Assessment of fox control in areas of wildlife rabies

Bulletin of the World Health Organization, 59 (2): 269-279 (1981) Assessment of fox control in areas of wildlife rabies K. BOGEL,1 H. MOEGLE,2 F. STECK,3 W. KROCZA,4 & L. ANDRAL 5 This paper describes a technique for the analysis of the interaction between rabies control measures and the annual turnover of a fox population. The basic conditions are deducedfrom data on the turnover ofa steadyfoxpopulation, which have beenfound to be representativefor largeparts ofcentralEurope. These conditions, together withfielddata on the critical density for rabies transmission and the recovery of reducedfox populations, provide a modelfor theprediction and evaluation ofvarious measures ofrabies control. The method is simplified by the introduction of a semigraphical procedure using the relative density ofa reducedfoxpopulation, defined as the ratio of the actualpopulation density to that of a non-reduced population. Simulation ofepidemics and control measures overconsecutivepopulation cyclesshows the limited effect of population control in a rabies-free area and demonstrates the questionable impact ofmeasures that reduce a regularfoxpopulation by less than 40%, even when such reduction is effected annually. The method is easy to apply in thefield and helps in assessing a number ofdisease and service indicators, as well as ecological factors in the planning and evaluation of comprehensive rabies control programmes. Within the framework of the WHO/FAO coordi- nated research programme on wildlife rabies in Europe, much knowledge has been accumulated on the role of different animal species in the spread of the disease (1-8),a as well as on the interaction between rabies, control operations, wildlife carnivores, and their prey animals (3, 6, 8-11 ). These studies have confirmed that the fox is the reservoir and principle transmitter of wildlife rabies in Europe. The predominant role of this species facili- tates the control of the disease, and should permit the development of relatively simple procedures for assessing the efficacy of control measures. In ad- dition, field studies have provided estimates for the following parameters: (a) the critical level of density for a fox population, below which chains of rabies infection break (3, 8, 9); (b) the annual turnover of fox populations not affected by rabies or specific control measures (8, 12); (c) the rate at which reduced fox populations return to their original density (13). 1 Veterinary Public Health, World Health Organization, 1211 Geneva 27, Switzerland. 2 Director of Veterinary Services, Regierungsprasidium, 74 Tubingen, Federal Republic of Germany. 3Swiss Rabies Centre, University of Bern, Bern, Switzerland. I Director, Federal Institute for Animal Disease Control, 2340 Modling, Austria. 5 Director, Centre national d'Etudes sur la Rage de Nancy, 54 Malzeville, France. a Report of a conference on surveillance and control of rabies, Frankfurt am Main, 15-19 November 1977, Copenhagen, WHO Regional Office for Europe, Document No. ICP/VPH 001, 1978. This paper describes an attempt to develop a pro- cedure based on the results of these studies, to predict the interaction between rabies, control measures, and the dynamics of the fox population. Emphasis is placed on a simple assessment procedure which can be used easily in the field by those concerned with rabies control. BASIC DATA AND DEFINITIONS Annual turnover offox populations The turnover of a fox population under standard conditions (12), described in Table 1, has been shown to be representative for wide areas of Europe. Rela- tively consistent results from various parts of Europe seem to justify the assumption that, in steady fox populations undisturbed by rabies or by special con- trol measures, about two-thirds of the post-breeding (maximum) population are removed annually by hunting, disease, and accidents (12). Regular hunting usually removes about 40/o of the maximum popu- lation, thus accounting for 60%o of the total losses, although hunting is exceptionally intensive in areas such as the upper Rhine basin, where hunters are particularly interested in small game. Steadyfox populations In the absence of detailed information on yearly changes in numbers, the populations studied are 4055 -269- 270 K. BOGEL ET AL. Table 1. Estimated annual turnover of fox population per km2 in a rabies-free area, without special measures for fox control Losses due to Density Density Losses disease Density before after due to and Total before breeding breeding hunting accidents losses breeding la 3b 1.2c 0.8 2b la a Determined