Recurrent epidemics in small world networks

The effect of spatial correlations on the spread of infectious diseases was investigated using a stochastic susceptible-infective-recovered (SIR) model on complex networks. It was found that in addition to the reduction of the effective transmission rate, through the screening of infectives, spatial correlations have another major effect through the enhancement of stochastic fluctuations, which may become considerably larger than in the homogeneously mixed stochastic model. As a consequence, in finite spatially structured populations significant differences from the solutions of deterministic models are to be expected, since sizes even larger than those found for homogeneously mixed stochastic models are required for the effects of fluctuations to be negligible. Furthermore, time series of the (unforced) model provide patterns of recurrent epidemics with slightly irregular periods and realistic amplitudes, suggesting that stochastic models together with complex networks of contacts may be sufficient to describe the long-term dynamics of some diseases. The spatial effects were analysed quantitatively by modelling measles and pertussis, using a susceptible-exposed-infective-recovered (SEIR) model. Both the period and the spatial coherence of the epidemic peaks of pertussis are well described by the unforced model for realistic values of the parameters.     

Stochastic epidemics in dynamic populations: quasi-stationarity and extinction

Empirical evidence shows that childhood diseases persist in large communities whereas in smaller communities the epidemic goes extinct (and is later reintroduced by immigration). The present paper treats a stochastic model describing the spread of an infectious disease giving life-long immunity, in a community where individuals die and new individuals are born. The time to extinction of the disease starting in quasi-stationarity (conditional on non-extinction) is exponentially distributed. As the population size grows the epidemic process converges to a diffusion process. Properties of the limiting diffusion are used to obtain an approximate expression for τ, the mean-parameter in the exponential distribution of the time to extinction for the finite population. The expression is used to study how τ depends on the community size but also on certain properties of the disease/community: the basic reproduction number and the means and variances of the latency period, infectious period and life-length. Effects of introducing a vaccination program are also discussed as is the notion of the critical community size, defined as the size which distinguishes between the two qualitatively different behaviours. Received: 14 February 2000 / Revised version: 5 June 2000 / Published online: 24 November 2000     

EXISTENCE OF MULTIPLE PERIODIC SOLUTIONS TO A NONLINEAR INTEGRAL EQUATION FROM THE THEORY OF EPIDEMICS

Thenonlinearintegralequation(1.1)isageneralizedmodelforthespreadofdiseaseswithseasonaldependence.Inthispaper,wehaveprovedtheexistenceofatleastthreenontrivialnonnegativeperiodicsolutionstothisequation.     

Development of cercospora blight epidemics and effect on the summer annual Heliotropium europaeum in the field

Heliotropium europaeum, common heliotrope, is a serious economic weed in southern Australia. Cercospora blight occurs on H. europaeum in both its native (Mediterranean) and non-native (Australian) range. The causal agents are genetically different forms of an asexual pathogen in the form-genus Cercospora in each region. Natural epidemics of cercospora blight killed weed infestations in both Australia and France. The epidemiology of the disease did not differ between the two regions once differences in rainfall had been considered. Rainfall was important for disease spread. In France, field inoculation experiments were conducted using different concentrations of conidia prepared from a monospore isolate. Cercospora blight reduced seed production 89%, but did not reduce viability. Increased inoculum concentration and inoculation of younger plants encouraged an early epidemic, but did not affect the rate of disease development once the epidemic took hold. In order to be effective at controlling this weed in Australia, these pathogens need to attack young hosts and have regular rain-splash to facilitate spread to new growth.     

Epidemic predictions in an imperfect world: modelling disease spread with partial data

‘Big-data’ epidemic models are being increasingly used to influence government policy to help with control and eradication of infectious diseases. In the case of livestock, detailed movement records have been used to parametrize realistic transmission models. While livestock movement data are readily available in the UK and other countries in the EU, in many countries around the world, such detailed data are not available. By using a comprehensive database of the UK cattle trade network, we implement various sampling strategies to determine the quantity of network data required to give accurate epidemiological predictions. It is found that by targeting nodes with the highest number of movements, accurate predictions on the size and spatial spread of epidemics can be made. This work has implications for countries such as the USA, where access to data is limited, and developing countries that may lack the resources to collect a full dataset on livestock movements.     

Two examples of the interplay between field observations and laboratory experiments from 35 years of research with planktonic organisms

Two studies of complicated ecological phenomena in Lake Maarsseveen (The Netherlands) are presented to illustrate that a combination of field and laboratory analysis might be a successful approach. In the first one, the yearly varying ratio of population abundance of two diatoms, Asterionella formosa and Fragilaria crotonensis during early spring is explained by a combination of abiotic and biotic factors. A fungal parasite blocks population development of the first species at temperatures higher than 3–5 °C . The second species then competes successfully for phosphate and develops a large population. The interaction between Asterionella and the fungus proved to be intricate. Several physiological mechanisms operate together and combined with variable climatic factors makes the prediction of what species will be dominant, impossible. In the second example diel vertical migration of the hybrid Daphnia galeata × hyalina is analysed in the field and the laboratory. Migration is confined to six to seven weeks in June–July when large shoals of juvenile perch are present in the pelagic zone of the lake. These fish exudate a kairomone that enhances the reaction of Daphnia to relative increases in light intensity of dawn. Especially accelerations in rate of relative increases enhance swimming velocity. The extent of enhancement depends, however, on the concentration of the kairomone and on food concentration. A Decision Making Mechanism is introduced and the relation between the response mechanism and the adaptive relevance of diel vertical migration is made.Finally considerations about research strategies and the importance of fundamental research are made. It is concluded that the development of limnology and aquatic ecology might be in danger when the present tendency to give prevalence to applied research continues.     

Learning from history, predicting the future: the UK Dutch elm disease outbreak in relation to contemporary tree disease threats

Expanding international trade and increased transportation are heavily implicated in the growing threat posed by invasive pathogens to biodiversity and landscapes. With trees and woodland in the UK now facing threats from a number of disease systems, this paper looks to historical experience with the Dutch elm disease (DED) epidemic of the 1970s to see what can be learned about an outbreak and attempts to prevent, manage and control it. The paper draws on an interdisciplinary investigation into the history, biology and policy of the epidemic. It presents a reconstruction based on a spatial modelling exercise underpinned by archival research and interviews with individuals involved in the attempted management of the epidemic at the time. The paper explores what, if anything, might have been done to contain the outbreak and discusses the wider lessons for plant protection. Reading across to present-day biosecurity concerns, the paper looks at the current outbreak of ramorum blight in the UK and presents an analysis of the unfolding epidemiology and policy of this more recent, and potentially very serious, disease outbreak. The paper concludes by reflecting on the continuing contemporary relevance of the DED experience at an important juncture in the evolution of plant protection policy.     

Influenza drift and epidemic size: the race between generating and escaping immunity

Influenza in humans is characterised by strongly annual dynamics and antigenic evolution leading to partial escape from prior host immunity. The variability of new epidemic strains depends on the amount of virus currently circulating. In this paper, the amount of antigenic variation produced each year is dependent on the epidemic size. Our model reduces to a one-dimensional map and a full mathematical analysis is presented. This simple system suggests some basic principles which may be more generally applicable. In particular, for diseases with antigenic drift, vaccination may be doubly beneficial. Not only does it protect the population through classical herd immunity, but the overall case reduction reduces the chance of new variants being produced; hence, subsequent epidemics may be milder as a result of this positive feedback. Also, a disease with a high innate rate of antigenic variation will always be able to invade a susceptible population, whereas a disease with less potential for variation may require several introduction events to become endemic.