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.

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.

Commentary on the use of the reproduction number during the COVID-19 pandemic.

Since the beginning of the COVID-19 pandemic, the reproduction number [Formula: see text] has become a popular epidemiological metric used to communicate the state of the epidemic. At its most basic, [Formula: see text] is defined as the average number of secondary infections caused by one primary infected individual. [Formula: see text] seems convenient, because the epidemic is expanding if [Formula: see text] and contracting if [Formula: see text].

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.

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.

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.

Comparison of continuous and discrete stochastic ion channel models.

The stochastic behaviour of ion channels can be described by a discrete model or by an approximate continuous approach. While the discrete approach is exact, it is also less computationally efficient, and so the continuous model is often the method of choice since it allows for incorporation into a multiscale environment. However, in recent years the accuracy of the stochastic continuous approach for calculating statistics of certain quantities in the Hodgkin-Huxley model has come into question.