Temporal patterns of domestic and wildlife rabies in central Namibia stock-ranching area, 1986–1996

Temporal patterns of domestic and wildlife rabies in

central Namibia stock-ranching area, 1986±1996

F. Courtina, T.E. Carpenterb, R.D. Paskinc, B.B. Chomela,*

aDepartment of Population Health and Reproduction, School of Veterinary Medicine, Davis, CA 95616, USAbDepartment of Medicine and Epidemiology, School of Veterinary Medicine, Davis, CA 95616, USA

cEpidemiology unit, Directorate of Veterinary Services, Private Bag 12022, Auspansplatz, Windhoek, Namibia

Accepted 23 July 1999

Abstract

Eleven years (1986±1996) of wildlife- and domestic-rabies data from the agriculture stock-

ranching area of central Namibia were studied using time-series analysis. Nine hundred and sixty

three rabies cases were observed in domestic ruminants (5.4 cases/mo), black-backed jackals (Canis

mesomelas, 1.3 cases/mo), domestic dogs (0.5 case/mo), and bat-eared foxes (Otocyon megalotis,

0.1 case/mo). The incidence of rabies for all species did not change significantly over the whole

study period. However, seasonal variations with an increase in the number of cases between June

and November of each year, as well as 3±4 yr cyclical fluctuations were identified in domestic

ruminants and black-backed jackals. The black-backed jackal time-series variable was a significant

predictor of the domestic-ruminant and dog time-series variables. The rainfall seasonality combined

with the seasonal reproductive pattern of the black-backed jackal appeared to be plausible

explanations for the seasonal variations of rabies. However, there was no overall significant

correlation between the cyclical weather fluctuations and the 3±4 yr cyclical rabies variations.

# 2000 Elsevier Science B.V. All rights reserved.

Keywords: Rabies virus; Time-series analysis; Black-backed jackal; Canis mesomelas; Namibia; Southern

Africa

1. Introduction

Rabies must have been present in the highveld plateau of Southern Africa since at least

the beginning of the 20th century. The disease was mainly affecting endogenous wild

Preventive Veterinary Medicine 43 (2000) 13±28

* Corresponding author. Tel.: 1-916-752-8112; fax: 1-916-752-2377.

E-mail address: [email protected] (B.B. Chomel)

0167-5877/00/$ ± see front matter # 2000 Elsevier Science B.V. All rights reserved.

PII: S 0 1 6 7 - 5 8 7 7 ( 9 9 ) 0 0 0 8 3 - 5

species of the Viverrid family, and sporadic spillovers were occurring in other wildlife,

domestic animal and human population (Meredith, 1982). This type of rabies (referred to

as `̀ viverrid rabies'') is still present in South Africa and possibly also in southern

Namibia (Swanpoel et al., 1993). The agent responsible for this disease is

philogenetically very distinct from the canid rabies strains that are found in Europe

and that invaded Southern Africa after World War II (Von Teichman et al., 1995). It is

believed that the relatively recent canid rabies epidemic started in the late 1940s from a

focus located in southern Angola/Zambia that expanded south into Namibia and east into

Zimbabwe. Wild canid species like the black-backed jackal (Canis mesomelas) and bat-

eared fox (Otocyon megalotis) have probably assisted in spreading the disease (Nel, 1993;

Smith et al., 1993; Von Teichman et al., 1995).

Between 1986 and 1996, apart from an epidemic that disappeared in kudu antelope

(Tragelaphus streptisiceros) (Hubschle, 1988), the geographical distribution of rabies

apparently has not changed since what has been described since 1976 (Depner, 1992;

Hubschle and Uanguta, 1995; Schneider, 1985). In the northern communal areas (NCA:

Opuwo, Ondangua, Rundu and Katima districts), human-population density is the highest

of the country, domestic dogs are many and wildlife is scarce. Rabies there is still found

mainly in dogs and represents a health hazard to the human and bovine populations.

Large commercial farms occupy the land in the central stock-ranching region. The

human-population density is low and wildlife abundant. Rabies surveillance there reports

most of Namibia's cases; these are found in domestic animals (cattle mainly) and wildlife

(black-backed jackal mainly). South of the district of Rehoboth, rabies occurs only

sporadically.