by field observations. b Because the maximum population will have to be reduced by j (determined figure) during the year to reach the initial level of 1 fox/km2. The total losses therefore amount to 2 foxes/km2. c Determined from bag records (number of foxes shot in suf- ficiently large reporting districts). regarded as being steady from year to year. This assumption is valid for most populations in central Europe where there are no dramatic outbreaks of such diseases as sarcoptic mange or rabies, where there is no variation in hunting pressure, and where there are no sudden changes in other environmental factors. Hunt- ing statistics indicate that under these conditions populations remain fairly steady if large areas of 500 km2 or more are considered. The steady population serves as the basis for a model of population turnover extending over several years. Actualpopulation density The actual population density (APD) describes the density of a fox population at any point in time in terms of number of foxes per km2. Over the year, therefore, the APD reflects the turnover of steady fox populations, as well as those reduced by rabies or con- trol measures (Fig. 1). The minimum and maximum 2ao- 0j 2 2.s 8 12 2 4 6 a 10 12tFirstI V d g (sy} ~~~Month of pwopu Cy o Yne Fig. 1. Effect on the actual population density of gassing operations before and after an outbreak of rabies. The top line represents the standard (non-reduced) population. APD during the year are recorded in the pre-breeding (February/March) and post-breeding periods (April/ May), respectively. Relative population density The relative population density (RPD) is defined for a given area and point in time as the ratio of the actual density of the fox population to the density of a hypothetical non-reduced population. A fox popu- lation not reduced by special control measures or rabies would therefore have an RPD of 1.0 at any point in time during the year. This definition of RPD permits computation of reduction and recovery of a population without knowledge of the actual number of foxes per unit area. For example, a reduction of 30%0 would lower the RPD of a population from 1.0 to 0.7, irrespective of the absolute density or stage in the annual population cycle at the time of reduction. Factors reducing thefox population In a steady fox population about two-thirds of the post-breeding population are removed before the next breeding season. Reduction factors acting under these regular conditions have been discussed in a previous publication (13). In areas of wildlife rabies, however, fox popula- tions are subject to additional pressure, both from the disease and from special control measures. At the height of an epidemic, rabies may kill up to 500o of the fox population.' The effect of gassing operations depends on the ecological conditions, which may vary considerably within Europe. This factor, as well as intensified hunting, is described in detail and analysed in the sections on procedure. Recovery rates of reducedfox populations Estimates of the rate at which reduced fox popula- tions recover have been reported previously (13). The rates given in Table 2 seem to correspond well with field observations under conditions for which the described standard population turnover is applicable (12). Although increased fertility has not so far been seen in foxes with a low population density in areas of rabies control in central Europe (8), annual reproduc- tion is sufficiently high to ensure that populations can compensate for a reduction of 20-30Oo within a single annual cycle and recover from an RPD of 0.3 within 3 years. Criticalfox population density in rabies Field observations of foxes suggest that an RPD of 0.3 represents the critical level for the spread of rabies in wide areas of Europe. Below this value, chains of b WHO report. See footnote a, page 269. ASSESSMENT OF FOX CONTROL 271 Table 2. Recovery rates of reduced fox populationsa Relative population density Population increase After first during first recovery Before recovery recovery year year (%) 0.10 0.17 70 0.15 0.25 67 0.20 0.33 63 0.25 0.40 60 0.30 0.47 57 0.35 0.54 54 0.40 0.60 50 0.45 0.66 47 0.50 0.71 42 0.60 0.82 37 0.70 0.92 31 0.80 0.99 24 a Under standard conditions (13). rabies infection seem to break.C As has been shown in areas of Denmark (9), Germany (3), and Switzerland (6, 8), rabies may disappear completely when the hunting indicator of the density of the fox population decreases from about 1.2 to 0.3 or from 1.0 to about 0.2 foxes shot annually per km2. Under standard con- ditions, the shooting of 1.2 foxes per km2 