Modelling Transmission of Bovine Tuberculosis in Red Deer and Wild Boar in Normandy, France


G. Zanella. Epidemiology Unit, Animal Health Laboratory, 23 avenue du Général-de-Gaulle, 94706 Maisons-Alfort Cedex, France. Tel.: +33 1 49773836; Fax: +33 143689762; E-mail:


In early 2001, Mycobacterium bovis infection was confirmed in red deer (RD) (Cervus elaphus) shot in Normandy region, France. An epidemiological survey conducted during the following hunting season in two connected forests confirmed the occurrence of the disease in both free-ranging RD and wild boar (WB) (Sus scrofa). This was the first detected bovine tuberculosis outbreak in wildlife in France. We present a simple deterministic age-structured model of the within- and between-species M. bovis transmission in RD and WB populations that distinguishes direct transmission (horizontal and pseudo-vertical) and indirect transmission through contaminated offal left behind by hunters. Results issued from the epidemiological surveys conducted in Normandy forests were used to estimate transmission parameters. Because data for RD and WB populations were not available, population sizes at demographic equilibrium were estimated and used to run the model. We qualitatively tested different control measure scenarios with our model, considering different mortality rates and offal harvesting, to determine which ones affect the success of infection control. The most realistic control scenario would combine the total depopulation of RD and good compliance with offal harvesting, because the model suggests that infected offal left by hunters represents the main transmission source of M. bovis in the field.


  •  Bovine tuberculosis is a transmissible disease, which mainly affects cattle but has been reported in various wildlife species. In 2001, it was detected in wildlife in France for the first time.
  •  Bovine tuberculosis control in wildlife is challenging.
  •  We used a simple deterministic model to simulate bovine tuberculosis transmission in two wildlife species in France to test different control measure scenarios.


Bovine tuberculosis is a transmissible disease, which mainly affects cattle (Morris et al., 1994). However, it has been reported in various wildlife species (Coleman and Cooke, 2001; Delahay et al. 2007), and wildlife reservoirs for Mycobacterium bovis have been documented (Gallagher and Clifton-Hadley, 2000; Coleman and Cooke, 2001; O’Brien et al., 2002; Parra et al., 2005). Mycobacterium bovis can survive in the environment from 7 days to 6 months according to temperature and humidity conditions (Phillips et al., 2003). Transmission from pasture, soil and faeces appears to be small in most environments compared with other mechanisms of transmission (Morris et al., 1994).

France was officially declared bovine tuberculosis free in 2000 by the European Commission and, at that time, there was no indication of a wildlife reservoir. In early 2001, macroscopic tuberculosis-like lesions were observed in three red deer (RD) (Cervus elaphus) that were shot by hunters in the Brotonne forest in Normandy. Mycobacterium bovis infection was confirmed by culture from affected organs. An epidemiological survey conducted during the following hunting season (2001–2002) in the Brotonne forest and the nearby Mauny forest confirmed the occurrence of bovine tuberculosis in both RD and wild boar (WB) (Sus scrofa) (Zanella et al., 2008a). This was the first known bovine tuberculosis outbreak in wildlife in France. The Brotonne forest (81 km2) and the nearby Mauny forest (10 km2), both in Normandy (49°21′–49°27′N, 0°51′–0°55′E), are connected by a strip of land that allows wild animals to move freely between the two. Both forests are bounded by the Seine River except in the South where they are bordered by a highway, which makes it practically impossible for wild animals to move between these two forests and other forests. No lesions, suggesting a M. bovis infection, were found in the hunted wild animals in the surrounding forests. RD and cattle often share the same pastures around the Brotonne forest. In all likelihood, the infection was originally transmitted to wild RD from cattle, the most abundant and natural host of M. bovis, when the prevalence of infection was high in livestock in the region; the infection then spread within the RD population. Molecular typing of the M. bovis strain isolated showed that it was the same as the one reported to have been circulating in cattle herds around the Brotonne and Mauny forests since at least 1995 (Zanella et al., 2008a). Once established in the RD population, it is very likely that the infection spread to the WB population through scavenging of contaminated RD offal left by hunters. Indeed, offal disposal was not then mandatory during the hunting season. Control measures were implemented in late 2002 and included the reduction in RD population levels, a ban on supplemental feeding and the destruction of offal from hunted animals. However, the occurrence of transmission from contaminated offal after this date cannot be excluded because offal disposal was not fully implemented. During the 2005–2006 hunting season, a second survey was conducted to evaluate the progression of the disease in the affected species and assess the effect of control measures.

