Relationship of speed of slaughter on infected premises and intensity of culling of other premises to the rate of spread of the foot-and-mouth disease epidemic in Great Britain, 2001

Estimated Dissemination Ratio-A Practical Alternative to the Reproduction Number for Infectious Diseases

Policymakers require consistent and accessible tools to monitor the progress of an epidemic and the impact of control measures in real time. One such measure is the Estimated Dissemination Ratio (EDR), a straightforward, easily replicable, and robust measure of the trajectory of an outbreak that has been used for many years in the control of infectious disease in livestock. It is simple to calculate and explain. Its calculation and use are discussed below together with examples from the current COVID-19 outbreak in the UK. These applications illustrate that EDR can demonstrate changes in transmission rate before they may be clear from the epidemic curve. Thus, EDR can provide an early warning that an epidemic is resuming growth, allowing earlier intervention. A conceptual comparison between EDR and the commonly used reproduction number is also provided.

Causes of delayed outbreak responses and their impacts on epidemic spread

Livestock diseases have devastating consequences economically, socially and politically across the globe. In certain systems, pathogens remain viable after host death, which enables residual transmissions from infected carcasses. Rapid culling and carcass disposal are well-established strategies for stamping out an outbreak and limiting its impact; however, wait-times for these procedures, i.e. response delays, are typically farm-specific and time-varying due to logistical constraints. Failing to incorporate variable response delays in epidemiological models may understate outbreak projections and mislead management decisions. We revisited the 2001 foot-and-mouth epidemic in the United Kingdom and sought to understand how misrepresented response delays can influence model predictions. Survival analysis identified farm size and control demand as key factors that impeded timely culling and disposal activities on individual farms. Using these factors in the context of an existing policy to predict local variation in response times significantly affected predictions at the national scale. Models that assumed fixed, timely responses grossly underestimated epidemic severity and its long-term consequences. As a result, this study demonstrates how general inclusion of response dynamics and recognition of partial controllability of interventions can help inform management priorities during epidemics of livestock diseases.

The ideal reporting interval for an epidemic to objectively interpret the epidemiological time course

The reporting interval of infectious diseases is often determined as a time unit in the calendar regardless of the epidemiological characteristics of the disease. No guidelines have been proposed to choose the reporting interval of infectious diseases. The present study aims at translating coarsely reported epidemic data into the reproduction number and clarifying the ideal reporting interval to offer detailed insights into the time course of an epidemic. We briefly revisit the dispersibility ratio, i.e. ratio of cases in successive reporting intervals, proposed by Clare Oswald Stallybrass, detecting technical flaws in the historical studies. We derive a corrected expression for this quantity and propose simple algorithms to estimate the effective reproduction number as a function of time, adjusting the reporting interval to the generation time of a disease and demonstrating a clear relationship among the generation-time distribution, reporting interval and growth rate of an epidemic. Our exercise suggests that an ideal reporting interval is the mean generation time, so that the ratio of cases in successive intervals can yield the reproduction number. When it is impractical to report observations every mean generation time, we also present an alternative method that enables us to obtain straightforward estimates of the reproduction number for any reporting interval that suits the practical purpose of infection control.

Space–time interaction as an indicator of local spread during the 2001 FMD outbreak in the UK

During the 2001 FMD outbreak in the UK, decisions on the level of implementation of control measures were supported by predictive models. Models were mainly used as macro-level tools to predict the behaviour of the disease in the whole country rather than at the local level. Here we explore the use of the magnitude and characteristics of the space-time interaction as an indicator of local spread and, indirectly, of the effectiveness of control measures aimed at reducing short-range transmission during the course of a major livestock disease epidemic. The spatiotemporal evolution patterns are described in the four main clusters that were observed during the outbreak by means of the hazard rate and space-time K-function (K(s,t)). For each local outbreak, the relative measure D(0)(s,t), derived from K(s,t), which represents the excess risk attributable to the space-time interaction was calculated for consecutive 20-day temporal windows to represent the dynamics of the space-time interaction. The dynamics of the spatiotemporal interaction were very different among the four local clusters, suggesting that the intensity of local spread, and therefore the effectiveness of control measures, markedly differed between local outbreaks. The large heterogeneity observed in the relative impact of being close in time and space to an infected premises suggests that the decision making in relation to control of the outbreak would have benefited from indicators of local spread which could be used to complement global predictive modelling results. Despite its limitations, our results suggest that the real-time analysis of the space-time interaction can be a valuable decision support tool during the course of a livestock disease epidemic.