The present study only addressed the situation in the central Namibia stock-ranching

area. One has to keep in mind that inner Namibia's distribution of animal-health status is

strongly influenced1 by the socio-economic and cultural disparities between the NCA and

the central-south parts of the country (Hubschle and Uanguta, 1995). It is a complex

heritage that for the most part explains the descriptive disparities seen in the previous

paragraph. In addition to that, the stability of the human population, the farming

settlements and the veterinary organization in the central Namibia stock-ranching area

allowed continuity and appropriate rabies surveillance over the 11 yr study period. The

same could not be said for the northern communal areas that were still a war zone

between 1986 and 1989.

The sylvatic type of rabies cycle that occurs in the central Namibia stock-ranching area

as well as other parts of Southern Africa (Von Teichman et al., 1995) is complex. It has

been approached from descriptive (Barnard, 1979; Bingham and Foggin, 1993),

molecular-epidemiologic (Von Teichman et al., 1995), and ecologic (Mckenzie, 1993)

perspectives. These studies have shown that black-backed jackal and dog rabies were

implicated in a common canine-type rabies cycle distinct from a viverrid. These studies

have raised several questions. What are the temporal trends? Does wildlife ecology play a

role in the pattern of the disease? Is the incidence of rabies weather related? Answers to

these questions are important for the development of efficient control strategies.

1 The Veterinary Cordon Fence that isolates the NCA from the rest of the country is still in use.

14 F. Courtin et al. / Preventive Veterinary Medicine 43 (2000) 13±28

The objectives of this study were to identify and quantify the temporal distribution of

rabies cases in central Namibia over the period 1986±1996.

2. Materials and methods

2.1. Surveillance data

Data were obtained from computer records of the Veterinary Services of Namibia for

the period 1986±1996. Rabies is a notifiable disease in Namibia and it is required that all

occurrences of this disease be reported (and should therefore appear in the database).

During the 11 yr study period, no significant change in human population, farming

settlements and operation of veterinary organization that could have affected the level of

cases discoveries and reporting from the field was noted. The records contained

information on species, place, time, clinical signs and laboratory confirmation of cases.

Laboratory work was performed primarily at the Central Veterinary Laboratory of

Windhoek, Namibia, but a limited number of samples were tested at the Grootfontein

Diagnostic Laboratory or the Onderstepoort Veterinary Institute, South Africa. Annual

stock census and vaccination numbers of cattle for the five districts of Grootfontein,

Otjiwarongo, Windhoek, Omaruru and Okahandja were also collected from the

Veterinary Services.

2.2. Weather data

Monthly total precipitation data for the weather stations of Grootfontein, Otjiwarongo,

Windhoek and Gobabis were obtained from the Namibian National Weather Bureau

(Windhoek, Namibia).

2.3. Case definition and other study restrictions

A case was defined as a temporal (day) and spatial (farm premises or any other location

of discovery) cluster of one or more animals of the same species clinically diagnosed as

rabid or carcass discoveries with rabies suspicion. In other words, if on a certain day at a

certain location, one or more animals of the same species were clinically diagnosed as

rabid or one or more carcasses of the same species were discovered and rabies was the

suspected cause of death, it constituted a case. If at least one sample from this cluster

were confirmed by immunofluorescent direct test or histopathologic examination, then

the cluster became a confirmed case. Only laboratory-confirmed cases (963/1,146; 84%

of total cases) in black-backed jackals, dogs, bat-eared foxes and domestic ruminants

(bovine, ovine and caprine) for the following 13 districts of central Namibia:

Grootfontein, Tsumeb, Outjo, Khorixas, Otjiwarongo, Otjinene, Okakarara, Gobabis,

Omaruru, Okahandja, Karibib, Windhoek and Rehoboth were used. Confirmed cases in

other animal species (viverrids, rodents, wild ungulates and other domestics) which

accounted for less than 1% of total confirmed cases were excluded. Because this study

F. Courtin et al. / Preventive Veterinary Medicine 43 (2000) 13±28 15

focused on the situation in stock-ranching areas, cases that occurred in the wildlife-

conservation reserve of Etosha were also excluded.

