Richard Marshall, Director in Willis Towers Watson’s UK Insurance Consulting and Technology practice [and member of the IFoA’s Health and Care Research Subcommittee], provides an overview of pandemic models and some of the challenges of replicating the complex dynamics of infectious disease transmission.
Models of this pandemic are spreading almost as fast as the virus itself, but what makes for a good model of an epidemic? We look at some key features of an outbreak and give an overview of how they’re reflected in models.
Every outbreak of infectious disease is essentially about one thing: some bacteria, virus or parasite passing from one individual to another. Repeat several million times and you probably have a pandemic.
Any good infectious disease model will need to reflect this process of transmission of the pathogen responsible for the disease. In some cases (as with COVID-19) the spread is human-to-human, but in others such as dengue fever, vectors (creatures which transport the pathogen from one human to another, such as mosquitoes) are involved. This means that different models will be needed.
For human-to-human transmission, it makes sense that the number of new infections will be somehow proportional to the number of currently infectious individuals and also to the number of people who can become infected (the susceptible population) – after all, it is contact between these which can generate new infections. This basic idea is the cornerstone of most pandemic models: ‘SIR’ models (‘susceptible’, ‘infected’, ‘removed’) and extensions of this structure.
Some diseases spread more quickly than others; this information, often encapsulated in the ‘R’ number which is constantly in the media, can be reflected in the rate at which new infections are generated relative to the sizes of these two populations.
In sophisticated models, the new infections could be allocated to different age and gender groups or geographical locations, though many simpler models treat the whole population as a single unit.
Adding in vector-mediated transmission leads to a different set of complexities – rather than factors affecting human-to-human contact, you have to consider things like bite rates and the probability of transmission of the pathogen during a bite event . Other factors, for instance rainfall or spraying of insecticides, can affect the population of vectors.
Disease progression and outcomes
Once we have a mechanism for determining how many new infections are generated (and perhaps amongst whom they are generated), we have to determine what happens post-infection.
Features which might be captured by some infectious disease models include:
- incubation periods – how long it takes for an individual to go from initial exposure to the pathogen to becoming infectious;
- duration of illness;
- probability of developing disease sufficiently severe to require hospital or ICU treatment (and as we’ve seen with COVID-19, there are many factors with which this could vary – not least age and gender);
- eventual case fatality rates; and
- whether individuals recovering from the disease become immune to the condition or not (and if so, for how long).
Of course, as we’ve learnt from COVID-19, determining an accurate estimate of parameters such as the case fatality rate can be a significant challenge due to incomplete data, exponential case growth and unresolved cases. At least half of the battle of pandemic modelling is coming up with some credible parameter estimates for the model to reflect the disease you’re modelling once you’ve decided on your preferred model structure.
Some models might consider longer-term impacts of a pandemic – changes in morbidity and mortality rates for survivors – but these will be few and far between, largely due to the dearth of data for model calibration.
Some of the features above have a natural link to the resources available to the population: healthcare provisions such as hospital beds and specialist equipment such as ventilators, as well as vaccines, antiviral medications and any other treatments which are relevant. Staffing of healthcare facilities will be an important consideration if there is a significant risk of hospital-acquired infections amongst healthcare workers .
Sophisticated models may attempt to allow for the limited nature of these resources and the effect of them being used up. As we saw early on in the Italian outbreak of COVID-19, an overburdened care system can mean higher mortality, as medics make the heart-breaking decisions as to who gets treatment and who does not. Both facilities and staffing levels will differ between geographical regions; models allowing for these will be more easily able to distinguish between the effects of the same pandemic across national borders.
Government policy and the public response
There are few catastrophes we could imagine in which the dynamic interplay between government policy and public behaviour has such a dramatic effect on the outcome as with a pandemic.
Over the past months we’ve seen the closure of schools and all but essential industry, social distancing rules implemented and changing advice on face masks or coverings. Similarly, we’ve seen a range of public responses from complete compliance to flagrant defiance of lockdown laws.
This is important for modelling; all of these policies and behaviours have an effect on the rate of spread of infections. It would be unusual to think that, faced with a major epidemic, there would be no effort to stop or slow its spread (though responses can differ in severity; compare the Italian lockdown to the responses in Brazil or Sweden, for example). Similarly, it would be unusual not to consider the effects of these policies and behavioural changes when modelling one.
All too complex
Any model is a simplification of the real-world phenomenon it is meant to replicate. Each model’s features will need to reflect its purpose.
Many infectious disease models produced in academia will choose just a handful of key features which are essential to answering the research question of interest. Models to support policy decisions will be more complex and granular.
Pandemic models can also be used to inform the pricing of financial instruments related to pandemic risk. Perhaps the best-known example of this is the two series of catastrophe bonds issued by the World Bank in 2017: the “Pandemic Emergency Financing Facility”. For such models, the level of detail (and the corresponding memory requirements) can be eye-watering.
Whilst we could look at the range of features we ‘really ought to model’ and decide that this is all too complex, we can console ourselves that even the simplest models can give us insight into how infectious diseases work.
It should be noted that much of the content of this blog-post has been deliberately simplified. For those looking for a more in-depth description of pandemic models, a wealth of academic literature is available covering a range of model features and based on different infectious agents.