annually represents a density of about 1 mature fox per km2 in the pre-breeding period (12). Allowing for a decrease in hunting efforts in areas where the fox population has already been reduced by rabies and gassing oper- ations, it may be postulated that in order to break the chain of infection, the fox population must be reduced from 1.0 to 0.3 foxes/km2. ASSESSMENT MODEL Combined effect of rabies and control measures. The model for the assessment of fox control is based on the assumption that different reduction factors act on the population in a competitive rather than an additive way. This is shown in Fig. 2. For example, if rabies reduces the RPD of a population by 407o from 1.0 to 0.6, then a gassing operation capable of reducing a population by 601o will affect only the remaining population. The RPD of 0.6 will thus be lowered to 0.24 (0.6 minus 6007o of 0.6) and not to zero. Thus: Final RPD = original RPD x product of all survival rates c WHO report. See footnote a, page 269. 1.07 I' .. _. ... 4.- 4 . -1---||:---....... .... ... .. .. ... ... ....... . . .. ... .... ..... .... j . ..... .... ...... .. .... .. ...... 0. 7 ,.,, ., .. .,... .. .... .. . .. ... .. ... ... .. .. ro--*a .... .,. X-- -^ .~~~~~~~~~~~~~~~.. !07 b Rs, . ...5 , .w,, ...... ..... .. .... . . .,.. .... .. .... .I .... 0.6 ~~~~~ a ~~~~~~~~~~~4_ '0~~~3 Criticil~~~~~densty. &27. t '.;_;;1-'~.. .... ....*- *--.-;;.':::-::t - : : :-.:: :::-: :: ::1 :: :::. ::1: i I---. ~ Li -TA I:.~~~~~~~~~~~~- 0 1 -t030 4 L OD 70 90D 90 I Reduction of population due to control memures Fig. 2. Combined effect on relative population density of rabies and control measures This formula for competitive factors applies not only to consecutive reductions of fox populations but also to simultaneous actions. Semigraphzical determination of changingfox population densities The computation of the population density over a complete annual cycle becomes difficult when reduc- tions due to various factors take place at different times. Reduction and recovery effects may be super- imposed on one another and calculation is even more complicated when conditions have to be simulated over several population cycles (Fig. 1). For the determination of the slopes in Fig. 1, actual density figures have to be calculated throughout the annual cycle. The calculation of the effect on the normal slope of gassing operations, intensified hunt- ing, and population recovery over a two-year cycle, is difficult and time-consuming. This procedure, how- ever, can be replaced by a simple semigraphical method which can be easily applied in daily field work. As shown in Fig. 3, calculations are simplified by expressing the level of the fox population in terms of the RPD. Reduction and recovery of the population are entered in a calculation chartd containing lines indicating the linear recovery of the RPD, starting from different levels (compare Table 2). Population reductions are drawn in the chart as vertical lines at the appropriate point in time. Since reduction factors are d Calculation charts are available from Veterinary Public Health, World Health Organization, CH-121 1 Geneva 27, Switzerland. 272 K. BOGEL ET AL. 1.0 '''''T ''"I'''-l' '-l'' 1' ~~~~~.... ,.._. _z__.. _ -_1.0 ~~~~~~~~~~~~~~~~~~. ..1.0. ~... .0 c0.9 _ ..- _ o .. . _ . . --. $ _ _ W _ _ _ _4 us. . - ! 5&-0_- 8 t 08 t-l 71---- 0L7 .0. .%.. .-. _. .-- 0.7x~~~~~~~~~~~~~~~ 1' L-:: 1 t l*_- - - _ _: .... ... -1E*: __-.... _!.. _.::.t... _'_....I.. o0.ol 4-= 08 >W:_T . *g ~~~.. ............. ..._ c 0.1 so ~~~~4% jot _ 7 1 .;. If _01 CO 60 %~ ~ ~ ~0 ... ..0275 0 .1 - . .... -L .0 o 1 '-& 'S .:|-'I''1 {. 1-'::( 1 :. .. 1 L~~~~~~~. '.1.1:'''.''' ..L.... .. 1 234 5 i!l 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 t ~~Months of first yearof population cycle tMonths of second yeer t (February) (Fetwuary) (Februery3} Fig. 3. Chart for determination of the relative population density, applied to the same examples as shown in Fig. 1. competitive, each single factor has to be accounted for by deducting the appropriate percentage of the RPD value at the time concerned. Recovery parallels the ascending lines. It should be understood that an increase of the RPD along these lines never represents an increase in the actual popu- lation density, since this can only occur in the breeding season. The upper horizontal line of the calculation chart (RPD = 1.0) represents all increases and de- creases of the APD of an undisturbed population. An increase in the RPD, therefore, simply reflects a relative population recovery due to a diminished mortality rate at reduced population