2.4. Monitoring of surveillance level during study period

Possible changes in the level of surveillance of the disease between 1986 and 1996,

which could be a source of bias, were evaluated using two indices: percentage submission

and percentage confirmation of submitted cases

1. The percentage submission is an indicator of change in the logistical organization of

veterinary laboratory submission of cases. It is calculated as 100�S/T, with S being the

number of submissions of rabies suspects and T the total number of reported suspected

rabies cases.

2. The percentage confirmation of submitted cases, under the hypothesis that laboratory

quality (test sensitivity) and submission percentage together have been stable, is an

indicator of the accuracy of rabies suspicion in the field by farmers and vets. It is

calculated as 100�C/S, with C being the number of confirmed cases and S the number

of submissions of rabies suspects.

3. Correlations between these annual indices and the annual rabies incidence data were

examined using Pearson's r. The null hypotheses for the two correlations (r � 0) were

examined with 2-tailed t-tests (Altman, 1991).

2.5. Temporal components of time series

Confirmed cases were grouped by species and month (t) of clinical diagnosis or carcass

discovery and formed 132 periods (months) for the time series (Yt) for each species.

Initial time-series analysis was performed using Minitab 11.1 (MTB Inc., State College,

PA 16801, USA) to identify the four components of the temporal additive model for each

species: long-term trend (Tt), seasonality (St), cyclicity (Ct), and irregularity (It):

Yt � Tt � St � Ct � It: (1)

The decomposition consisted of three steps. First, Tt was analyzed by fitting a least-

squares regression line to the time series. Second, St was identified using a ratio-to-

moving-average method (Lapin, 1973) with a length of 12 periods. Third, deseasonalized

(has trend and error components; season effect removed) and detrended (has season and

error components; trend effect removed) data were smoothed with a single exponential

process to remove It and identify Ct. During this process, the program identified the best

weight of the exponential average by minimizing the sum of squared errors.

The autocorrelation function (ACF) (Minitab, 1996) calculated the correlation

coefficient rk, a measure of linear relationship (Daniel, 1991) of the ratio between a

species-specific time series and itself lagged by k time periods. The default number of

lags, 33 (i.e. n/4, where n � the number of observations in the series) was selected. This

function gave a way to test for the significance of seasonality in a time series by

examining the ACF at seasonal lags of 12 mo intervals. Correlation coefficients from the

ACF were tested by Z-tests (Daniel, 1991).


2.6. Temporal associations between species time series

Cross-correlations (Minitab, 1996) Ð measures of linear relationships (Daniel, 1991)

between two different species-specific time series lagged by k periods Ð were run for

lags �10 mo (sufficient to cover large incubation periods for rabies) using Minitab. The

significance of these cross-correlations was calculated with a Z test for the correlation

coefficient (Daniel, 1991).

When the result of this analysis indicated association between the time series of two

different species, the nature of this association was investigated further with a dynamic

regression approach using Forecast Pro software (BFS, Belmont, MA 02178, USA). A

dynamic regression time-series model evaluates the relationship between a dependent

variable and both lagged values of itself and other explanatory variables. This method

allowed construction of a model for prediction of a dependent time-series variable (Y)

with explanatory time-series variables (X1, X2, ..., Xn) and an error term based on past

error autocorrelations e(t) :

Y � �0 � �1X1 � �2X2 � � � � � �nXn � e�t�: (2)

Model selection was performed by including variables in a forward stepwise manner.

First, the variables of interest (time series of the two species for which an association was

found) were forced into the model. Improved models were evaluated as follows:

additional variables (such as cattle population numbers and vaccination coverage) were

selected for entry based on statistical significance (p < 0.05) of the coefficient. Overall

goodness-of-fit of the model was tested with a Ljung-Box goodness-of-fit test

(Stellwagen and Goodrich, 1994):

Q � T�T � 2�Xp

1

�r2i =�Tÿi�� (3)

in which p is the number of parameters, T is the number of time periods in the series,

ri is the autocorrelation at lag i month. Q is a weighted sum of squared correlations

that has approximately a chi-square distribution with Lÿp degrees of freedom, where

L is the lag. This statistic was used to test for overall autocorrelation of the fitted errors

of the model. If there is significant autocorrelation, then future errors can be predicted

from past errors. If this is true, Q is significant and the model is not valid and needs

improvement.

