Vaccination strategies for foot-and-mouth disease (reply)

Searching for the most cost-effective strategy for controlling epidemics spreading on regular and small-world networks

We present a combined epidemiological and economic model for control of diseases spreading on local and small-world networks. The disease is characterized by a pre-symptomatic infectious stage that makes detection and control of cases more difficult. The effectiveness of local (ring-vaccination or culling) and global control strategies is analysed by comparing the net present values of the combined cost of preventive treatment and illness. The optimal strategy is then selected by minimizing the total cost of the epidemic. We show that three main strategies emerge, with treating a large number of individuals (global strategy, GS), treating a small number of individuals in a well-defined neighbourhood of a detected case (local strategy) and allowing the disease to spread unchecked (null strategy, NS). The choice of the optimal strategy is governed mainly by a relative cost of palliative and preventive treatments. If the disease spreads within the well-defined neighbourhood, the local strategy is optimal unless the cost of a single vaccine is much higher than the cost associated with hospitalization. In the latter case, it is most cost-effective to refrain from prevention. Destruction of local correlations, either by long-range (small-world) links or by inclusion of many initial foci, expands the range of costs for which the NS is most cost-effective. The GS emerges for the case when the cost of prevention is much lower than the cost of treatment and there is a substantial non-local component in the disease spread. We also show that local treatment is only desirable if the disease spreads on a small-world network with sufficiently few long-range links; otherwise it is optimal to treat globally. In the mean-field case, there are only two optimal solutions, to treat all if the cost of the vaccine is low and to treat nobody if it is high. The basic reproduction ratio, R(0), does not depend on the rate of responsive treatment in this case and the disease always invades (but might be stopped afterwards). The details of the local control strategy, and in particular the optimal size of the control neighbourhood, are determined by the epidemiology of the disease. The properties of the pathogen might not be known in advance for emerging diseases, but the broad choice of the strategy can be made based on economic analysis only.

How to make predictions about future infectious disease risks

Formal, quantitative approaches are now widely used to make predictions about the likelihood of an infectious disease outbreak, how the disease will spread, and how to control it. Several well-established methodologies are available, including risk factor analysis, risk modelling and dynamic modelling. Even so, predictive modelling is very much the ‘art of the possible’, which tends to drive research effort towards some areas and away from others which may be at least as important. Building on the undoubted success of quantitative modelling of the epidemiology and control of human and animal diseases such as AIDS, influenza, foot-and-mouth disease and BSE, attention needs to be paid to developing a more holistic framework that captures the role of the underlying drivers of disease risks, from demography and behaviour to land use and climate change. At the same time, there is still considerable room for improvement in how quantitative analyses and their outputs are communicated to policy makers and other stakeholders. A starting point would be generally accepted guidelines for ‘good practice’ for the development and the use of predictive models.

The role of pre-emptive culling in the control of foot-and-mouth disease

The 2001 foot-and-mouth disease epidemic was controlled by culling of infectious premises and pre-emptive culling intended to limit the spread of disease. Of the control strategies adopted, routine culling of farms that were contiguous to infected premises caused the most controversy. Here we perform a retrospective analysis of the culling of contiguous premises as performed in 2001 and a simulation study of the effects of this policy on reducing the number of farms affected by disease. Our simulation results support previous studies and show that a national policy of contiguous premises (CPs) culling leads to fewer farms losing livestock. The optimal national policy for controlling the 2001 epidemic is found to be the targeting of all contiguous premises, whereas for localized outbreaks in high animal density regions, more extensive fixed radius ring culling is optimal. Analysis of the 2001 data suggests that the lowest-risk CPs were generally prioritized for culling, however, even in this case, the policy is predicted to be effective. A sensitivity analysis and the development of a spatially heterogeneous policy show that the optimal culling level depends upon the basic reproductive ratio of the infection and the width of the dispersal kernel. These analyses highlight an important and probably quite general result: optimal control is highly dependent upon the distance over which the pathogen can be transmitted, the transmission rate of infection and local demography where the disease is introduced.