Robust Mathematical Modelling of Household-Stratified Epidemic Time-series

Lead Research Organisation: University of Manchester
Department Name: Mathematics


Infectious diseases affect us all, and are one of the main risks to human health and quality of life worldwide. Despite advances in our understanding of them, a great many questions remain about the way in which infectious diseases actually transmit through human populations. Some open questions, even for common diseases like influenza, relate to estimation of quite basic quantities: how infectious is the illness in different contexts; how long cases of different ages are infectious for; and how much immunity to re-infection is conferred upon recovery.

Other more fundamental questions relate to more subtle issues. Many human pathogen species are differentiated into strains that can be identified using modern laboratory techniques, but the way that these interact with each other - for example, whether previous infection with one strain confers immunity to another - is complex and hard to determine. At the same time, the relationship between severity of illness, and how infectious as case is, can be quite complex.

Answering these and other questions requires study of disease transmission in a natural setting, but simply measuring the amount of illness in a population does not yield sufficient information to resolve them. Conducting a household cohort study, which involves measuring infections in several whole households over time, offers the promise of much more information. Such studies are being run with increasing frequency.

This project is about developing the mathematics needed to analyse household cohort studies in a way that extracts as much novel epidemiological information as possible. There are several steps to be taken: a first question might be how likely a given set of study results are to be observed if we knew every relevant quantity. By creating methods to calculate such a quantity efficiently on a computer, it can become possible to invert the process and gain insight into the epidemiological mechanisms that generate the data.

Ultimately, by knowing more about the way in which diseases spread through the human population, we can improve our control of them. For example, if new cases of a disease do not become infectious for several days, then this gives time for quarantine to be an effective control measure. If within-household transmission is much more intense than between-household transmission, then interventions should be focused on the household.

Planned Impact

The ultimate destination for impact of the research is to improve human health worldwide by controlling infectious diseases more efficiently. There is quite a well defined route through from fundamental infectious disease research to this outcome. The first step is for the methodological research to be published in peer-reviewed journals and presented at scientific conferences, and for code to be disseminated as appropriate. These methods can then be applied to data collected by medical researchers, to yield epidemiological insights. The results from this process are then combined into policy-relevant research, often itself involving mathematical modelling, to inform decisions made by the healthcare system.

An additional economic and societal impact from the research is common to most research in scientific subjects: through the training of individuals with technical and quantitative skills through work on the projects. This benefits both the trained individuals, who enhance their skill set, and society more generally through the additional value given to the trained individuals' future work.


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Description This award has led to significant improvements in our ability to understand infection spread in populations split into closely connected subgroups. The work has also generated methods that can be applied to COVID, other infections, and some non-infectious diseases, beyond scabies and influenza as initially considered.

We have obtained methodological innovations for optimal inference that have been applied to scabies in care homes, which is leading to impact in two directions: first, on policy on scabies treatment, and secondly on infection control in care homes generally.

We have also found robust results concerning optimal design of household stratified time series that have been applied, including in the current coronavirus outbreak.
Exploitation Route Design and analysis of epidemiological / infectious disease studies. Future work on scabies policy and care homes. Pandemic response.
Sectors Healthcare,Government, Democracy and Justice

Description This work has influenced the design of household trials for infectious disease, including the 'containment' surveillance protocol developed for the start of the ongoing coronavirus outbreak and the ONS Coronavirus Infection Survey. The work has also been used to model policies such as "bubbling", various household / care home modelling policies in the current pandemic, including writing of SAGE and SPI-M papers. The work has influenced control of Scabies in residential care homes, with a policy letter on the use of Ivermectin carried in the Lancet, and policy on control of infections in care homes in general, have been affected by the work.
First Year Of Impact 2018
Sector Healthcare,Government, Democracy and Justice
Impact Types Societal,Policy & public services