- Research article
- Open Access
- Open Peer Review
Emergency vaccination of rabies under limited resources – combating or containing?
BMC Infectious Diseases volume 5, Article number: 10 (2005)
Rabies is the most important viral zoonosis from a global perspective. Worldwide efforts to combat the disease by oral vaccination of reservoirs have managed to eradicate wildlife rabies in large areas of central Europe and North-America. Thus, repeated vaccination has been discontinued recently on a geographical scale. However, as rabies has not yet been eradicated globally, a serious risk of re-introduction remains. What is the best spatial design for an emergency vaccination program – particularly if resources are limited? Either, we treat a circular area around the detected case and run the risk of infected hosts leaving the limited control area, because a sufficient immunisation level has not yet been built up. Or, initially concentrate the SAME resources in order to establish a protective ring which is more distant from the infected local area, and which then holds out against the challenge of the approaching epidemic.
We developed a simulation model to contrast the two strategies for emergency vaccination. The spatial-explicit model is based on fox group home-ranges, which facilitates the simulation of rabies spread to larger areas relevant to management. We used individual-based fox groups to follow up the effects of vaccination in a detailed manner. Thus, regionally – bait distribution orientates itself to standard schemes of oral immunisation programs and locally – baits are assigned to individual foxes.
Surprisingly, putting the controlled area ring-like around the outbreak does not outperform the circular area of the same size centred on the outbreak. Only during the very first baitings, does the ring area result in fewer breakouts. But then as rabies is eliminated within the circle area, the respective ring area fails, due to the non-controlled inner part.
We attempt to take advantage of the initially fewer breakouts beyond the ring when applying a mixed strategy. Therefore, after a certain number of baitings, the area under control was increased for both strategies towards the same larger circular area. The circle-circle strategy still outperforms the ring-circle strategy and analysis of the spatial-temporal disease spread reveals why: improving control efficacy by means of a mixed strategy is impossible in the field, due to the build-up time of population immunity.
For practical emergency management of a new outbreak of rabies, the ring-like application of oral vaccination is not a favourable strategy at all. Even if initial resources are substantially low and there is a serious risk of rabies cases outside the limited control area, our results suggest circular application instead of ring vaccination.
Rabies is life-threatening for humans  and the most important viral zoonosis from a global perspective . In Europe and North-America, wildlife is the main reserve (i.e. foxes or raccoons). Aerial distribution of vaccine filled baits proved to be a method which can be used for controlling rabies in these species, as they are attainable via baits, and an efficient oral rabies virus vaccine is available [3, 4]. Therefore, disease managers have been making huge efforts in rabies control over the last 25 years [2, 5–9]. Long-term and large scale oral vaccination of wildlife eradicated rabies at the regional scale in central Europe and the Americas [10–16]. Consequently, repeated vaccination in these regions has now ended [8, 16, 17] and, eventually, its host populations will be completely susceptible to new rabies infection. Therefore, we must be aware of a reintroduction as long as rabies persists anywhere in the world,  and we have to develop emergency measures designed for a local outbreak in non-immunised wildlife populations. Thus recent contingency planning appears comparable to the situation in the UK at the end of the last century when an introduction from continental Europe was expected [19–23]. A lot of literature is available from that period concerning how a newly introduced rabies epidemic potentially spreads or will be controlled [21, 22, 24, 25]. However, empirical knowledge has been accumulated in the mean time regarding large-scale field application of oral vaccination, recognition of successful strategies or operating population immunity levels, and termination of repeated baiting. It appears worthwhile to exploit these sources, in order to adjust contingency plans for future rabies control in general and the event of rabies re-introduction in particular.
How should disease management react to re-introduction, i.e. detection of an infection within a rabies-freed area? Revitalising country-wide vaccination campaigns appears to be not very well-adapted to detection of a local rabies outbreak . A WHO  recommendation suggests 5,000 sq. km of compact vaccination area as the minimum sustainable strategy, but there are no details regarding the plausible spatial configuration. Field practice demonstrates that modern aerial distribution of vaccine-filled baits performs precisely, even on complex spatial distribution patterns [28, 29].
Thus, alternative control application schemes can be considered as emergency strategies, which 1) are able to restrict the spatial extent of the control area, 2) are able to eradicate the disease and finally, 3) are logistically practicable.
Disease managers usually think of combating an outbreak by immediately controlling all areas at risk . But in an emergency, when the outbreak is very local at first, to what spatial extent must a control area be designed to cover "all areas at risk", or in practice, to what distance might the disease spread until a protective immunisation level has been built up [24, 26, 30]? How can we exclude potential breakouts of infected hosts just before the control measures succeed in the controlled area? The most appealing counter-measure would fence in the epidemic first and eradicate afterwards. The "fence" could be realised by a ring-shaped area of competently vaccinated hosts at an adequate distance from the detected outbreak (see for example ). The host population of such a ring area is already well immunised before first infections will reach the inner border of the ring – hence the outbreak is actually contained. But, the ring approach promises another advantage: Although we BAIT an equally sized area compared to circle application, the larger spatial extent of the ring allows for an increased control area because the outer border of the ring is beyond the circle of respective size. Indeed, the inner part of the ring must not be treated in the beginning which could be important if we have to cope with logistic and/or resource limitations immediately after an outbreak (Vos, pers. comm). While aiming at a serious contingency plan, we still have to analyse the comparability of the two different approaches from the epidemiological discussion: Centred on the detected outbreak, we treat either a circular compact area or the equal-sized area, but arrange it in a ring around an omitted inner part (i.e. equal size of baited area, equal baiting program, equal number of baits and same bait density).
We have identified two strategic alternatives: (i) Combating – refers to vaccination applied in a circle which (a) aims at immediate treatment of the surrounding area of the outbreak to keep the number of rabies cases low, but (b) accepts the risk of early breakout due to an unfinished build up of immunisation level. (ii) Containing – refers to ring vaccinations applied at a distance from the outbreak which (a) aims to prevent a breakout of rabid animals through a readymade immunisation level within the ring, before the epidemic reaches it, but (b) accepts higher numbers of cases in the inner part (Fig. 1).
We use an explicit simulation model of the fox-rabies system to compare the different spatial designs of vaccination. We analyse how long the circle or the ring design can keep the rabies epidemic inside the control area. We compare the two spatial designs for the application of mixed strategies, i.e. the definition of most-rewarding-point-in- time, in order to change from ring to circle, as compared to a pure circle strategy. In case of a rabies outbreak in a previously rabies-free region, the results determine which of the strategies should be applied and how to benefit the most from limited resources.