levels. The recovery in terms of actual population density is shown in Fig. 1. Disregarding the problem of accuracy of data, the semigraphical procedure is probably as precise as the purely mathematical approach. At the end of the second population cycle the calculated figures of0.325 and 0.275 are identical with the values determined graphically (Fig. 1 and 3). A similar agreement was found for a number of examples, the maximum dis- crepancy in the RPD being 0.02. APPLICATION OF THE SEMIGRAPHICAL ASSESSMENT PROCEDURE Determination of the effect ofgassing operations For the assessment of gassing operations it is essen- tial to estimate the vulnerable proportion of the fox population. In large areas of Europe, comprising plains or slightly hilly areas with mixed forests and agricultural land, about 80%o of the fox population may use dens that can be gassed. Fox populations in such areas are much more vulnerable to gassing oper- ations than those in areas of high ground water levels, or mountains with rock underground, where only 45%o (Alps) or 55% (Jura mountains) of the litters were found in accessible dens (8).e Where the fox population has already been under control, the proportion vulnerable to gassing may be even smaller. This is particularly the case where control teams do not reopen the dens so that they are less easily accepted in the breeding season of the following year. Changes in denning habits from year to year may be estimated from the ratio of dens gassed per km2 to the "hunting indicator of the population density" (HIPD), or the forecasted RPD. In calculating the effect of gassing operations, one should assume the worst possible conditions. Very rigorous control operations in favourable areas may thus remove about 80%o of the vulnerable fox popu- lation. Under favourable conditions, approximately 75%o of foxes would be vulnerable, resulting in a reduction in the total population of not more than 60%o. In view of changing denning habits, gassing operations in the next breeding season will probably remove not more than 50% of the total population, and the efficiency will decrease further in subsequent years. The success of the operations depends largely on the cooperation of farmers, game wardens, and hunters. The efforts to locate dens generally wane as the e WHO report. See footnote a, page 269. ASSESSMENT OF FOX CONTROL frequency of local rabies cases decreases, and there may be a general decrease in public awareness and interest in control measures. Also, the continued disturbance of their dens causes the foxes to avoid them for whelping so that gassing procedures become less efficient. For the purposes of assessment therefore, one should assume a total reduction in the fox population of not more than 60% at the first gassing operation, 50% at the second, and about 30% in subsequent years. On the basis of the assumed recovery rates (13), an annual reduction of 30% would allow the popu- lation eventually to reach an equilibrium RPD of about 0.7 before and 0.49 after annual control oper- ations. This would be consistent with field obser- vations (15), since fox populations have been shown to be able to support reinfection in an area where den gassing had been applied over some years in the absence of the disease. An annual reduction of 40% over many years would be an unrealistically high assumption under these circumstances since this would lead to equilibrium at around the critical level. In areas where only about 50% of the fox popu- lation can be considered vulnerable to gassing oper- ations in the first year (e.g., alpine areas), the above figures have to be modified accordingly, the maxi- mum reduction being 407o of the total population in the first year, 33% in the second year, and 20% in subsequent years. Determination of the effect of intensified hunting Unlike gassing operations, which can be considered as sudden or single-hit reduction, the additional press- ure of intensified hunting often extends over the whole year or legal hunting period. It is improbable that doubling the hunting intensity would double the number of foxes shot annually, and the formula of diminishing returns (15) seems more appropriate. The application of a hunting indicator of population den- sity (HIPD) is based on the assumption of a relatively close and linear correlation between the density of fox populations and the hunting success. This would also be consistent with the formula for the combined effect of competitive reducing factors, whereby regular hunting removes a certain percentage of the actual population, irrespective of the population density. A