Finally, the Bayesian Information Criterion (BIC) (Stellwagen and Goodrich, 1994)

was used to discriminate among the (typically several) satisfactory models that were

found:

BIC � MSE � T �p=2T�: (4)

The BIC rewards goodness-of-fit (as measured by the mean squared error; MSE), and

penalizes for complexity (Stellwagen and Goodrich, 1994). Reducing the MSE implies

both better fit and (as can be seen in Eq. (4)) reduces the BIC; clearly, smaller BIC is

preferred. The BIC is used to avoid poor forecasting often seen when a model is very

complex (several parameters).


2.6.1. Effects of weather, stock numbers and vaccinations of domestic animals

Independence between cumulative yearly rainfall (September through August) and

cumulative yearly rabies cases (all 4 species combined; January through December) was

tested with a two-tailed Spearman rank test (Hajek, 1969). Analyses were conducted for

the period 1986±1995 and the study area as a whole, using mean annual rainfall from all

regions. It was also done individually for Grootfontein, Otjiwarongo and Windhoek

districts where complete rainfall data were available.

Yearly cattle population numbers and vaccination coverage over the study period were

examined for possible variations and potential confounding. These two variables were

offered to each of the four species-specific models (Eq. (2)).

3. Results

3.1. Overall results and monitoring of surveillance level

Totals of 713 confirmed cases in domestic ruminants (5.4 cases/mo) Ð 169 in black-

backed jackals (1.3 cases/mo), 65 in dogs (0.5 case/mo) and 16 in bat-eared foxes (0.1

case/mo) Ð were reported during 1986±1996. Epidemio-surveillance indices (% of total

cases that were submitted and % of laboratory submitted cases that were confirmed) were

consistently high (�79%) throughout the study period (Table 1). However no substantial

bias was believed to exist because the correlations between confirmed cases and the

surveillance indices were small (0.11, 0.24, and 0.23) and non-significant (P > 0.3).

3.2. Long-term trend

Long-term trend was almost negligible. Over the 11 yr period it amounted to �0.9,

ÿ0.5, �0.3 and �0.1 cases in domestic ruminants, black-backed jackals, dogs and bat-

eared foxes, respectively.

Table 1

Indices of rabies surveillance level in central Namibia, 1986±1996

Year Total

reported

cases

Total

confirmed

cases

% of total reported

cases that were

submitted

% of laboratory-

submitted cases

that were confirmed

1986 90 65 79 91

1987 114 86 86 88

1988 151 113 94 80

1989 115 104 92 98

1990 101 89 95 93

1991 79 65 95 86

1992 111 106 97 98

1993 56 50 98 91

1994 81 71 98 89

1995 145 131 95 95

1996 95 83 99 88


3.3. Seasonality

Two distinct and continuous periods were observed in all species (Fig. 1). In general,

the number of cases was below average in the first semester and above average in the

second semester. Seasonality was confirmed by the autocorrelation coefficient for the 12

mo lag (r12) in domestic ruminants (r12 � 0.18, p � 0.06) and black-backed jackals

(r12 � 0.31, p < 0.01). However the autocorrelation coefficient for the 12 mo lag

(r12 � ÿ0.01, p � 0.44) in dogs was not significant although that for the 24 mo lag was

(r24 � 0.20, p � 0.02). In bat-eared foxes, 63% of the cases (10/16) occurred between

June and September. However, categorization by season was not conducted for this

species due to small number of cases.

Two distinct rainfall seasons are also present but `̀ reversed'' compared to rabies (Fig.

1). Rainfall seasonality was also supported by the significant (p < 0.01) autocorrelation

coefficient for the 12-month lag (r12 � 0.50).

3.4. Cyclical variations

A 3±4 yr cycle in the number of cases in domestic ruminants and black-backed jackals

was observed (Fig. 2). Rabies in black-backed jackal exhibited similar fluctuations, with

three peaks approximately in phase with those in domestic ruminants. Cyclical variations

for dogs and bat-eared foxes were not examined due to the small numbers of cases seen in

these species.