We evaluated the management strategies with a model of the rabies-fox system which is tailored to emergency control planning. We applied a spatially-explicit, individual-based, time-discrete modelling approach [32–34]. This approach had already proved practical in studying the spread and control of rabies in foxes [26, 35–37] and to provide useful management support . Thus, previous models [26, 35, 36] were enhanced in order to cope with the new question. The rules of rabies dynamics between the fox family groups, as well as individual dispersal of juveniles after maturity, were adopted from the basic model [35, 36]. The spatial unit of a fox group home-range was also maintained because it had proven suitable for studying the disease spread on the regional scale [20, 38, 39]. Group home-ranges are implemented within regular grid cells, and the obtained results would not change if the grid cells were replaced by irregular shaped home-ranges of a given mean-size. This is because the dispersal movements are modelled relative to group home-range size [35, 40, 41] and not in metric measures [36, 42–45]. This approach incorporates an implicit adjustment of the fox density effect . A metric reference to fox densities within central Europe is realised by means of the mean-fox-group home-ranges (i.e. cells) corresponding to 1 sq. km. Compared to previous rabies models which had addressed an introduction of rabies [20, 25, 31, 47, 48], it was necessary to extend the simulation area (i.e. 256 times 256 cells corresponding to ~65.536 sq. km in a central European scenario) in order to allow relevant dimensions of the control area. The representation of the control area by a regular ring or circle within the model is an abstraction. When applied to real landscapes the vaccination areas are non-regular, as they are usually determined by administrative borders, hence certain excess areas must be baited additionally. Thus the geometric simplification in the model represents the required core area, which must at least be covered by the vaccination area defined along administrative units. But, the aim of our study necessitates a further step in scaling down the basic model . The temporal resolution was refined to a weekly time step, since the success of an emergency vaccination depends on the time of introduction of rabies into the fox population, the time until detection of the epidemic, and the timing of the initial vaccination campaign [7, 17, 20]. The model rules were complemented with ecological characteristics of, and disease transmission between, individual foxes of a group. The individual-based representation enables a locally varying immunisation level due to non-homogeneous bait uptake [50, 51] or individual foxes moving across the border of the vaccination area. The effect of these issues might be negligible for vaccination success on a geographical scale,  but it becomes serious for the few rabid animals after an outbreak or a spatially limited vaccination area WITHIN a landscape.
Basic fox population model
Each cell comprises a family group [38, 52] of age-classified individual foxes (juvenile, adult). Fox groups in the field contain on average 2–3 adults (i.e. 1 male and 1–2 females) before reproduction [52–55]. The pattern is realised in the model by assuming a maximum group size of 5 adults [46, 56] together with the mortality and dispersal process. For parameterisation see Table 1.
Reproduction is scheduled in the first week of April. All non-empty cells produce a litter of a normally distributed number of cubs with mean of 5.5 and a standard deviation of 1.5 [44, 57, 58, 62–64]. Fox groups which consist of exactly one individual reproduce with 50% probability. This rule accounts for floaters and multiple mating males as well as for non-reproducing males [53, 65, 66].
With these population dynamics, on average 3.5 juveniles per group emerge in the maturity dispersal (Goretzki, pers. comm.). The dispersal occurs for 8 weeks from October to November [64, 67]. Thus, during that phase per time-step one eighth of all cells are selected randomly. Out of each selected cell, all juveniles move consecutively according to the following dispersal algorithm. The dispersing individual is randomly assigned with a main direction from 8 cells of 360 degrees, which is maintained in each step with 50% probability [60, 67–69]. In the remaining steps the individual deviates to the left or to the right by one cell with equal probability (i.e. 25%; see ). The probability to settle in a cell (PSettle) increases with the distance travelled (PSettleDistance; ), but decreases with the number of adult foxes already in there (CrowdingFactor):
PSettle = PSettleDistance(Step) * CrowdingFactor(NumAdultFoxes)
PSettleDistance(Step) = (15% + (1-0.15) * Step/60)
The dispersal of one individual is limited to 100 steps, i.e. a maximum of 100 fox group home-ranges will be passed [43, 70]. During each step we assume a mortality of 2% (adjusted to 22% dispersed foxes found dead by ). The emerging frequency distribution of dispersal distances is shown in Figure 2.
Each fox has a disease state (susceptible, infected, infectious, or immune). The state is updated according to weekly time-steps. If infection was introduced in a cell by neighbourhood contact one adult fox is randomly selected. If this fox is not susceptible but "immune", nothing happens, otherwise its state changes from "susceptible" to "infected". The "infected" fox gets infectious after a negative exponential distribution with a minimum of 2 weeks and an effective mean of 3.5 weeks [71–74]. During the following infectious period of 1 week, a fox can transmit the disease [41, 75]. It is assumed that infected cubs will die of rabies, but can only transmit the infection if their incubation period ends after the dispersal .
If there is at least one infected fox in a cell, then the 8 neighbouring cells have a probability of 14% of getting infected [36, 76], i.e. approach of Infection Communities  or 'group infection rate' in .
Mating Contacts (additionally in January and February)
Distribution of baits
Standard vaccination protocol on the regional scale comprises biannual campaigns with 18–20 baits distributed per sq km [7, 10, 11, 13, 17, 79]. Accordingly, two vaccination events are performed in the model: one in the first week of April and one in the second week of September.
Grid cells represent the spatial equivalent of home-ranges of fox families,  which do not have equal area size  and hence will not receive an equal number of baits [81, 82]. We approximate this non-equal assignment of bait pieces to spatial fox group home-ranges by simulating the distribution of effective bait numbers on the ground found for standard aerial delivery (Fig. 3) . The baits randomly drawn to fall into a fox group home-range are assumed to be lost with 80% probability according to empirical findings, i.e. baits lost to competitors [51, 83–88], baits unfound or only partly consumed [17, 88–90]. The baits remaining in a particular cell are distributed randomly to the respective individuals, independent of their state. The "susceptible" foxes permanently turn towards "immune" two weeks after receiving at least one piece of bait [73, 90, 91]. With these rules an immunisation level of 70–80% emerges after 2 campaigns (Fig. 4) as empirically documented by vaccination campaigns in the field with 18–20 baits per sq. km [16, 88, 92, 93].
The mid cell of the grid receives an external infection during a randomly chosen week of the year. Subsequently, any rabies case will be detected with a probability of 2% [16, 24, 93, 94]. Rabid juvenile foxes will be detected only from August onwards .
First vaccination campaign
If one infected fox is detected, we assume a preparation time of 2 months until the first vaccination campaign is scheduled (Vos, pers. comm.). Further campaigns are performed according to the standard protocol: autumn and spring [7, 17, 79] – with the only exception being that the second campaign will not be performed less than two months after the initial baiting.
Spatial design – ring vs. circle
The relative assessment of the competing spatial designs is based on regular edges. Using the Moore neighbourhood, adjacent and diagonal cells are assumed to have equally scaled distances. The modelled emergency area is always centred on the first detected rabies case ignoring other "infected" cells on the grid.
