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The Actuary The magazine of the Institute & Faculty of Actuaries

The influenza agenda

Insurers perennially cite a pandemic as one of the major risks they face, but are the industry’s modelling approaches keeping pace with the wider body of available knowledge? Matthew Edwards and Richard Marshall investigate


The influenza agenda

It has been a long and widely held belief that the most plausible pandemic scenario is an influenza pandemic.This is largely due to the rapid evolution of different strains of the influenza virus and the ease and speed of transmission of certain strains of the virus. 

Estimates of the transmissibility of different strains of influenza virus vary greatly across populations and studies. The base reproductive number is a measure of the number of new cases that one case of a virus may generate and is denoted ‘R0’. If a virus has an R0 less than one, it will eventually die out, since there will be fewer new cases with each generation of infection.

Figure 1 (below) shows the medians, interquartile ranges and full ranges of estimates of R0 for the main pandemic strains of the past 100 years, along with those for seasonal influenza. Note that a few outliers widen the overall ranges significantly. The interquartile ranges are a better indication of the spread of the estimates for R0.

Historically, pandemic strains have often occurred in at least two waves. The 1918 H1N1, the 1968 H3N2 and the 2009 H1N1 strains all unfolded in this manner. The factors underlying this characteristic are thought to include school holidays and weather conditions, since the influenza virus has been estimated to have a higher base reproductive number in children than in adults, and humidity is believed to affect how the virus is transmitted. 

Infection attack rates, base reproductive numbers and wave structures are important in determining the size and timing of the impact of a pandemic on different age groups and therefore in quantifying the impact on an insurance portfolio. For this reason, a comprehensive approach to pandemic modelling should allow for single- and double-wave pandemics, age-specific infection rates and rates of transmission that can vary for treatment status, seasonality and patterns of social contact, in each case parameterised using the latest national statistics and medical data. This approach gives more robust estimates of the effect of a modern pandemic on a particular portfolio. 

Figure 1 Estimates of R0 from survey by Biggerstaff et al. (BMC Infectious Diseases, 2014)
Figure 1: Estimates of R0 from survey by Biggerstaff et al. (BMC Infectious Diseases, 2014)

For insurers with material pandemic risk, understanding the nature of their exposure requires a more sophisticated internal model approach

Prevention and treatment

One of the challenges faced by vaccine developers is ‘antigenic drift’, whereby accumulated mutations in the virus lead to a new virus strain that is impervious to existing treatments. 

Cell-based and recombinant methods of vaccine production have cut the delay from identification of a strain of influenza to the availability of vaccines for distribution over the past few years. Vaccine efficacy against antigenically matched strains of influenza virus has been shown to be almost 84%. But while vaccines may provide protection against existing strains, effectiveness against novel strains is materially lower.

Some strains of the 2009 H1N1 virus have been observed to be resistant to Tamiflu®. In the UK, 45 out of 5,587 viruses tested were resistant, and further resistant cases emerged in the 2010/11 influenza season. Antigenic drift could cause rates of resistance to increase dramatically, especially when a drug is widely used in response to an outbreak. 

While the technologies becoming available to fight pandemics show promise, the nature of the influenza virus is that it presents something of a moving target. A suitable model calibration must devote equal attention to the subjects of virus virulence and spread to those of antiviral effectiveness and response. 

UK preparedness for a pandemic

The current UK pandemic preparedness strategy was last published in 2011 and proposed that the nation should hold a stockpile of antiviral medicines to treat pandemic influenza, but not to protect against infection prior to exposure. The five phases of the UK’s response are shown in Figure 2.

Figure 2
Figure 2

The UK’s Scientific Pandemic Influenza Advisory Committee has published a ‘reasonable worst case scenario’ for the purpose of emergency planning in the UK. This shows the likely infection rates, peak illness rates, case hospitalisation rates, intensive care requirements and case fatality ratios in the event of a severe pandemic influenza outbreak. The national response to a pandemic is crucial to the progression and impact of a viral strain. The UK’s preparedness plan gives an indication of the range and severity of action that may be taken, and the reasonable worst-case scenario provided by the UK’s advisory committee offers an insight into the parameterisation that might be considered in determining capital requirements. 

Industry approaches 

The Standard Formula Life Catastrophe risk sub-module specifies a level uplift to mortality rates of 15 basis points applied over a period of 12 months, which gives excess mortality of 1.5 deaths per mille owing to a combination of different potential catastrophic events, of which one is a pandemic. 

This approach, however, poorly represents the actual risks faced by any company with exposure to pandemic risk. This is because it specifies excess deaths per year, not their time distribution. Pandemics can be concentrated within a period of a few weeks and in one or more waves. The Standard Formula approach also assumes excess deaths are distributed evenly across all ages. In reality, certain age groups are affected more than others. 

The Standard Formula also fails to adequately allow for: 

  • Operational risks – for example, the effect of a pandemic on absentee rates
  • Increases in temporary income protection policy claims
  • Changes in policyholder behaviour 
  • Impacts on non-life products – for example, travel insurance or business interruption insurance
  • Effectiveness of reinsurance programmes.  

As to the overall level of the calibration, the Standard Formula specifies 1.5 deaths per mille across a year, but a variety of models with different structures and a range of historical estimates of mortality from previous pandemics suggest excess deaths ranging from 0.1 to 4 per mille based on influenza alone. 

As progress is made towards the development of a universal influenza vaccine, the focus for future pandemic modelling may even shift away from influenza, so it is important to have an understanding of a wider range of possible pandemic scenarios. Given the threats of emerging resistance to antibiotics, it is not beyond the realms of possibility that bacterial infections – for instance, extensively drug-resistant tuberculosis – could be responsible for a future pandemic.

Where companies have a significant exposure to a wide range of possible risks from pandemics, models need to progress beyond benchmarked calibrations of excess deaths alone in order to determine the impact on a company’s overall portfolio. 

Overcoming shortfalls of the Standard Formula

For insurers with material pandemic risk, understanding the nature of their exposure requires a more sophisticated internal model approach. The impact on capital might be small, but the information and understanding gained will improve preparedness and allow more effective risk mitigation approaches to be employed.

Typical approaches to pandemic modelling in academia have included SIR models (“Susceptible”, “Infected”, “Recovered”/”Removed”), possibly with additional states for latent infections and complications. Some sophisticated models break with the Markov assumption and allow for time-inhomogeneity in incubation periods and recovery rates. Industry models have generally lagged behind, however; curve fitting and factor-based models (eg severity and lethality) are typical approaches among those known to be modelling pandemic risk at all.

To implement effective risk management, insurers should ideally be able to understand the wide range of potential impacts of government policy, social distancing and limitations of healthcare provisions on the outcomes of a pandemic. As well as capturing key viral characteristics (transmission rates, incubation periods, infectious durations and complication rates), models will need to have regard to:

  • The availability of, and strain on, medical care
  • Time to vaccine production and vaccine efficacy
  • The impacts of changes in patterns of travel on geographical spread

It will also be important to understand the sensitivity of the results to changes in the population and health-care assumptions. These insights could come from a sophisticated multi-state approach, building on the strengths of those models from the world of academia.

Medical approaches to tackling the threat of pandemics have moved on; modelling of the ensuing insurance risks should do likewise.

Matthew Edwards is head of mortality and longevity in Willis Towers Watson’s life insurance practice

Richard Marshall is senior analyst at Willis Towers Watson