Dynamics and control of infectious disease epidemics: scaling from within-host to population-level models

The threat posed by infectious disease epidemics, as evidenced by the 2014-2016 Ebola outbreak in West Africa, is a huge ongoing concern. Mathematical models are increasingly being used to predict the progression of epidemics and to plan interventions. Commonly used epidemiological models typically assume each infectious host is equally infectious. In reality, both infectiousness and symptom expression will vary over the course of an infection.

In this project, we will develop methods for nesting within-host pathogen dynamics inside population-level models. We will investigate whether including within-host dynamics in models affects predictions as to the effectiveness of control interventions. Differences between the predictions of different models are likely to be of interest to policy-makers, who seek accurate forecasts.

This project will be split into four parts, which are summarised below.
1. Linking different approaches for including variable infectiousness in epidemic models. Time-dependent infectiousness may be incorporated into an ordinary differential equation (ODE) compartmental model by including multiple infectious compartments, through which a host progresses and between which their infectiousness varies. An alternative approach is to use an integro-differential equation (IDE) model. We aim to link rigorously these two approaches for the first time, by considering the limit in which the number of infectious compartments in the ODE model tends to infinity.
2. The effect of variability in symptom expression on surveillance. Infectious disease surveillance is usually modelled as an observation process. In other words, some proportion of infectious hosts are assumed to be detected, with the detection probability of each host assumed to be the same. In reality, however, the detection probability changes over the course of an infection. We will use the ODE model described in 1 above to investigate the effect of this variability on model predictions of observed epidemic dynamics. We will also develop new models in which surveillance is modelled as a dynamic process, involving not only detection but also control of infectious hosts.
3. Linking stochastic and deterministic models. Whilst deterministic epidemic models are fast to numerically solve, real-world epidemiological systems are inherently stochastic. Deterministic equations, which describe not only the mean behaviour over many epidemics but also the variability, may be derived from a stochastic model through the use of moment closure techniques. We aim to develop novel moment closure techniques and apply them to stochastic epidemiological models incorporating variable infectiousness. In this way, we can see how our models developed in 1 and 2 above compare to those that include stochasticity.
4. Application to control of Ebola outbreaks. The level of infectiousness and symptom expression both vary significantly during the course of an Ebola infection. Previously, the simple SEIR compartmental model has been used to model Ebola spread and control. However, variations in infectiousness and symptoms within a host will affect, for example, when an infection is likely to be detected and how many secondary infections are likely to be generated before this time. We will perform a literature search to find data describing temporal variations in both infectiousness and symptom expression during an Ebola infection, and use this data to parametrise the ODE model described in 1. This model may then be used by policy-makers to test different proposed control interventions.

This project falls within the EPSRC Mathematical Biology research area, within the Mathematical Sciences and Healthcare Technologies themes.

Possible collaborators
1. Dr Kit Yates, University of Bath
2. Dr Oliver Morgan, World Health Organization
3. Jonathan Polonsky, World Health Organization