The parameter vaccination area (PVacArea) corresponds to the maximum amount of cells that could be treated immediately after detection. PVacArea is set to be 6,400, 10,800 or 16,000 cells. The values are selected to provide useful width of the ring area (i.e. 20 km, 30 km or 40 km wide ring areas respectively). The area could be calculated into a necessary amount of baits after scaling the mean area of fox group home-ranges. For instance, in rural Europe fox group density of ~1 per sq. km is agreed [20, 51] which fixes the mean area of the cells in the model at 1 sq. km Thus, the amount of baits per campaign used in the three scenarios is roughly: 128,000, 216,000 or 320,000 respectively when applying 20 baits per sq. km.
The vaccinated area is compact around the detected outbreak and implemented in the model as a solid square. According to PVacArea, the region is 80*80, 104*104 or 126*126 cells respectively.
60*60 cells remain without baits. This inner part should compensate for an annual spread of rabies of 30 km [27, 41]. Around the interior, a ring of cells is assumed to be treated with baits. The treated area is determined by PVacArea and corresponds to a width of 20, 30 or 40 cells respectively . The surrounded area (i.e. not baited + baited) thus covers: 10,000, 14,400 and 19,600 cells respectively. Figure 5(a) and 5(b) show screen shots of the simulations with these strategies treating an area of equal size.
Simulation experiments are performed on a grid of 256 × 256 which totals 65,536 cells. We ran each simulation scenario 10,000 times to cover stochastic effects.
Experiment 1 – Containment of the epidemic with fixed resources
We assess which strategy performs better at confining the epidemic inside the control area over the short and long term. The frequency of infected foxes outside the control area provides the quantitative measure. The 3 sizes of vaccinated areas (PVacArea) remain constant throughout a simulation run.
Experiment 2 – Search for the optimal switch point from ring to circle strategy with increasing resources
The aim is to identify the strategy or a mixture of strategies which performs best in final eradication of the epidemic. The inner part of the ring has to be baited in the end to achieve eradication. Thus resource limitation is assumed to be eased at some point in time, and the baited area (PVacArea) is doubled afterwards. The resource extension is assumed with a lag of either 1 or up to 5 vaccination campaigns. Again, initial vaccination areas (PVacArea) will have 3 different sizes but they are doubled after the time lag. Technically, the following spatial configuration is applied in this experiment: Either we already start baiting the circle whose surface gets doubled after the time lag. Or, we start baiting the ring of the same size and after the time lag we continue baiting the circle of doubled surface, which of course contains the ring. Hence, the final treated area is always a solid square of 112*112, 146*146 or 178*178 cells respectively. Figure 5(c) shows an example of the configuration.
We followed the pattern-orientated approach [49, 95–98] for validation of the experimental results and qualitative debugging of the model logic [99, 100]. Hence, we compared population parameters as re-read from the model to empirical data. The model successfully reproduces the fox ecology (e.g. fox densities during the year from around 1.5 to 3 foxes per sq. km [44, 68, 77, 101], the dispersal distances (Fig. 2), the spread of rabies (Fig. 5b) [102, 103], the development of immunisation level (Fig. 4a) [16, 87, 91–93, 104] and the time period up to local eradication of an epidemic (Fig. 6c) [16, 91, 105]).
When parameters of the model were altered, only the quantitative results changed, but neither the qualitative results nor the conclusions did. But there is one noteworthy difference between large-scale and local vaccination concerning immunisation level. In emergency control the relatively small baited areas are surrounded by a susceptible neighbourhood and thus non-immunized foxes will regularly disperse into the baited region and vice versa. Indeed, the immunisation level maintained by the circle or ring strategy was measured lower than for the large-scale application (Fig. 4a), in particular at the edges of the control areas (Fig. 4b). Nevertheless, the resulting immunisation in the model was still sufficient to eradicate rabies locally, which is in agreement with recent findings about potential over-baiting during the past control programs in Europe [15, 50, 82, 106, 107].
Experiment 1: Containing with fixed resources
In all scenarios we found noteworthy frequency of rabies infections spreading beyond the vaccinated area (Fig. 6a). For the medium amount of resources, about 1% of all simulation runs ended up with breakouts after 2 years. Independent of the amount of applied resources in the long run, the ring strategy performs worse than the circle strategy. In the ring strategy the number of rabies cases rises quickly (Fig. 6b) and the epidemic is not eradicated. On the other hand, by distributing the same resources in the circle strategy, the epidemic often gets eradicated (Fig. 6c). Only for the first two vaccination campaigns the ring strategy performs better in containing rabies.
We detail the spatio-temporal dynamics of the simulated epidemic (Fig. 7 &8) to understand why the sole ring strategy performs badly. The strategy is characterised by an increasing risk of breakouts over time. Early breakouts are seldom due to the distant outer border of the control area (Fig. 7b &8b; black line). But only the ring itself is treated with baits and the epidemic can spread out within the non-vaccinated inner part (Fig. 7b). The growing number of infections close to the baited area challenges the ring (Fig. 7b; olive line) and, eventually, infections beyond the outer border of the ring rise with time (Fig. 8b; compare black and olive line). By contrast, the risk of breakouts associated with the circle strategy decreases with time. Soon after the outbreak, infections occur outside the circular control area, which would still be inside the control area under the respective ring strategy (comp. Fig. 8a &8b). However, the probability of eradication increases with time i.e. the number of vaccination campaigns (Fig. 6c), and thus the risk of still having an epidemic which could breakout diminishes (Fig. 8a; compare black and olive line).
Figure 9 illustrates, qualitatively, the risk of breakouts over time. From this risk analysis we expect a crossover point before which the ring strategy has a lower risk and after which the circle strategy has the lower risk of breakouts. To check the prediction, we re-analyse data of Figure 8. We directly equate the risk of breakouts to the number of infections beyond the control area that are actually caused by foxes leaving the control area, and secondary infections are ignored (Fig. 10). Indeed, initially fewer infections are found beyond the outer border of the control area of the ring and later beyond that of the circle. Therefore, we attempt to profit from the initial advantage of ring vaccination by mixing strategies, i.e. starting control with ring vaccination (left down in Fig. 9) and later switching to the circle strategy (right down branch in Fig. 9).
Experiment 2: Eradication with increasing resources
According to Figure 10 we expect at least one mixed strategy (switching from ring to circle after k baitings) to perform better than the continuous circle approach. Following this idea, we conducted experiment 2: The initial strategy is changed after k vaccination campaigns towards a circle application. In practice, the change could commence when resource limitations are overridden. Thus resources are doubled after the switch and the final circular control areas are IDENTICAL for all mixed strategies, i.e. ring-circle and circle-circle.