substantial increase in hunting intensity is required if this measure is intended to supplement other control operations. Since regular hunting removes about 40% of the fox population annually (12), an increase of 100%7o in the hunting intensity could remove 400/o of the remaining population (i.e., 24% at the most). From the bag records, there is little evidence that hunting intensity is ever increased by more than 30-50% during a year of rabies control (3, 16). If maintained over a year, this increased effort could reduce the fox population by only 10-15%, and the reduction achieved during the first few months of the population cycle would be compensated for by the recovery factor operative during the rest of the year. A special aspect of rabies control is related to the time of the year at which the hunting is intensified. If it is increased by 100%1o during the months of June and July, this could result in a reduction in the summer population of foxes of 10-15%. For example, in Bavaria, foxes are hunted mostly during the summer months, maximum values being reported for June and July. During these two months, about 30% of the annual bag is recorded, which, under standard con- ditions, would represent 12%o of the total population (17). A 100% increase in hunting intensity during these two months would remove 12%o of the popu- lation then present, i.e., 8.4%o of the maximum population as measured in the post-breeding period. Although this decrease is relatively small and subject to recovery in the following months, it may have an influence on the dispersal of young foxes in the autumn and therefore on the activation of the natural foci of rabies. It is not yet fully understood whether and how intensified hunting causes foxes to leave their territory and thus supports the spread of rabies. Some observations-particularly in areas of small game hunting where particular efforts have been made for decades to reduce the fox population- suggest that very intensive fox hunting inhibits the spread and case frequency of rabies in wildlife (10). In any case, a further reduction of 10%7o in the popu- lation can be decisive during periods when rabies and gassing operations have already reduced the popu- lation density close to the critical level for the epidemic. Similarly, intensified hunting during the winter months up to the breeding season is important, since recovery factors are less significant then and there is a direct impact not only on the number of animals born but also on the transfer of the disease to the new generation. Assessment of annual population cycles The reduction of fox populations and the recovery process can be followed over consecutive population cycles using the calculation chart (Fig. 3). The reduc- tion factors that act on the population for periods of up to 3-4 months can be considered as a single action at one point in time. In the examples given in Fig. 3, the reduction due to rabies is shown as an event hap- pening once only, although the losses that occur at the height of an epidemic may be spread over a period of at least four months, from November to February or March (4). In these examples, rabies is considered to 273 274 K. BOGEL ET AL. remove about 50% of a population not previously reduced by control measures, or 40/o of an already diminished population. This presupposes that the incidence is higher in populations of greater density. These figures are very rough estimates based on a few observations which indicate that rabies can indeed reduce the population by about half of its original density! The figures used above probably reflect maximum mortality rates. The evaluation of data from some cantons of Switzerland suggests that in certain areas about 20-40% of foxes are killed at the height of an epidemic (6). On the other hand, estimates of20-30% mortality appear to be rather low in view of the fact that rabies can extinguish itself in certain areas with- out any additional population reduction. Even a reduction of 40%o would not be enough to cause the elimination of the disease unless an additional per- centage of the population acquired immunity against it. The proportion of animals acquiring immunity would not be higher than about 10-20%o of the remaining population (7). Any immunity to rabies infection, whether acquired naturally or induced by the application of vaccine, would decrease the susceptible fox population. The semigraphical method can therefore also be used for the evaluation of vaccination programmes. The recovery of reduced fox populations is inte- grated in the calculation chart. As can be seen from the two