Statistical inference with mechanistic models on heterogeneous data: improving the control of infectious diseases

Influenza epidemics occur every year, resulting in large amounts of illness in the community, many early deaths, major disruption to the health services, and significant economic losses. This is despite widespread vaccination. Although the vaccine contains three strains, it is not possible to say ahead of the epidemic which (if any) of the strains will circulate, and how severe will the resultant epidemic be. This means that planning by public health authorities, physicians, and hospitals is difficult, resulting in significant inefficiencies (such as the unnecessary cancelling elective surgeries, etc).

The size of an influenza epidemic is governed, amongst other things, by the level of immunity in the population (it is for this reason that pandemics are so feared, as the novel virus tends to be very different from existing strains, and so the level of immunity in the population is low). The emergence of a novel H1N1 (swine flu) virus in 2009 has been closely monitored and studied. The UK has one of the best influenza surveillance systems in the world, and has amassed a great deal of data on the spread, severity, and population immunity to this virus. Despite this, the virus has surprised public health officials and mathematical modellers alike, as a significant epidemic was observed during the winter of 2010/11 despite apparently high levels of population immunity. What may happen in the coming years is equally unknown. The emergence of this virus and the wealth of data available provide an unique opportunity to better understand the dynamics of a new influenza virus following its introduction into the human population. We intend to develop and test a number of different mathematical models to build a better picture of the dynamics and evolution of influenza in the population. The models will be fitted to the range of epidemiological data using state-of-the art statistical techniques, which will have general applicability within the fields of infectious disease dynamics and statistical inference. The statistical framework will shed light on the effective level of protection in the population against subsequent drifted variants, and pave the way for the next generation of predictive tools. These investigation are critical to improve the effectiveness of public health measures, like vaccination, and determine which data should be prioritised to help make predictive models of seasonal and pandemic influenza.

This multi-disciplinary project involves many different stakeholders, including the bodies that are collecting the data, experts in disease transmission and host-pathogen interactions, mathematical modellers who formalize biological mechanisms, statisticians who develop rigorous and robust methods to confront models to data, and finally, public health experts who ask the questions that the model must address. It is envisaged that the project will help improve public health policy in this high-profile area, develop new methods for fitting models to data, and provide an ideal training ground for the lead applicant to become an established leader in mathematical epidemiology.

Understanding what governs the size and severity of seasonal influenza epidemics is a key public health priority. This can be obtained by fitting mechanistic models to the many different and varied surveillance data available in the UK to draw inference on key epidemiological drivers. However, the non-linear and stochastic nature of epidemiological processes pose serious challenges to classical statistical methods.

To address these issues we will consider three classes of algorithms that have recently been developed to perform inference on partially observed Markov processes: Approximate Bayesian Computation [Toni et al. 2009 J R Soc Interface], Particle Markov Chain Monte Carlo [Andrieu et al. 2010 J R Stat Soc B] and Maximum Likelihood via Iterated Filtering [Ionides et al. 2006 PNAS]. An attractive feature of these new methodologies is that the only operation applied to the underlying Markov process model is the generation of a draw from the transition density.

The accuracy, precision, robustness and practical use of these different methods on simulated data sets will be compared in order to select the most appropriate one to analyse the uniquely rich and detailed influenza data available in the UK. These include serological, virological, immunological, epidemiological and sociological data available at both the individual and population level over many years.
These data will be combined and linked to the statistical models through observation processes accounting for noise, overdispersion and biases (e.g. negative-binomial). These heterogeneous data will be exploited in a quantitative and rigorous manner to test alternative hypotheses on the mechanisms underlying disease spread.

In the medium term this will facilitate accurate near-to-real-time predictions on the severity and extent of a given epidemic of influenza. In addition, it will help design more efficient and cost-effective vaccination policies.

Influenza remains one of the most serious public health threats, with as many as 10,000 deaths annually attributed to influenza in the UK, despite the existence of widespread vaccination programmes. The threat of a pandemic causing large-scale morbidity and mortality has not receded, despite the emergence of nH1N1 in 2009. Understanding what drives the emergence, spread and evolution of seasonal influenza, and how pandemic strains become established in the population are therefore key public health questions. The surprising spread of H1N1 during the winter of 2010/11 despite apparently high levels of pre-existing immunity, and the resultant impact on deaths, and primary and secondary care demonstrates our lack of a good quantitative understanding of seasonal influenza dynamics.

Public health officials, general practitioners and acute care trusts are therefore expected to be amongst the major beneficiaries of this project. The methods developed will help determine how immunity is built up within individuals, how this maps to population level immunity, and how this is passed from one year to the next. In the medium term this may facilitate accurate near-to-real-time predictions on the severity and extent of a given epidemic of influenza. In addition, by building statistically rigorous mechanistic models of influenza that take account of the dynamics of immunity, we will help design more efficient and cost-effective vaccination policies. Improved vaccine decision-making in the new post-pandemic era, are expected within the time-frame of the fellowship. It is also envisaged that this work may help design more efficient surveillance systems by demonstrating which aspects (e.g. serology) are most important for helping to understand and predict the spread of influenza. In addition, the results will be communicated to national and international scientific advisory bodies, such as the JCVI and Scientific Pandemic Influenza Advisory Group (SPI). This will be facilitated through Professor Edmunds, who regularly advises these bodies and is a member of SPI and SPI-M (its modelling subgroup), as well as WHO's QUIVER (Quantitative Immunisation and Vaccine Related Research Committee).