Surprisingly, the strategy which immediately starts with a circle is still favourable (Fig. 11a). Indeed, the mixed strategy results in more breakouts and less eradication. Eradication also takes longer when using the mixed strategy as compared to the circle strategy (Fig. 11b), because the time lag before vaccination starts in the inner part of the ring is simply added to the time until eradication.
Expert knowledge and biological data about the host, the epidemiology of the infection or even the efficacy of management measures are quite often vague in the sense that they are never measured, they are examined with highly differing results or they are even difficult to sample precisely [52, 108]. Nevertheless, it is necessary to overcome these uncertainties because management decisions have to be made . Usually, modelling studies tend to select one particular configuration and substantiate the parameter choice with the help of logical arguments. We suggest an approach that is oriented to robust conclusions for practical management in terms of different or even antagonistic model assumptions. There are initial studies in the literature [109, 110] which opt for the development of a more general methodology. The approach parallels standard techniques of model validation or sensitivity analysis. But we are no longer troubleshooting at the level of particular values which the model acquires in relation to slight changes in assumed parameters. We are only interested in changes at the level of conclusions made for management application, i.e. whether there are hypothetical scenarios which could falsify the management decision just derived from the model results. That is how practical management often performs . Thus, while targeting useful support for these decisions, we have already covered the need for 'robustness' during the shaping of our management proposal.
We compared two spatial strategies of local emergency vaccination for controlling a rabies outbreak. One refers to the immediate control of infection within a smaller treated area. The alternative was theorised to overcome the drawback of a spatially limited strategy by providing equal resources in a ring around the affected area which contains the infection at the cost of more cases in the centre.
Simulation of the two spatial strategies revealed the true dynamics of the models. The ring strategy in general does not outperform the circle strategy. The predicted advantage of the ring strategy can only be found in the short term (Fig. 6a). Therefore, we determined mixed strategies and searched for the most rewarding point in time for switching between the ring strategy, which was better in the short term, and the circle strategy, which was better in the long term (Fig. 10).
Why aren't we able to identify the switch point as suggested by the risk analysis? Figure 10 actually proposes a switch around the third campaign. However, no matter which point we chose for switching from ring to circle in experiment 2, we did not find a clear advantage at all for the mixed strategy. There is only one plausible reason for this disagreement between the mind and the simulation model. The switch between the two strategies comprises a time lag until the protection level is reached inside the ring, i.e. until the inner part of the former ring actually acts like a circle. Our qualitative risk assessment (Fig. 9) assumes a perfect change between strategies. In practice however, we have to consider the temporal delay of building up population immunity which was shown to be at least 2 vaccination campaigns [16, 87, 91–93, 104] in noteworthy agreement with our simulations (Fig. 4a). Thus the change in strategy has to take place two baitings in advance of the theoretical suggestion in order to profit with the mixed strategy. But the ideal switch point found in the simulation is around the 3rd baiting campaign (Fig. 10). After subtracting the building up time of 2 vaccination campaigns in practice we need to change at baiting 1, i.e. we must apply the circle strategy from the very beginning.
Consequently, in the field we cannot benefit from the alternative baiting scheme and hence are forced to focus contingency planning on a compact control area around the detected outbreak. After testing the respective models, we can reject a-priori any pure vaccination field trial that attempts to distribute vaccine baits with a ring-like strategy.
Our findings are not contradicted by the successful application of cordon-sanitaire vaccination at borders of large-scale vaccination areas in the field [17, 27, 111–115]. In fact, the basic difference between a ring-like vaccination around a new outbreak and the cordon-sanitaire is the aim of control: In the outbreak situation we do not need to accept the rabies inside the ring, but in the second, the border situation, we have to. Rabies persists "on the other side" of the cordon, i.e. if neighbouring countries have not (successfully) combated the disease. Although the ring-like emergency vaccination does provide some protection for the surrounding area in the same manner in which the cordon-sanitaire vaccination does, in the emergency situation we aim for ultimate eradication, and in order to achieve this, our results clearly require the treatment of a compact circle-like control area.
The only threat for success of control is the migration of infected foxes from the limited area under treatment into the non-vaccinated surroundings. We cannot limit the distance infected foxes disperse, but we can reduce the number of them by means of the control itself. It is the circle strategy in which the number of rabies infections is lowered right from the beginning.
We present only 3 widths of the ring (Table 2). This is because ring width below 20 km cannot be expected to be protective . Even though we analysed ring dimensions of 50 km and more in accordance with EU recommendations , there is no need to present these results. The difference between ring and circle strategy is less pronounced compared to that of the 40 km ring (Fig. 11a). Indeed, wider rings do provide decreasing gain in the outer radius due to the non-linear relationship between radius and area (Table 2, line 4). When the inner non-vaccinated part is reduced, there is no useful gain left, thus circle and ring become equivalent (Table 2, line 5). On the other hand, an extended inner part reduces the protective ability of the ring and simultaneously triples the non-vaccinated area (Table 2, line 6).
If the ring design strategically loses, i.e. in eradicating rabies, are there other benefits which outweigh the disadvantage? There are two other potential benefits to consider: economy and public health. With modern aerial bait disposal controlled by the GPS, logistic costs do not differ substantially between the two spatial designs (Mürke, pers. comm.). The cost is mainly linked to the total number of baits needed for the program. However, we demonstrated that in the ring design the time lag until the spared inner part is vaccinated directly adds to the time until eradication (Fig. 11b). This increases the cost of the ring design as compared to the earlier eradication in the circle design.
The remaining public health issue is the principal objective [7, 71, 116]. Eradication of the disease is the only method for achieving this objective . However, within the inner part of the ring the epidemic roams freely and thus imposes a risk to humans and livestock which makes it less competitive than the compact circle approach. Additionally, eradication takes longer and thus the threat to public health is prolonged. Consequently, we can rule out the ring as a non-viable approach in terms of eradication, economy and public health.
In all respects we concluded that the circle performs better. But we still have to deal with possible early breakouts. Whilst zero risk strategies perhaps represent political demand, they are probably neither possible nor the most cost-effective approach. However, additional measures could be applied for an improvement of the performance of the circle strategy and will be considered in the ongoing analysis: Firstly, better monitoring programs could lower the time until detection of an outbreak, which consequently leads to an earlier eradication. Secondly, it is not clear whether immediate vaccination with a risk of imperfect placement performs better than waiting with the first vaccination until a monitoring program has provided a better understanding of the spatial extent of the outbreak. Thirdly, circles baited with spatially varying density of baits could provide both, the required fast suppression of the epidemic and the largest possible control area (see  for a combined simulation of poisoning and ring vaccination). And finally, follow-up programs can be designed. Indeed, the circle strategy with a control area of 10.800 sq. km has already provided a very low likelihood of breakouts. Thus, the strategic approach could extend the initial circular area to a non-circular control area (but still vaccinated on a regular basis), according to detected breakouts. Raised awareness after the reintroduction of rabies and particular border surveillance around the baited area, would guarantee fast detection of breakouts. Thus, we recognise the need for a more detailed cost-benefit, which explores the cost of extensions of the control area, versus the benefit of reducing the amount of resources applied to the initial hazard area.