examples in Fig. 3, there is very little difference in the outcome of two control programmes, one of which involved gassing operations in the spring before the height of an epidemic and the other the application of gassing in the spring following a winter of maxi- mum case frequency. Intensive fox control operations are justified in rabies-free areas only if there is an immediate threat of disease! There are a number of reasons for carrying out gassing operations in rabies- free areas, though their effect on the spread of the disease may be negligible. From the example shown in Fig. 2, it is obvious that the absolute number of rabid foxes at the height of the epizootic is smaller (about 0.3 foxes/kM2) if rabies spreads into a reduced popu- lation, than into one that has not been reduced (about 0.7 foxes/kM2). This reduction in case frequency has a beneficial effect on all case-related consequences, in particular the number of persons exposed and treated, as well as losses in domestic animals and costs of case investigation, including laboratory services. The calculation chart can be used to estimate the relative effect of gassing before the spread of rabies. In the example without gassing, the RPD is reduced by rabies from 1.0 to 0.5 (difference 0.5), whereas in the population that has been reduced by gassing, rabies lowers the RPD from 0.54 to 0.33 (difference 0.21). f WHO report. See footnote a, page 269. The ratio of 0.5:0.21 shows the difference in the levels of case-related consequences of rabies for the two situations. Where it is intended to stop the movement of an epi- demic wave, the number of foxes should be reduced in a protective zone about 30-60 km wide.! Efforts should also be concentrated on a zone ranging from the core of the epidemic wave to a line about 20 km ahead of the frontline, as measured in March or April. The further movement of the epidemic in autumn seems to depend less on the cases recorded in spring- time at the extreme limit of the epidemic than on those at the core of the epidemic wave, where the high frequency of cases facilitates the transfer of the disease to the new fox generation (1). Therefore, control operations limited to a zone ahead of the epidemic and not including its core are likely to fail. Control operations preceding the epidemic wave must be carefully analysed by means of the method presented here, in view of the possible effect of popu- lation recovery. Special control operations, carried out between April and July and removing 20% of the population, are partly compensated for by recovery factors, the RPD increasing from 0.8 to 0.93 before the end of the population cycle. If, however, a reduc- tion of 20% is effected during December-February, there is no significant recovery before the next breed- ing season, and the RPD of 0.8 will not increase by more than 0.03. A period of very intensive hunting during the summer before the epidemic enters an area would therefore have little effect on subsequent popu- lation cycles. Such additional control measures are, however, most important and effective when there is a high case frequency, in the winter and the following months, until the disease is eliminated from the area. Complementary monitoring offield conditions The method described here will only be of value if it is continually adjusted for different conditions of population turnover, recovery rates, and effects of control measures. There are several ways of monitor- ing control programmes. Disease indicators concern the number of rabid animals per unit of surface area. An analysis of the frontwave of an epidemic appears to be most import- ant for planning control operations (1), while towards the end of an epidemic, disease surveillance is essential for the assessment of the control programme. Infor- mation on the number of persons exposed and/or receiving post-exposure treatment is of socioeconomic significance. In addition to the essential data on the spread of the disease and the frequency of cases in animals, indi- g WHO report. See footnote a, page 269. ASSESSMENT OF FOX CONTROL cators of ecological conditions are also important (18). Monitoring should therefore include the hunting indicator of population density (HIPD) of foxes, i.e., the number of foxes shot annually per km2 (3). Some information is also required on the proportion of litters raised in dens that are accessible and vulnerable to gassing operations. Relevant data can be obtained from surveys in selected areas. Changes in denning habits can also be estimated from the ratio of dens gassed per km2 to the HIPD. The proportion of dens used by