Bärbel F. Finkenstädt’s research while affiliated with University of Warwick and other places

A stochastic discrete-time susceptible-exposed-infectious-recovered (SEIR) model for infectious diseases is developed with the aim of estimating parameters from daily incidence and mortality time series for an outbreak of Ebola in the Democratic Republic of Congo in 1995. The incidence time series exhibit many low integers as well as zero counts requiring an intrinsically stochastic modeling approach. In order to capture the stochastic nature of the transitions between the compartmental populations in such a model we specify appropriate conditional binomial distributions. In addition, a relatively simple temporally varying transmission rate function is introduced that allows for the effect of control interventions. We develop Markov chain Monte Carlo methods for inference that are used to explore the posterior distribution of the parameters. The algorithm is further extended to integrate numerically over state variables of the model, which are unobserved. This provides a realistic stochastic model that can be used by epidemiologists to study the dynamics of the disease and the effect of control interventions.

Since influenza in humans is a major public health threat, the understanding of its dynamics and evolution, and improved prediction of its epidemics are important aims. Underlying its multi-strain structure is the evolutionary process of antigenic drift whereby epitope mutations give mutant virions a selective advantage. While there is substantial understanding of the molecular mechanisms of antigenic drift, until now there has been no quantitative analysis of this process at the population level. The aim of this study is to develop a predictive model that is of a modest-enough structure to be fitted to time series data on weekly flu incidence. We observe that the rate of antigenic drift is highly non-uniform and identify several years where there have been antigenic surges where a new strain substantially increases infective pressure. The SIR-S approach adopted here can also be shown to improve forecasting in comparison to conventional methods.

A stochastic discrete time version of the susceptible-infected-recovered model for infectious diseases is developed. Disease is transmitted within and between communities when infected and susceptible individuals interact. Markov chain Monte Carlo methods are used to make inference about these unobserved populations and the unknown parameters of interest. The algorithm is designed specifically for modelling time series of reported measles cases although it can be adapted for other infectious diseases with permanent immunity. The application to observed measles incidence series motivates extensions to incorporate age structure as well as spatial epidemic coupling between communities. Copyright 2005 Royal Statistical Society.

Epidemic dynamics pose a great challenge to stochastic modelling because chance events are major determinants of the size and the timing of the outbreak. Reintroduction of the disease through contact with infected individuals from other areas is an important latent stochastic variable. In this study we model these stochastic processes to explain extinction and recurrence of epidemics observed in measles. We develop estimating functions for such a model and apply the methodology to temporal case counts of measles in 60 cities in England and Wales. In order to estimate the unobserved spatial contact process we suggest a method based on stochastic simulation and marginal densities. The estimation results show that it is possible to consider a unified model for the UK cities where the parameters depend on the city size. Stochastic realizations from the dynamic model realistically capture the transitions from an endemic cyclic pattern in large populations to irregular epidemic outbreaks in small human host populations.

The study focuses on the selection of the order of a general time series process via the conditional density of the latter, a characteristic of which is that it remains constant for every order beyond the true one. Using simulated time series from various nonlinear models we illustrate how this feature can be traced from conditional density estimation. We study whether two statistics derived from the likelihood function can serve as univariate statistics to determine the order of the process. It is found that a weighted version of the log likelihood function has desirable robust properties in detecting the order of the process.

A key issue in the dynamical modelling of epidemics is the synthesis of complex mathematical models and data by means of time series analysis. We report such an approach, focusing on the particularly well-documented case of measles. We propose the use of a discrete time epidemic model comprising the infected and susceptible class as state variables. The model uses a discrete time version of the susceptible–exposed–infected–recovered type epidemic models, which can be fitted to observed disease incidence time series. We describe a method for reconstructing the dynamics of the susceptible class, which is an unobserved state variable of the dynamical system. The model provides a remarkable fit to the data on case reports of measles in England and Wales from 1944 to 1964. Morever, its systematic part explains the well-documented predominant biennial cyclic pattern. We study the dynamic behaviour of the time series model and show that episodes of annual cyclicity, which have not previously been explained quantitatively, arise as a response to a quicker replenishment of the susceptible class during the baby boom, around 1947.

Epidemiologists usually study the interaction between a host population and one parasitic infection. However, different parasite species effectively compete, in an ecological sense, for the same finite group of susceptible hosts, so there may be an indirect effect on the population dynamics of one disease due to epidemics of another. In human populations, recovery from any serious infection is normally preceded by a period of convalescence, during which infected individuals stay at home and are effectively shielded from exposure to other infectious diseases. We present a model for the dynamics of two infectious diseases, incorporating a temporary removal of susceptibles. We use this model to explore population-level consequences of a temporary insusceptibility in childhood diseases, the dynamics of which are partly driven by differences in contact rates in and out of school terms. Significant population dynamic interference is predicted and cannot be dismissed in the limited case-study data available for measles and whooping cough in England before the vaccination era.

A major debate in ecology concerns the relative importance of intrinsic factors and extrinsic environmental variations in determining population size fluctuations. Spatial correlation of fluctuations in different populations caused by synchronous environmental shocks,, is a powerful tool for quantifying the impact of environmental variations on population dynamics,. However, interpretation of synchrony is often complicated by migration between populations,. Here we address this issue by using time series from sheep populations on two islands in the St Kilda archipelago. Fluctuations in the sizes of the two populations are remarkably synchronized over a 40-year period. A nonlinear time-series model shows that a high and frequent degree of environmental correlation is required to achieve this level of synchrony. The model indicates that if there were less environmental correlation, population dynamics would be much less synchronous than is observed. This is because of a threshold effect that is dependent on population size; the threshold magnifies random differences between populations. A refined model showsthat part of the required environmental synchronicity can be accounted for by large-scale weather variations. These results underline the importance of understanding the interaction between intrinsic and extrinsic influences on population dynamics.

An important question in metapopulation dynamics is the influence of external perturbations on the population's long-term dynamic behaviour. In this paper we address the question of how spatiotemporal variations in demographic parameters affect the dynamics of measles populations in England and Wales. Specifically, we use nonparametric statistical methods to analyse how birth rate and population size modulate the negative density dependence between successive epidemics as well as their periodicity. For the observed spatiotemporal data from 60 cities, and for simulated model data, the demographic variables act as bifurcation parameters on the joint density of the trade-off between successive epidemics. For increasing population size, a transition occurs from an irregular unpredictable pattern in small communities towards a regular, predictable endemic pattern in large places. Variations in the birth rate parameter lead to a bifurcation from annual towards biennial cyclicity in both observed data and model data.