If vaccination is the only approved measure for fighting a rabies outbreak within a completely susceptible fox population, then the only feasible contingency plan is to vaccinate a compact area centred on the epidemic. The ring strategy which leaves an inner part non-vaccinated must be ruled out in all concerns: strategically, since it under-performs in eradication levels, economically, since eradication takes longer and public health, since it allows more cases of rabies.
Yet even in the circle strategy, there remains some risk of early breakouts of rabies from the control area. Thus, further studies should concentrate on optimizing the emergency strategy concerning timing and benefits of additional monitoring programs. Furthermore, a detailed cost-benefit analysis of potential strategic alternatives is needed in order to improve the outcome of a contingency plan.
Rupprecht CE, Smith JS, Fekadu M, Childs JE: The ascension of wildlife rabies: a cause for public health concern or intervention?. Emerg Infect Dis. 1995, 1: 107-114.
Hanlon CA, Childs JE, Nettles VF: Recommendations of a national working group on prevention and control of rabies in the United States. III: Rabies in wildlife. J Am Vet Med Assoc. 1999, 215: 1612-1619.
Johnston DH, Voigt DR, MacInnes CD, Bachmann P, Lawson KF, Rupprecht CE: An aerial baiting system for the distribution of attenuated or recombinant rabies vaccines for foxes, racoons and skunks. Rev Infect Dis. 1988, 10 (Suppl 4): 660-664.
Johnston DH, Bachmann P, Lawson KF, MacInnes CD, Voigt DR, Pond BA, Nunan CP, Ayers NR: Design considerations for aerial bait distribution of rabies vaccines. Wildlife Rabies Control. Edited by: Bögel K, Meslin FX and Kaplan M. 1992, Kent, Wells Medical Ltd., 160-167.
Meslin FX: Zoonoses in the world - Current and future trends. Schweiz Med Wochenschr. 1995, 125: 875-878.
Stöhr K, Karge E, Gädt H, Kokles R, Ehrentraut W, Witt W, Fink HG: Orale Immunisierung freilebender Füchse gegen Tollwut - Vorbereitung und Durchführung der ersten Feldversuche in den ostdeutschen Bundesländern. Mh Vet Med. 1990, 45: 782-786.
Stöhr K, Meslin FX: Progress and setbacks in the oral immunisation of foxes against rabies in Europe. Vet Rec. 1996, 139: 32-35.
Müller WW: Review of reported rabies cases data in Europe to the WHO Collaborating Centre in Tübingen from 1997 to 2000. Rabies Bulletin Europe. 2000, 24: 11-19.
Zanoni RG, Kappeler A, Müller UM, Müller C, Wandeler A, Breitenmoser U: Tollwutfreiheit der Schweiz nach 30 Jahren Fuchstollwut / Rabies free status of Switzerland after 30 years of fox rabies. Schweiz Arch Tierheilkd. 2000, 142: 423-429.
Breitenmoser U, Müller U, Kappeler A, Zanoni RG: The final stage of rabies in Switzerland [German]. Schweiz Arch Tierheilkd. 2000, 142: 447-454.
Brochier B, Deschamps P, Costy F, Hallet L, Leuris J, Villers M, Péharpré D, Mosselmans F, Beier R, Lecomte L, Mullier P, Roland H, Bauduin B, Kervyn T, Renders C, Escutenaire S, Pastoret PP: Elimination de la rage en Belgique par la vaccination du renard roux (Vulpes vulpes). Ann Med Vet. 2001, 145: 293-305.
Müller WW: Where do we stand with oral vaccination of foxes against rabies in Europe. Arch Virol Suppl. 1997, 13: 83-94.
Bruyere V, Janot C: La France bientôt déclarée officiellement indemne de rage. Bulletin épidémiologique mensuel de la rage animale en France. 2000, 30: 1-2.
Müller T, Schlüter H: Oral immunization of red foxes (Vulpes vulpes L.) in Europe – a review. J Etlik Vet Microbiol. 1998, 9: 35-39.
Vos A: Oral vaccination against rabies and the behavioural ecology of the red fox (Vulpes vulpes). J Vet Med B. 2003, 50: 477-483. 10.1046/j.1439-0450.2003.00712.x.
MacInnes CD, Smith SM, Tinline RR, Ayers NR, Bachmann P, Ball DGA, Calder LA, Crosgrey SJ, Fielding C, Hauschildt P, Honig JM, Johnston DH, Lawson KF, Nunan CP, Pedde MA, Pond B, Stewart RB, Voigt DR: Elimination of rabies from red foxes in eastern Ontario. J Wildlife Dis. 2001, 37: 119-132.
European Commission: Report of the Scientific Committee on Animal Health and Animal Welfare: The oral vaccination of foxes against rabies [http://www.europa.eu.int/comm/food/fs/sc/scah/out80_en.pdf]. 2002, Brussels
MacKenzie D: Will rabies bite back?. New Sci. 1997, 24-25.
Harris S, Smith GC: If rabies comes to Britain. New Sci. 1990, 128: 20-21.
Smith GC, Harris S: Rabies in urban foxes (Vulpes vulpes) in Britain: the use of a spatial stochastic simulation model to examine the pattern of spread and evaluate the efficacy of different control regimes. Philos Trans R Soc Lond Biol Sci. 1991, 334: 459-479.
White PCL, Harris S, Smith GC: Fox contact behaviour and rabies spread: a model for the estimation of contact probabilities between urban foxes at different population densities and its implications for rabies control in Britain. J Appl Ecol. 1995, 32: 693-706.
Evans ND, Pritchard AJ: A control theoretic approach to containing the spread of rabies. IMA J Math Appl Med Biol. 2001, 18: 1-23.
MAFF: Report of the committee of inquiry into rabies. Final report. 1971, London, HMSO, Ministry of agriculture fisheries and food
Bacon PJ: The consequences of unreported fox rabies. J Environ Manage. 1981, 13: 195-200.
Smith GC: Modelling rabies control in the UK: the inclusion of vaccination. Mammalia. 1995, 59: 629-637.
Thulke HH, Tischendorf L, Staubach C, Selhorst T, Jeltsch F, Schlüter H, Wissel C: The spatio-temporal dynamics of a post vaccination resurgence of rabies in foxes and emergency control planning. Prev Vet Med. 2000, 47: 1-21. 10.1016/S0167-5877(00)00167-7.
