Spatial pattern formation facilitates eradication of infectious diseases

Abstract

Control of animal-born diseases is a major challenge faced by applied ecologists and public health managers. To improve cost-effectiveness, the effort required to control such pathogens needs to be predicted as accurately as possible. In this context, we reviewed the anti-rabies vaccination schemes applied around the world during the past 25 years.We contrasted predictions from classic approaches based on theoretical population ecology (which governs rabies control to date) with a newly developed individual-based model. Our spatially explicit approach allowed for the reproduction of pattern formation emerging from a pathogen's spread through its host population.We suggest that a much lower management effort could eliminate the disease than that currently in operation. This is supported by empirical evidence from historic field data. Adapting control measures to the new prediction would save one-third of resources in future control programmes.The reason for the lower prediction is the spatial structure formed by spreading infections in spatially arranged host populations. It is not the result of technical differences between models.Synthesis and applications. For diseases predominantly transmitted by neighbourhood interaction, our findings suggest that the emergence of spatial structures facilitates eradication. This may have substantial implications for the cost-effectiveness of existing disease management schemes, and suggests that when planning management strategies consideration must be given to methods that reflect the spatial nature of the pathogen-host system.

Fig. 1

Confirmed cases of rabies in central Europe in 2005, second quarter (red dots). After a large-scale vaccination programme, central Europe is nearly free of sylvatic rabies, whereas it remains an issue in eastern Europe. Data provided by the WHO Collaborating Centre for Rabies Surveillance and Research in Europe, Wusterhausen, Germany.

Fig. 2

Hunting bag of Germany compared with fox population densities of (a) the population model (Anderson et al. 1981) (K = 3, K_t = 1) and (b) the simulation model. Hunting bag data (grey line) are given relative to hunted area (Bellebaum 2003). The figures show population (left, model) and hunting density (right, data) with epidemic rabies and after successful eradication. Vaccination in the models started in 1988. For reference scaling, the disease-free situation was used, i.e. a spring density of 3 foxes km⁻² corresponds to 2 hunted foxes throughout the year. The population reduction by the disease as well as the rate of recovery after the onset of vaccination resulted independently from both modelling approaches.

Fig. 3

Snapshots of the simulation model, (a) the original and (b) the experimental variant without spatially structuring processes. The snapshot of the full version of our model shows the typical wave pattern and epidemic foci as produced by the predominant neighbourhood infection. Local transmission is depicted by an arrow from the infected fox group (red square) to the susceptible fox group (green square). As a result of global transmission the experimental variant without spatially structuring processes shows completely mixed infected and susceptible foxes, effectively meaning that every infected fox might infect any susceptible fox, however distant they may be (indicated by the long arrow).

Fig. 4

Required immunization level necessary for successful elimination as predicted by the population model (grey line; cf. Fig. 5 in Anderson et al. 1981) and the simulation model (black line) for different disease-free densities. Our model predicts a minimum level lower by about 10%. Specifically, with a disease-free density of 3 foxes km⁻², we found a threshold of about 57% in contrast to the 67% predicted by the population model. The stochastic simulation model also yields some chance of eradication in the area below the black line (even lower immunization level; see Fig. S1 in the supplementary material); however, here we show 100% eradication (i.e. all 1000 repetitions must have resulted in eradication).

Fig. 5

The relationship between desired immunization level and baiting effort in the model assuming a disease-free density of 3 foxes km⁻². (a) The graph represents the relative increase in baiting effort if the target level of population immunization is increased. The linear relationship reveals a non-linear increase in absolute baiting effort per unit of target immunization level. This is the result of bait competitors and foxes consuming multiple baits. For example, applying a 10% higher management target increases baiting effort by 42%. (b) Adopting recent safe-side baiting practice from the field that targets a 75% immunization coverage (right vertical grey line) by applying 20 baits km⁻² (upper horizontal line), we explored the relationship to find out what would result from a reduction in the target level by 10% (left vertical line) and came to 14 baits km⁻² (lower horizontal line). Whiskers represent 5% and 95% percentiles from all repetitions.