Thought Pieces

Beyond Influenza

Beyond Influenza

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Tom McCarthy explores how to model a pandemic

All of the talk of “modelling” in the wake of new variants hitting the UK may have left you scratching your head. While much of the detail behind modelling for pandemics is not openly available, there is a vast amount of literature available on modelling pandemics and epidemics which we can look at to get an idea of what approaches are used by the Government’s panels of public health experts.

There are fundamentally two approaches to modelling real world phenomena, whether it be pandemics, hospital bed usage, weather patterns or drive-through queuing systems:

  • a ‘pure’ mathematical model, which seeks to generalise the progression of real-world phenomena into a series of idealised equations which can then be solved.
  • a simulation model, where digital approximations of real-world events or objects are created, and their behaviour analysed as time progresses.

Both approaches are widely used and have their benefits and drawbacks. Causality is often easier to interpret in a mathematical model, as differential equations can show how key variables change with respect to each other. However, purely mathematical models are incredibly difficult to construct and tread a fine line between being simple enough to be solvable, and complex enough to be useful. Examples of mathematical modelling in the real world include a recent paper which used mathematical modelling to calculate the transmissibility of Novel Coronavirus (Chen et al, 2020).

Simulation models, on the other hand, are relatively easy to construct and can contain quite a lot of complexity (in terms of interactions, statistical distributions, level of granularity etc.) but causality is often difficult to infer and trial-and-error often has to be used to show relationships between variables – at great computation expense.The UK Influenza Pandemic Preparedness Strategy (DHSSPS, 2011) draws upon

modelling conducted by the Scientific Pandemic Influenza Group on Modelling very heavily for its evidence behind key government strategies for social distancing measures such as school and workplace closure. The modelling work contained in the SPI-M Modelling Summary (Scientific Pandemic Influenza Group on Modelling, 2018) effectively lays out the modelling work which influences the government’s policy on managing epidemics and pandemics. The modelling also shows when cases and hospitalisations would be expected to peak based on the levels of interventions in place and the transmissibility and severity of the disease.

SARS and H5N1 influenza, as well as several other epidemics and pandemics have provided rich sources of data to refine modelling processes, and properly conducted modelling has tended to be accurate in predicting the propagation of disease. The big issues with any modelling work of this kind are:

Accuracy of the data – Ascertaining accurate contagion rates, case mortality, and case numbers can be incredibly difficult during a fast-moving international pandemic and it is unlikely that real-time data will be completely accurate. During pandemics, mortality statistics whose denominator is “confirmed cases” should be treated with caution, as many milder cases are likely to pass without ever being formally confirmed through testing.

Complexity of interactions – As previously outlined, a model will always, to some level, be an abstraction of real-world processes and events – as such it will rarely capture all the complex and chaotic interactions between actors and processes.

Assumptions, assumptions, assumptions… – Where there are complete unknowns with limited observed data then we make assumptions. Whilst measures can be taken to ensure these assumptions are as robust as possible, like taking the average of many estimates made by subject matter experts; there is still a large amount of room for error.

Apart from the use of large models created by multi-disciplinary panels of experts which are used to guide government policy in cases of pandemics/epidemics, modelling is also a valuable educational tool which can elegantly demonstrate the epidemiological concepts such as quarantining, herd immunity and social distancing.

As is easily seen from the Government’s reasoning behind their strategy to combat Covid-19, modelling is becoming a crucial tool to enable effective, evidence-based strategic decision making. We are all learning quickly the new modelling vocabulary that has become central to all our lives.

 

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