WHO: Report of WHO Seminar on wildlife rabies control, Geneva 2-5 July 1990. 1992, Geneva, WHO
Vos A, Mührke HH, Holzhofer E, Gschwender P, Schuster P: A satellite navigated and computer supported fully automatic system for distributing oral vaccine-baits against rabies: SURVIS: 2001. 2001, Peterborough, Canada, Proceedings of the XIIth International Meeting on Advances in Rabies Research and Control in the Americas, Nov. 12-16, 28-
Müller T, Stöhr K, Teuffert J, Stöhr P: Erfahrungen mit der Flugzeugbeköderung von Ködern zur oralen Immunisierung der Füchse gegen Tollwut in Ostdeutschland. Dtsch Tierärztl Wochenschr. 1993, 100: 203-207.
van den Bosch F, Metz JAJ, Diekman O: The velocity of spatial population expansion. J Math Biol. 1990, 28: 529-565. 10.1007/BF00164162.
Smith GC, Wilkinson D: Modeling control of rabies outbreaks in red fox populations to evaluate culling, vaccination, and vaccination combined with fertility control. J Wildl Dis. 2003, 39: 278-286.
Mollison D, Kuulasmaa K: Spatial Epidemic Models: Theory and Simulations. Population Dynamics of Rabies in Wildlife. Edited by: Bacon PJ. 1985, London, Academic Press, 291-309.
Durrett R: Spatial Epidemic Models. Epidemic Models - Their Structure and Relation to Data. Edited by: Mollison D. 1995, Cambridge, Cambridge University Press, 187-201.
DeAngelis DL, Gross LJ: Individual-based models and approaches in ecology: populations, communities and ecosystems. 1992, London, Chapman Hall
Jeltsch F, Müller MS, Grimm V, Wissel C, Brandl R: Pattern formation triggered by rare events: lessons from the spread of rabies. Proc R Soc Lond B. 1997, 264: 495-503. 10.1098/rspb.1997.0071.
Tischendorf L, Thulke HH, Staubach C, Müller MS, Jeltsch F, Goretzki J, Selhorst T, Müller T, Schlüter H, Wissel C: Chance and risk of controlling rabies in large-scale and long-term immunized fox populations. Proc R Soc Lond B. 1998, 265: 839-846. 10.1098/rspb.1998.0368.
Suppo C, Naulin JM, Langlais M, Artois M: A modelling approach to vaccination and contraception programmes for rabies control in fox populations. Proc R Soc Lond B. 2000, 267: 1575-1582. 10.1098/rspb.2000.1180.
Macdonald DW: The ecology of carnivore social behaviour. Nature. 1983, 301: 379-384. 10.1038/301379a0.
Thulke HH, Tischendorf L, Staubach C, Müller MS, Schlüter H: Neue Antworten zur Frage der weiteren Tollwutbekämpfung in Deutschland. Dtsch Tierärztl Wochenschr. 1997, 104: 492-495.
Trewhella WJ, Harris S, McAllister FE: Dispersal distance, home range size and population density in the red fox (Vulpes vulpes): a quantitative analysis. J Appl Ecol. 1988, 25: 423-434.
Macdonald DW, Bacon PJ: Fox society, contact rate and rabies epizootiology. Comp Immunol Microbiol Inf Dis. 1982, 5: 247-256. 10.1016/0147-9571(82)90045-5.
Garnerin P, Hazout S, Valleron AJ: Estimation of two epidemiological parameters of fox rabies: the length of incubation period and the dispersion distance of cubs. Ecol Modell. 1986, 33: 123-135. 10.1016/0304-3800(86)90036-0.
Jensen B: Movements of red fox (Vulpes vulpes L.) in Denmark investigated by marking and recovery. Danish Review of Game Biology. 1973, 8: 3-20.
Goretzki J, Ahrens M, Stubbe C, Tottewitz F, Sparing H, Gleich E: Zur Ökologie des Rotfuchses (Vulpes vulpes L.,1758) auf der Insel Rügen: Ergebnisse des Jungfuchsfanges und der Jungfuchsmarkierung. Beitr Jagd- u Wildforsch. 1997, 22: 187-199.
Englund J: Yearly variations of recovery and dispersal rates of fox cubs tagged in swedish coniferous forest. Biogeographica Vol.18 - The Red Fox. Edited by: Zimen E. 1980, The Hague, Dr.W.Junk B.V. Publishers, 195-205.
Goszczynski J: Home ranges in red fox: territoriality diminishes with increasing area. Acta Theriol. 2002, 47: 103-114.
David JM, Andral L, Artois M: Computer simulation model of the epi-enzootic disease of vulpine rabies. Ecol Modell. 1982, 15: 107-125. 10.1016/0304-3800(82)90056-4.
Ball FG: Spatial models for the spread and control of rabies incorporating group size. Population Dynamics of Rabies in Wildlife. Edited by: Bacon PJ. 1985, London, Academic Press, 197-222.
Thulke HH, Grimm V, Müller MS, Staubach C, Tischendorf L, Wissel C, Jeltsch F: From pattern to practice: a scaling-down strategy for spatially explicit modelling illustrated by the spread and control of rabies. Ecol Modell. 1999, 117: 179-202. 10.1016/S0304-3800(98)00198-7.
Johnston DH: Improving efficiency and reducing costs in oral rabies vaccination programs: 2001. 2001, Peterborough, Canada, Proceedings of the XIIth International Meeting on Advances in Rabies Research and Control in the Americas, Nov. 12-16, 28-28.
Trewhella WJ, Harris S, Smith GC, Nadian AK: A field trial evaluating bait uptake by an urban fox (Vulpes vulpes) population. J Appl Ecol. 1991, 28: 454-466.
Cavallini P: Variation in the social system of the red fox. Ethol Ecol Evol. 1996, 8: 323-342.
Niewold FJJ: Aspects of the social structure of red fox populations: a summary. Biogeographica Vol.18 - The Red Fox. Edited by: Zimen E. 1980, The Hague, Dr.W.Junk B.V. Publishers, 185-193.
Macdonald DW: Social factors affecting reproduction amongst red foxes (Vulpes vulpes L., 1758). Biogeographica Vol.18 - The Red Fox. Edited by: Zimen E. 1980, The Hague, Dr.W.Junk B.V. Publishers, 123-175.
Baker PJ, Robertson CPJ, Funk SM, Harris S: Potential fitness benefits of group living in the red fox, Vulpes vulpes. Anim Behav. 1998, 56: 1411-1424. 10.1006/anbe.1998.0950.
Von Schantz T: Female cooperation, male competition, and dispersal in red fox, Vulpes vulpes. OIKOS. 1981, 37: 63-68.