foxes and its correlation with the population density deserve particular attention in future field investigations since these data will provide important information for the planning and evaluation of gas- sing operations. Results may indicate the need for supplementary fox control measures. In general, service indicators are essential components of the feedback mechanism between control programmes and surveillance. The number of dens gassed, foxes shot or poisoned, bounties paid, etc., can provide valuable information. Also, infor- mation on the location of dens each year and the time spent searching for new denning places, is valuable as a service indicator. Most of these surveillance data are useful for moni- toring control operations in areas of more than 2000 km2. The HIPD may be unreliable if applied to smaller areas. In general, data for consecutive years should be used only for the comparison of conditions within an area. For the comparison of two or more areas, the data should be from sufficiently large areas in which all the ecological conditions are well understood. DISCUSSION In assessing the reduction and recovery of fox popu- lations, two characteristics of the procedure presented here should be borne in mind. Firstly, the method is simplified by the introduction of the term RPD, thus ignoring a number of variables that determine and influence the annual cycle of popu- lation density. The relationship between RPD and APD should always be determined and borne in mind. Secondly, the calculation chart presented includes defined recovery rates that have been deduced from field data (13). In some areas, actual values may differ from these rates, and therefore, the use of this pro- cedure in the monitoring of rabies control operations should be considered as a further stage in assessing the validity of the model. Suggestions for this critical use of the procedure, its adaptation to different conditions in the field, and the interpretation of results have been discussed in the preceding sections. The authors would in particular like to draw attention to the section entitled Comple- mentary monitoring offield conditions, which gives guidance for further examination of the semigraphical assessment technique presented in this paper. Only experience will show the limits of this procedure in estimating critical population densities and in pre- dicting and evaluating the success or failure of rabies control programmes. The World Health Organization invites field officers and scientists to apply, examine, and improve the procedure, and to inform us of the experience thus gained. RU RESUME EVALUATION DE LA DESTRUCTION DES RENARDS DANS DES ZONES DE RAGE DES ANIMAUX SAUVAGES Cet article expose une methode qui permet d'analyser l'interaction entre les mesures de lutte contre la rage et le renouvellement annuel d'une population de renards. Les conditions de base sont deduites des donn&es sur une population stable de ces animaux, qui se sont revelees repr&- sentatives de ce qui se passe dans de grandes parties de l'Europe centrale. D'apres ces conditions, ainsi que les donnees de terrain sur la densite critique pour la trans- mission de la rage et la restauration des populations reduites de renards, un modele est elabore pour la prevision et l'eva- luation de diffrentes mesures de lutte antirabique. La methode est simplifiee par l'introduction d'un procede semi- graphique, la densite relative d'une population reduite de renards etant ainsi exprimee sous la forme du rapport de la densite reelle de la population a celle d'une population non reduite. La simulation d'epidemies et de mesures de lutte portant sur des cycles consecutifs de population montre l'effet limite d'une restriction de la population dans une zone exempte de rage et met en evidence l'efficacite douteuse des mesures reduisant une population normale de renards de moins de 4007o, meme si une telle reduction peut etre effectu&e annuellement. Cette methode est aisee A appliquer sur le terrain et elle aide A tenir compte d'un certain nombre d'indicateurs de maladie et de services, de meme que de facteurs ecologiques, dans la planification et l'evaluation de programmes complets de lutte contre la rage. 275 276 K. BOGEL ET AL. REFERENCES 1. BOGEL, K. ET AL. 