3.5. Temporal associations between species-specific time series

1. Domestic ruminants and canids (black-backed jackals and dogs): The domestic-

ruminant (DOM_RUM) time series was positively cross-correlated with jackal

(JACKAL) and dog (DOG) time series at and around lag 0 (Table 2). A dynamic

regression model was therefore built with DOM_RUM as the dependent variable and

JACKAL and DOG as explanatory variables. The final model selected was:

DOMRUM � 1:55� 0:62 JACKAL� 0:57 DOMRUM �ÿ1�ÿ0:37 AR �ÿ1�All coefficients including JACKAL were highly significant (p < 0.001); the DOG variable

was dropped from the model because its coefficient became non-significant (p � 0.08) as

the other variables entered in the model. (The model can be interpreted as is typical of

regression; e.g., when all other variables were held constant an increase of one black-

backed jackal case in a given month was associated with an increase of 0.62 cases in

domestic ruminants.) The DOM_RUM[ÿ1] term expressed the presence of a significant

autocorrelation of lag 1 (r1 � 0.4) in the time series DOM_RUM, which is a typical

feature of time series. Observed and model-predicted data are presented in Fig. 3,

goodness-of-fit statistics in Table 3.

2. Dogs and black-backed jackals: JACKAL at time tÿ1 was positively cross-correlated

with DOG at time t (r � 0.2, p � 0.004). Dynamic regression with DOG as the

dependent variable and selected JACKAL[ÿ1] as the only statistically significant


Fig. 1. Seasonal indices obtained by additive decomposition of time series of rabies laboratory-confirmed cases in domestic ruminants, black-backed jackals and

domestic dogs between 1986 and 1996, and of average rainfall between 1986 and 1995 over central Namibia.

20

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Fig. 2. Cyclical variation of rabies confirmed cases in central Namibia, 1986±1996, obtained by single exponential smoothing of deseasonalized data.

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Table 2

Cross-correlations between different time series by species of confirmed rabies cases lagged by k time periods, central Namibia, 1986±1996

Species k (mo)

t t � k ÿ10 ÿ9 ÿ8 ÿ7 ÿ6 ÿ5 ÿ4 ÿ3 ÿ2 ÿ1 0 1 2 3 4 5 6 7 8 9 10

Jackals Domestic

ruminants

0.2 0.1 0.0 ÿ0.1 ÿ0.2 ÿ0.2 ÿ0.2 ÿ0.1 0.1 0.3a 0.4a 0.4a 0.3a 0.2 0.0 ÿ0.1 ÿ0.2 ÿ0.3a ÿ0.2a ÿ0.2 ÿ0.1

Dogs Domestic

ruminants

0.0 ÿ0.1 ÿ0.2 ÿ0.1 0.0 0.0 0.0 0.1 0.2 0.3a 0.3a 0.3a 0.1 0.0 ÿ0.1 ÿ0.2 ÿ0.1 ÿ0.1 ÿ0.1 0.0 0.0

Jackals Dogs 0.1 0.2 0.1 0.0 ÿ0.1 0.0 ÿ0.1 ÿ0.1 0.0 0.1 0.1 0.2a 0.2 0.1 0.1 0.1 ÿ0.1 ÿ0.1 ÿ0.1 ÿ0.2 ÿ0.1

a P < 0.01.

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Fig. 3. Observed and predicted (dynamic regression model) time series of rabies laboratory confirmed cases in domestic ruminants over central Namibia, 1986±1996.

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explanatory variable and resulted in the following model:

DOG � 0:37� 0:10 Jackal �ÿ1�JACKAL[ÿ1] appeared here not only as being statistically significantly (p � 0.01)

associated with the DOG variable but also as either being a potential causal predictor or

infected earlier from a common source as the dog. An increase of one black-backed

jackal case at month tÿ1 predicted an increase of 0.10 cases in dogs at month t. However,

the interpretation of the analysis of the DOG variable should be done with caution

because the time series of dog rabies had a small number of cases, and the graph was also

uninformative because of many months with no cases. Goodness-of-fit statistics are

presented in Table 3.

3.6. Effects of rainfall on rabies seasonal and cyclical fluctuations

On a monthly basis, as we have seen in Fig. 2, rainfall (Tables 4 and 5) and rabies

series have a seasonal pattern. They also appear negatively correlated, with a high number

of cases during periods of low rainfall and vice versa. The analysis of cross-correlations

between the two series confirmed this observation: the correlation coefficient was

negative at and around lag 0 for example rlag 1 � ÿ0.39 with p < 0.001, and positive when

the series were lagged by approximately half a year (rlag7 � 0.54; p < 0.001).