Ansorge H: Daten zur Fortpflanzungsbiologie und zur Reproduktionsstrategie des Rotfuchses, Vulpes vulpes, in der Oberlausitz. Säugetierkd Inf. 1990, 3: 185-199.
Stiebling U: Untersuchungen zur Habitatnutzung des Rotfuches, (Vulpes vulpes L., 1758), in der Agrarlandschaft als Grundlage für die Entwicklung von Strategien des Natur- und Artenschutzes sowie der Tierseuchenbekämpfung. 2000, PhD thesis. HU Berlin
Tackmann K, Löschner U, Mix H, Staubach C, Thulke HH, Ziller M, Conraths FJ: A field trial to control Echinococcus multilocularis-infections of the red fox (Vulpes vulpes) in an endemic focus in Brandenburg, Germany. Epidemiol Infect. 2001, 127: 577-587.
Harris S, Trewhella WJ: An analysis of some of the factors affecting dispersal in an urban fox (Vulpes vulpes) population. J Appl Ecol. 1988, 25: 409-422.
Allen SH, Sargeant AB: Dispersal patterns of red foxes relative to population density. J Wildl Manage. 1993, 57: 526-533.
Stubbe M, Stubbe W: Zur Populationsbiologie des Rotfuchses Vulpes vulpes (L.). Hercynia N F , Leipzig. 1977, 14: 160-177.
Vos AC: Aspekte der Dynamik einer Fuchspopulation nach dem Verschwinden der Tollwut. 1993, PhD thesis. Ludwig-Maximillians-Universität München, Forstwirtschaftliche Fakultät
Lloyd HG: The red fox. 1980, London, B.T.Batsford Ltd.
Macdonald DW, Bunce RGH: Fox populations, habitat characterization and rabies control. J Biogeogr. 1981, 8: 145-151.
Zimen E: Long range movements of the red fox, Vulpes vulpes. Acta Zool Fennica. 1984, 171: 267-270.
Storm GL, Montgomery GG: Dispersal and Social Contact among Red Foxes: Results from Telemetry and Computer Simulation. The Wild Canids. Edited by: Fox MW. 1975, New York, Van Nostrand Reinhold Co., 237-246.
Storm GL, Andrews RD, Phillips RL, Bishop RA, Siniff DB, Tester JR: Morphology, reproduction, dispersal, and mortality of midwestern red fox populations. Wildl Monogr. 1976, 49: 1-82.
Woollard T, Harris S: A behavioural comparison of dispersing and non-dispersing foxes (Vulpes vulpes) and an evaluation of some dispersal hypotheses. J Anim Ecol. 1990, 59: 709-722.
Steck F, Wandeler A: The epidemiology of fox rabies in Europe. Epidemiol Rev. 1980, 2: 71-96.
Aubert MFA: Epidemiology of fox rabies. Wildlife rabies control. Edited by: Bögel K, Meslin FX and Kaplan M. 1992, Kent, Wells Medical Ltd., 9-18.
Bacon PJ: A Systems Analysis of Wildlife Rabies Epizootics. Population Dynamics of Rabies in Wildlife. Edited by: Bacon PJ. 1985, London, Academic Press, 109-130.
Barrat J, Aubert MF: Current status of fox rabies in Europe. Onderstepoort J Vet Res. 1993, 60: 357-363.
Reichert HU: Simulationsstudien zur Ausbreitung und Bekämpfung der Tollwut bei Füchsen mit einem stochastischen, räumlichen Modell. 1989, PhD thesis. University Frankfurt a. Main
Charlton KM: The pathogenesis of rabies. Rabies. Edited by: Campball JB. 1988, Bosten, Cluever Acad. Publ., 101-150.
Müller MS: Ein gitterbasiertes Modell zur Tollwutausbreitung bei Füchsen (Vulpes vulpes). 1995, Diploma thesis. University Marburg/Lahn
Toma B, Andral L: Epidemiology of fox rabies. Adv Virus Res. 1977, 21: 1-36.
Kappeler A: Untersuchungen zur Altersbestimmung und zur Altersstruktur verschiedener Stichproben aus Rotfuchspopulationen (Vulpes vulpes) in der Schweiz. 1985, Universität Bern
Wachendörfer G, Frost JW, Gutmann B, Hofmann J, Schneider LG, Eskens U, Dingeldein W: Experiences with oral immunization of foxes against rabies in Hesse [German]. Tierärztl Praxis. 1986, 14: 185-196.
Dekker JJA, Stein A, Heitkonig IMA: A spatial analysis of a population of red fox (Vulpes vulpes) in the Dutch coastal dune area. J Zool. 2001, 255: 505-510.
Breitenmoser U, Müller U: How to do the wrong thing with the highest possible precision - a reflection on the use of GPS in rabies vaccination campaigns. Rabies Bulletin Europe. 1997, 21: 11-13.
Thulke HH, Selhorst T, Müller T, Wyszomirski T, Müller U, Breitenmoser U: Assessing anti-rabies baiting - what happens on the ground?. BMC Infect Dis. 2004, 4: 9-10.1186/1471-2334-4-9.
Linhart SB: Some factors affecting the oral rabies vaccination of free-ranging carnivores. Rev Sci Tech. 1993, 12: 109-113.
Selhorst T, Thulke HH, Müller T: Cost-efficient vaccination of foxes (Vulpes vulpes) against rabies and the need for a new baiting strategy. Prev Vet Med. 2001, 51: 95-109. 10.1016/S0167-5877(01)00209-4.
Bachmann P, Bramwell RN, Fraser SJ, Gilmore DA, Johnston DH, Lawson KF, MacInnes CD, Matejka FO, Miles HE, Pedde MA: Wild carnivore acceptance of baits for delivery of liquid rabies vaccine. J Wildl Dis. 1990, 26: 486-501.
Marks CA, Bloomfield TE: Bait uptake by foxes (Vulpes vulpes) in urban Melbourne: the potential of oral vaccination for rabies control. Wildl Res. 1999, 26: 777-787.
Brochier B, Thomas I, Iokem A, Ginter A, Kalpers J, Paquot A, Costy F, Pastoret PP: A field trial in Belgium to control fox rabies by oral immunisation. Vet Rec. 1988, 123: 618-621.
Vos A, Müller T, Schuster P, Schlüter H, Neubert A: Oral vaccination of foxes against rabies with SAD B19 in Europe, 1983-1998: a review. Veterinary Bulletin. 2000, 70: 1-6.
Kappeler A: Die orale Immunisierung von Füchsen gegen Tollwut in der Schweiz. 1991, PhD thesis. Universität Bern
Müller WW: Review of rabies in Europe. Med Pregl. 1998, 1 (S1 Suppl): 9-74.
