rate ranged between 891 and 2,489 diagnoses per 100,000 persons. Testing and diagnosis rates increased between 2000 and 2012 in women and men across all age groups using minimum or maximum estimates, with greatest increases seen among 15-24-year-olds. Our dataset can be used to parameterise and validate mathematical models and serve as a reference dataset to which trends in chlamydia-related complications can be compared. Our analysis highlights the complexities of combining monitoring and surveillance datasets

Stochastic models of ion channel dynamics and their role in short-term repolarisation variability in cardiac cells

Sudden cardiac death due to the development of lethal arrhythmias is the dominant cause of mortality in the UK, yet the mechanisms underlying their onset, maintenance and termination are still poorly understood. Therefore biomarkers are used to determine arrhythmic risk within patients and of new drug compounds. In recent years, the magnitude of variations in the length of successive beats, measured over a short period of time, has been shown to be a powerful predictor of arrhythmic risk. This beat-to-beat variability is thought to be the manifestation of the random opening and closing dynamics of individual ion channels that lie within the membrane of cardiac cells. Computational models have become an important tool in understanding the electrophysiology of the heart. However, current state-of-the-art electrophysiology models do not incorporate this intrinsic stochastic behaviour of ion channels. Those that do use computationally costly methods, restricting their use in complex tissue scale simulations, or employ stochastic simulation methods that result in negative numbers of channels and so are inaccurate. Therefore, using current stochastic modelling techniques to investigate the role of stochastic ion channel behaviour in beat-to-beat variability presents difficulties.In this thesis we take a mathematically rigorous and novel approach to develop accurate and computationally efficient models of stochastic ion channel dynamics that can be incorporated into existing electrophysiology models. Two different models of stochastic ion channel behaviour, both based on a system of stochastic differential equations (SDEs), are developed and compared. The first model is based on an existing SDE model from population dynamics called the Wright-Fisher model. The second approach incorporates boundary conditions into the SDE model of ion channel dynamics that is obtained in the limit from the discrete-state Markov chain model, and is called a reflected SDE. Of these two methods, the reflected SDE is found to more accurately capture the stochastic dynamics of the discrete-stateMarkov chain, seen as the ‘gold-standard’ model and also provides substantial computational speed up. Thus the reflected SDE is an accurate and efficient model of stochastic ion channel dynamics and so allows for detailed investigation into beat-to-beat variability using complex computational electrophysiology models. We illustrate the potential power of this method by incorporating it into a state-of-the-art canine cardiac cell electrophsyiology model so as to explore the effects of stochastic ion channel behaviour on beat-to-beat variability. The stochastic models presented in this thesis fulfil an important role in elucidating the effects of stochastic ion channel behaviour on beat-to-beat variability, a potentially important biomarker of arrhythmic risk.</p

Modeling ion channel dynamics through reflected stochastic differential equations

Ion channels are membrane proteins that open and close at random and play a vital role in the electrical dynamics of excitable cells. The stochastic nature of the conformational changes these proteins undergo can be significant, however current stochastic modeling methodologies limit the ability to study such systems. Discrete-state Markov chain models are seen as the "gold standard," but are computationally intensive, restricting investigation of stochastic effects to the single-cell level. Continuous stochastic methods that use stochastic differential equations (SDEs) to model the system are more efficient but can lead to simulations that have no biological meaning. In this paper we show that modeling the behavior of ion channel dynamics by a reflected SDE ensures biologically realistic simulations, and we argue that this model follows from the continuous approximation of the discrete-state Markov chain model. Open channel and action potential statistics from simulations of ion channel dynamics using the reflected SDE are compared with those of a discrete-state Markov chain method. Results show that the reflected SDE simulations are in good agreement with the discrete-state approach. The reflected SDE model therefore provides a computationally efficient method to simulate ion channel dynamics while preserving the distributional properties of the discrete-state Markov chain model and also ensuring biologically realistic solutions. This framework could easily be extended to other biochemical reaction networks. © 2012 American Physical Society

Resource Allocation for Epidemic Control Across Multiple Sub-populations.

The number of pathogenic threats to plant, animal and human health is increasing. Controlling the spread of such threats is costly and often resources are limited. A key challenge facing decision makers is how to allocate resources to control the different threats in order to achieve the least amount of damage from the collective impact. In this paper we consider the allocation of limited resources across n independent target populations to treat pathogens whose spread is modelled using the susceptible-infected-susceptible model. Using mathematical analysis of the systems dynamics, we show that for effective disease control, with a limited budget, treatment should be focused on a subset of populations, rather than attempting to treat all populations less intensively. The choice of populations to treat can be approximated by a knapsack-type problem. We show that the knapsack closely approximates the exact optimum and greatly outperforms a number of simpler strategies. A key advantage of the knapsack approximation is that it provides insight into the way in which the economic and epidemiological dynamics affect the optimal allocation of resources. In particular using the knapsack approximation to apportion control takes into account two important aspects of the dynamics: the indirect interaction between the populations due to the shared pool of limited resources and the dependence on the initial conditions

Challenges of integrating economics into epidemiological analysis of and policy responses to emerging infectious diseases

COVID-19 has shown that the consequences of a pandemic are wider-reaching than cases and deaths. Morbidity and mortality are important direct costs, but infectious diseases generate other direct and indirect benefits and costs as the economy responds to these shocks: some people lose, others gain and people modify their behaviours in ways that redistribute these benefits and costs. These additional effects feedback on health outcomes to create a complicated interdependent system of health and non-health outcomes. As a result, interventions primarily intended to reduce the burden of disease can have wider societal and economic effects and more complicated and unintended, but possibly not anticipable, system-level influences on the epidemiological dynamics themselves. Capturing these effects requires a systems approach that encompasses more direct health outcomes. Towards this end, in this article we discuss the importance of integrating epidemiology and economic models, setting out the key challenges which such a merging of epidemiology and economics presents. We conclude that understanding people’s behaviour in the context of interventions is key to developing a more complete and integrated economic-epidemiological approach; and a wider perspective on the benefits and costs of interventions (and who these fall upon) will help society better understand how to respond to future pandemics

Getting the most out of maths: how to coordinate mathematical modelling research to support a pandemic, lessons learnt from three initiatives that were part of the COVID-19 response in the UK

In March 2020 mathematics became a key part of the scientific advice to the UK government on the pandemic response to COVID-19. Mathematical and statistical modelling provided critical information on the spread of the virus and the potential impact of different interventions. The unprecedented scale of the challenge led the epidemiological modelling community in the UK to be pushed to its limits. At the same time, mathematical modellers across the country were keen to use their knowledge and skills to support the COVID-19 modelling effort. However, this sudden great interest in epidemiological modelling needed to be coordinated to provide much-needed support, and to limit the burden on epidemiological modellers already very stretched for time. In this paper we describe three initiatives set up in the UK in spring 2020 to coordinate the mathematical sciences research community in supporting mathematical modelling of COVID-19. Each initiative had different primary aims and worked to maximise synergies between the various projects. We reflect on the lessons learnt, highlighting the key roles of pre-existing research collaborations and focal centres of coordination in contributing to the success of these initiatives. We conclude with recommendations about important ways in which the scientific research community could be better prepared for future pandemics. This manuscript was submitted as part of a theme issue on “Modelling COVID-19 and Preparedness for Future Pandemics”