Table 3

Goodness-of-fit statistics for the dynamic regression time series models of rabies in central Namibia, 1986±1996

Model Variables t statistic p Ljung-Box

statistic

p Bayesian

Information

Criterion

DOM_RUM JACKAL 4.33 <0.001 9.93 0.07 3.18

DOM_RUM[ÿ1] 7.28 <0.001

CONSTANT 3.57 <0.001

Auto regressive ÿ3.70 <0.001

DOG JACKAL[ÿ1] 2.56 0.021 16 0.41 0.72

CONSTANT 4.72 <0.001

Table 4

Spearman rank correlations between annual rainfall and annual rabies cases for all species combined (n � 963)

and for black-backed jackal (n � 169) in different districts of central Namibia, 1986±1995a

Regional weather

station/district

Species Number of paired

observations (years)

Correlation p

All districts All species 10 ÿ0.32 0.17

All districts Black-backed jackal 10 0.05 0.45

Otjiwarongo All species 9 ÿ0.87 0.01

Windhoek All species 10 0.13 0.34

Windhoek Black-backed jackal 10 ÿ0.45 0.10

Grootfontein All species 10 ÿ0.34 0.15

a No weather data available for 1996.


3.7. Variations in livestock population and vaccination coverage

During the study period, the variation in cattle population was small (never exceeding

15% of total cattle population, which at its highest was 500 844 heads. Vaccination

coverage was also small; it varied between 2 and 10% of the total cattle population.

4. Discussion

As mentioned in the case-definition section, if a cluster (�1 animal of a single species)

of suspected cases was a confirmed rabies case, only a single confirmed case would be

reported. This definition was necessarily restrictive because the reporting system did not

record multiple submissions of a single species captured at a single time and location.

The obvious potential bias resulting from such a recording system would be

underreporting of cases. However, we felt that the bias was minimal, given the small

number of suspected cases reported per month and the random movement of rabies-

infected animals.

Evaluation of the different factors (surveillance, population and preventive measures)

that could have differently influenced through the years the number of confirmed cases

reported in the database did not indicate any important potential variability. Therefore,

the temporal variations of observed confirmed rabies cases were considered credible

indicators of the temporal variation of rabies in the field.

A common seasonal pattern was observed among all species, with an increase in cases

from June through November. This pattern has been reported from other regions of

southern Africa where black-backed jackal rabies is reported (Barnard, 1979; Bingham

and Foggin, 1993). In the present study, dynamic regression has shown evidence that the

black-backed jackal might play a role in the temporal dynamics of the disease in domestic

ruminants and dogs. The seasonal pattern of rabies can be explained on the basis of

environmental considerations related to black-backed jackal ethology. Contact rates

among black-backed jackal populations increase as home range increases when the

availability of water and food become scarce during the dry season (Ferguson et al., 1983;

Table 5

Annual rainfall (mm) in weather stations of central Namibia, 1986±95

Year Windhoek Gobabis Otjiwarongo Grootfontein Average

1986 438 292 N/A 541 424

1987 415 271 403 420 377

1988 449 436 446 417 437

1989 390 338 333 477 384

1990 348 291 361 393 348

1991 196 428 529 453 402

1992 337 335 499 351 380

1993 249 310 467 501 382

1994 320 399 453 879 513

1995 196 81 189 318 196


Mckenzie, 1993). The dry season (May±November) in central Namibia immediately

precedes the dispersal (April) and includes the mating season (June±July) of the black-

backed jackals when new pairs are being formed and new territories established

(Bingham and Foggin, 1993; Ferguson et al., 1983; Mckenzie, 1993). This combination

of factors results in favorable conditions for yearly rabies epidemics after an appropriate

incubation period following exposure. The dry season appears to be a risk factor for

rabies exposure. However, we were not able to differentiate between the individual effects

of absence of rain on the one hand and the behavioral ecology of black-backed jackals on

the other hand because they were seasonally confounded.