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ASSESSMENT OF FOX CONTROL Annex 1 DATA AND ASSUMPTIONS FOR THE ASSESSMENT OF RABIES CONTROL IN WILDLIFE Basic parameters Assumptions References Limitations Annual turnover of steady fox population Recovery rate of reduced fox population Ratio of 1 :3, before and after breeding season 24-70% increase in first recovery year, depending on level of preceding reduction (1) (1) Valid for large areas only. Different ratios would influence the APD but not the RPD. Explained by increased life expect- ancy and not by increased litter size. Recovery is assumed not to exceed density level of original population. Different conditions would influence both APD and RPD. Competitive effect of different reduc- tion factors Final population density = original population density x product of all survival rates Proportion of foxes killed by regular hunting Critical level of population density Area directly threat- ened by rabies 40% of post-breeding population, if hunting effort is evenly distributed over the year No rabies in areas of APD <0.25 foxes/km2 (adult springtime population) and HIPD of <0.3 foxes shot per km2 per year Up to 30 km from out- breaks, the major spread occurring from November to March in most areas (13, 16) (3, 6, 9) (1, 4) In areas of small game hunting, the fox hunting may be concen- trated on June-September. This does influence the APD (Fig. 1) but not the slope of the RPD (Fig. 2). HIPD <0.3 valid for large areas only (> 1000 or 2000 kM2 ) and standard conditions. In areas of small game hunting the HIPD appears to be high even with a relatively low population density. The seasonal cycle of case fre- quency may differ from area to area. In alpine mountain villages the spread of the disease may show different patterns. See section: Assessment model 277 K. BOGEL ET AL. Annex 2 THE APPLICATION OF THE SEMIGRAPHICAL PROCEDURE Reduction factors acting on the fox population over several months (e.g., rabies at the height of the epidemic, seasonally intensified hunting) can be introduced into the calculation chart at one point of time in the middle of the period concerned (cf. Fig. 1 and 2). Factors and conditions Hunting intensity 100% increase over regular hunting annual average monthly average X % increase over regular hunting Application to calculation chart Reduce the RPD by 40% of the existing value at month 6 (e.g., from RPD 0.45 to 0.27) Reduce the RPD by 4.2% at corresponding month (multiply RPD by 0.958) Reduce the RPD as above by X x 400% or X x 4.2 %'100 100r/0 respectively Limitations and assumptions (a) The reduction factor may have to be increased in areas of small game hunting and reduced in areas of inadequate hunting. (b) In areas of inadequate hunting or without hunting (e.g., urban areas) the social structure of fox populations may differ from that of the assumed standard population. (c) The reduction factor varies according to month and season, depending on the efforts made in regular and intensified hunting. Gassing operation Percentage of fox popu- lation denning under conditions vulnerable to gassing operations: 80% (mixed land- scape: forest/pasture/ cultivated land, at alti- tudes up to 1500 m) 1st year 2nd year 3rd year 50% (areas of high ground water level, Karst, rocks, Alps, Jura) 1st year 2nd year 3rd year The assumptions and reduction factors should be modified as appropriate for local conditions. Reduce the RPD at the month of operation by the following percentages 60% 48% 42% The proposed calculation factors are based on the assumption that only 75% of all denning places vulnerable to gassing operations are traced and successfully treated. In addition, it is assumed that the vulnerable proportion of the fox population is 20% less in the second year of gassing operations and 30% lower in subsequent years. 37.5% 30% 26.25% 278 ASSESSMENT OF FOX CONTROL Factors and conditions Application to calculation chart Limitations and assumptions Wildlife rabies (a) 50% mortality can be assumed for large Density of fox areas of central Europe with landscape population prior to infec- favourable to foxes (mixed land use, tion (referred to adult forests, agriculture) population in springtime) (b) 40% mortality is assumed for areas ofhigh (>1 fox/kM2) Reduce RPD by 50% for months extended forests (e.g., Black Forest) or of maximum rabies frequency with otherwise less suitable habitat. This medium (0.6-0.9 mortality can also be applied to foxes/kM2) Reduce RPD by 40% favourable habitats if the fox population low (<0.6 foxes/kmi2) Reduce RPD by 30% or less was reduced by control measures prior to infection. (c) Mortality rates of 30% or less are applicable in areas into which rabies does not spread easily because of unsuitable habitat, special hunting habits, control measures, or a combination of these factors. This mortality can also be applied to a second year of relatively high rabies frequency in areas described under (a) or (b). 279