Masson E, Aubert MFA, Barrat J, Vuillaume P: Comparison of the efficacy of the antirabies vaccines used for foxes in France. Veterinary Research. 1996, 27: 255-266.
Stöhr K, Stöhr P, Müller T: Orale Fuchsimpfung gegen Tollwut - Ergebnisse und Erfahrungen aus den ostdeutschen Bundesländern. Tierärztl Umschau. 1994, 49: 203-211.
Schlüter H, Müller T: Tollwutbekämpfung in Deutschland. Ergebnisse und Schlubfolgerungen aus über 10-jähriger Bekämpfung. Tierärztl Umschau. 1995, 50: 748-758.
Braunschweig AV: Ein Modell für die Fuchspopulation in der Bundesrepublik Deutschland. Biogeographica Vol.18 - The Red Fox. Edited by: Zimen E. 1980, The Hague, Dr.W.Junk B.V. Publishers, 97-106.
Grimm V: Mathematical models and understanding in ecology. Ecol Modell. 1994, 75/76: 641-651. 10.1016/0304-3800(94)90056-6.
Grimm V, Frank K, Jeltsch F, Brandl R, Uchmánski J, Wissel C: Pattern-oriented modelling in population ecology. Sci Total Environ. 1996, 183: 151-166. 10.1016/0048-9697(95)04966-5.
Wiegand T, Jeltsch F, Hanski I, Grimm V: Using pattern-oriented modeling for revealing hidden information: a key for reconciling ecological theory and application. OIKOS. 2003, 100: 209-222. 10.1034/j.1600-0706.2003.12027.x.
Railsback SF: Concepts from complex adaptive systems as a framework for individual-based modelling. Ecol Modell. 2001, 139: 47-62. 10.1016/S0304-3800(01)00228-9.
Grimm V: Visual debugging: a way of analyzing, understanding, and communicating bottom-up simulation models in ecology. Nat Resourc Model. 2002, 15: 23-38. 10.1216/nrm/1030539095.
Hansen F, Tackmann K, Jeltsch F, Wissel C, Thulke HH: Controlling Echinococcus multilocularis - ecological implications of field trials. Prev Vet Med. 2003, 60: 91-105. 10.1016/S0167-5877(03)00084-9.
Wandeler A, Wachendörfer G, Förster U, Krekel H, Schale W, Müller J, Steck F: Rabies in wild carnivores in central Europe: I. Epidemiological studies. Zentralblatt für Veterinärmedizin B. 1974, 21: 735-756.
Hengeveld R: The stochastic structure of the wave front of rabies in central Europe. Dynamics of biological invasions. Edited by: Hengeveld R. 1989, London, Chapman & Hall, 116-125.
Sayers BMA, Ross JA, Saengcharoenrat P, Mansourian BG: Pattern analysis of the case occurrences of fox rabies in Europe. Population dynamics of rabies in wildlife. Edited by: Bacon PJ. 1985, London, Academic Press, 235-254.
Brochier B, Costy F, Pastoret PP: Elimination of fox rabies from belgium using a recombinant vaccinia-rabies vaccine - an update. Vet Microbiol. 1995, 46: 269-279. 10.1016/0378-1135(95)00091-N.
Masson E, Bruyere V, Vuillaume P, Lemoyne S, Aubert M: Rabies oral vaccination of foxes during the summer with the VRG vaccine bait. Vet Rec. 1999, 30: 595-605.
Farry SC, Henke SE, Beasom SL, Fearneyhough MG: Efficacy of bait distributional strategies to deliver canine rabies vaccines to coyotes in southern Texas. J Wildl Dis. 1998, 34: 23-32.
Thomson PC, Algar D: The uptake of dried meat baits by foxes and investigations of baiting rates in Western Australia. Wildl Res. 2000, 27: 451-456.
Zimen E: Fox social ecology and rabies control. Biogeographica Vol.18 - The Red Fox. Edited by: Zimen E. 1980, The Hague, Dr.W.Junk B.V. Publishers, 277-285.
Selhorst T, Thulke HH, Müller T: Threshold analysis of cost-efficient oral vaccination strategies against rabies in fox (vulpes vulpes) populations: 2000. 2000, Edinborough, Society for Veterinary Epidemiology and Preventive Medicine, 71-84.
Hansen F, Jeltsch F, Tackmann K, Staubach C, Thulke HH: Processes leading to a spatial aggregation of Echinococcus multilocularis in its natural intermediate host Microtus arvalis. Int J Parasit. 2004, 34: 37-44. 10.1016/j.ijpara.2003.10.003.
Ulbrich F: Ergebnisse der oralen Fuchsimmunisierung gegen Tollwut im Freistaat Sachsen im Zusammenhang mit der grenzüberschreitenden Tollwutgefährdung. Tierärztl Umschau. 1999, 54: 219-223.
Murray JD, Stanley EA, Brown DL: On the spatial spread of rabies among foxes. Proc R Soc Lond B. 1986, 229: 111-150.
Murray JD, Seward WL: On the spatial spread of rabies among foxes with immunity. J Theor Biol. 1992, 156: 327-348.
Brandl R, Jeltsch F, Grimm V, Müller MS, Kummer G: Modelle zu lokalen und regionalen Aspekten der Tollwutausbreitung. Z Ökol Nat schutz. 1994, 3: 207-216.
Wandeler A, Capt S, Gerber H, Kappeler A, Kipfer R: Rabies epidemiology, natural barriers and fox vaccination. Parassitologia. 1988, 30: 53-57.
Hanlon CA, Niezgoda M, Morrill PA, Rupprecht CE: The incurable wound revisited: progress in human rabies prevention?. Vaccine. 2001, 19: 2273-2279. 10.1016/S0264-410X(00)00516-8.
Gortazar C, Ferreras P, Villafuerte R, Martin M, Blanco JC: Habitat related differences in age structure and reproductive parameters of red foxes. Acta Theriol. 2003, 48: 93-100.
The pre-publication history for this paper can be accessed here:http://www.biomedcentral.com/1471-2334/5/10/prepub
DE was partly funded by Impfstoffwerke Dessau-Tornau GmbH. We gratefully acknowledge improvements according to referees' comments.
The author(s) declare that they have no competing interests.
DE and HHT developed the model, and drafted the manuscript. DE implemented the code, and performed the simulation experiments. HHT, TS and TM developed the alternative strategy. TM provided the background of practical rabies management. All read and approved the final manuscript.
Authors’ original submitted files for images
Below are the links to the authors’ original submitted files for images.
About this article
Cite this article
Eisinger, D., Thulke, H., Selhorst, T. et al. Emergency vaccination of rabies under limited resources – combating or containing?. BMC Infect Dis 5, 10 (2005) doi:10.1186/1471-2334-5-10
- Control Area
- Mixed Strategy
- Vaccination Campaign
- Immunisation Level