The 3±4 yr cyclical patterns found in domestic-ruminant rabies as well as in black-

backed jackal rabies are consistent with prior reports of peaks in 1982 and 1985 for the

same species in the whole country (Hubschle, 1988; Veterinary Services Namibia,

unpublished). A subjective impression was reported that relatively dry years were

associated with high incidence of rabies and vice versa in other words, a negative

correlation with rainfall (Hubschle and Uanguta, 1995). However, our investigation found

no strong statistical evidence of this type of association: out of 6 tests, only one

significant negative correlation was found. In Europe, the cyclical variations of sylvatic

rabies have been explained by variations through time of the population dynamics in the

red-fox reservoir species (Chomel, 1993).

Although developed for the analysis of economic data, time-series analysis is a fruitful

analytical tool for understanding temporal patterns of infectious diseases like rabies

(Childs et al., 1997; Curk and Carpenter, 1994). There are various time-series-analysis

methods available. One could make the reasonable assumption that the merit of a

particular method could be based on its ability to forecast. On a large-scale study

involving the forecasting of 1001 different time series data sets, Makridakis et al. (1982)

found that when confronted with irregular, monthly seasonal data like ours,

decomposition of the time series followed by single exponential smoothening of the

deseasonalized data (such as conducted in this study) outperformed more-complicated

commonly used methods like ARIMA or Holt-Winters. As an example to illustrate the

extent of variation in our data, the irregular component of the domestic ruminant rabies

variable accounted for 56% of the time series variability.

In their work on rabies in rodents and lagomorphs in the eastern United States, Childs

et al. (1997) used cross-correlations between the different species time series to

investigate possible disease interaction between species. Those authors found associa-

tions among the different species studied; however, those relationships were more

complex than were ours Ð involving longer lags (3 mo) and sometimes biseasonal (6 mo)

cross-correlations. In central Namibia, the rabies temporal shape appears homogeneously

centered on the time series of the black-backed jackal.

In the temporal analysis the domestic-dog variable was of secondary importance. We

believe it likely that the cycle is self-maintained in the jackal population and that dog

cases may be the consequence of fights with rabid black-backed jackals. In Europe, the

rabies cycle appears to be self maintained in the red fox population and rare canine cases

originate from spillovers (Aubert, 1995). This would have consequences on the choice of

control strategies. Strain identification using bio-molecular techniques would offer a

valuable means to further investigate the genetic relatedness of cases between jackals and


dogs found in spatial-temporal clusters of disease (Smith et al., 1993; Von Teichman

et al., 1995).

Cyclical forecast is predicting the next rise in rabies cases in central Namibia in 1998

or 1999. Therefore, a major vaccination effort should be considered for these 2 yr. Based

on the seasonal pattern and a conservative mean incubation period in cattle of 2±3 mo,

domestic animals should be immunized before May.

In the long-term, vaccination of dogs alone appears unlikely to solve the problem and

oral vaccination of the black-backed jackal should be considered (Bingham and Foggin,

1993; Bingham et al., 1995). Baits could be strategically deposited at the beginning of

April when the dry season and the dispersal of young jackals start. In southern Texas,

encouraging results have been obtained after three oral vaccination campaigns (1995,

1996 and 1997) with dropping of 30 baits/km2 to immunize coyotes (Canis latrans)

(Fearneyhough et al., 1997). The semi-arid acacia savanna of southern Texas (Department

of the Interior, 1970) is rather similar to the one of central Namibia (Istituto Geografica

de Agostini, 1976). Coyotes and black-backed jackals have very similar ethology

(Foggin, 1992; Mckenzie, 1993), therefore these vaccination campaigns offer good

background information on how a control plan could successfully be implemented in

central Namibia. However, the area to be covered in central Namibia is substantially

larger (200 000 km2) than the one in Texas (85 264 km2) Ð making the economic and

practical feasibility of such a project more difficult. Further studies would also have to be

conducted to estimate how the population dynamics in the black-backed jackal would

react to the removal of rabies infection, and how it would affect the ecological balance in

the central stock-ranching areas of Namibia.

Acknowledgements

The authors thank Bertchen Kohrs from the Directorate of Veterinary Services of

Namibia and James Case from the California Veterinary Diagnostic Laboratory, Davis,

CA, for their help in conducting this study. This study was supported by the 96±97

Lavoisier grant from the French Ministry of Foreign Affairs, as well as a grant from the

Merial company, Department of Preventive Strategies, Lyon, France.

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Documents

Temporal patterns of domestic and wildlife rabies in central Namibia stock-ranching area, 1986–1996