Several mathematical models have been developed to represent bovine tuberculosis transmission and to assess control measures in wildlife species, namely badger (Meles meles), possum (Trichosurus vulpecula) and white-tailed deer (Odocoileus virginianus) (Smith, 2001). Most of these models consider only one M. bovis host. The first model for bovine tuberculosis in badgers, developed by Anderson and Trewhella (1985), was a deterministic susceptible-exposed-infectious (SEI) density-dependent transmission model, which included pseudo-vertical transmission. This model was revisited to take into account different aspects of transmission or badger population dynamics and control measures (Bentil and Murray, 1993; Barlow, 1996; Ruxton, 1996; Swinton et al., 1997). Spatial simulation models were also developed to examine tuberculosis in badger populations (White and Harris, 1995b) and its possible control measures (White and Harris, 1995a,b; White et al., 1997). Smith et al. (1995, 1997) investigated differential transmission in badgers and control measures (infectious and super-infectious states) in an individual-based small-scale model. It was further extended onto a larger grid to examine sex differences in transmission and included cattle herds in a simplified form (Smith et al., 2001). Transmission between badgers and cattle was studied in an SI model (Cox et al., 2005). Differential equation models have also been developed to study tuberculosis transmission in possums (Barlow, 1991b, 1996). More complex possum tuberculosis models include different contact rate functions (Roberts, 1996; Roberts and Saha, 1999), dynamic population (Roberts and Kao, 1998), spatial disease spread (Barlow, 1993, 2000; Fulford et al., 2002) and individual-based models (Pfeiffer, 1994). Some of these models were used to test different tuberculosis control measures in possum populations (Barlow, 1991a, 1996; Roberts, 1996). Kao and Roberts (1999) developed a combined possum-cattle tuberculosis model, which included the economics of control options. Bovine tuberculosis has also been modelled in a white-tailed deer population in the USA with a probabilistic Markov chain model (McCarty and Miller, 1998).

The objective of this paper is to present a simple model of within- and between-species M. bovis transmission in RD and WB populations, taking into account transmission through infected offal. Results obtained from the epidemiological surveys conducted in the Brotonne and Mauny forests were used to estimate transmission parameters. The model developed was used to test qualitatively different control measure scenarios.

Materials and Methods


Three epidemiology surveys were conducted during the 2001–2002, 2005–2006 and 2006–2007 hunting seasons. Hunters were asked to cooperate by presenting the hunted animals for necropsy. RD age was estimated for the 2001–2002 and 2005–2006 hunting seasons. Prevalence data were therefore computed according to two age categories: ≤1-year-old and >1-year-old animals (Table 1). For WB, only the overall number of animals hunted per year was available, with no indication of age. Prevalence was estimated according to M. bovis culture results except for RD in the 2005–2006 hunting season when it was estimated from the occurrence of macroscopic lesions.

Table 1.   Observed and predicted Mycobacterium bovis prevalence in red deer (RD) and wild boar (WB) by epidemiological survey year in the Brotonne and Mauny forests
Hunting seasonSpecies
≤2 years old>2 years old≤2 years old>2 years old
  1. aEstimated from macroscopic lesions.

2001–20020.11 (n = 27)0.13 (n = 45) (n = 84)0.29
2005–20060.14 (n = 59)0.32 (n = 79)0.150.320.37 (n = 155)0.34
2006–20070.07a (n = 149)0.260.32 (n = 255)0.32


The model is a deterministic, state transition model of M. bovis transmission in two populations: a RD population and a WB population. It incorporates both within- and between-species disease transmissions. Time is discrete with a time step of 1 year: a time step begins with the birth of the animals and ends with the hunting season. A population of species A (either RD, denoted RD or wild boar, denoted WB) is represented by a state variable structured according to age and health state. Three health states are considered: susceptible (denoted S), latent (denoted E) and infectious (denoted I). The duration of the latent phase is assumed to be 1 year. Three age categories are defined: ≤1 year old (category 1), 1–2 years old (age category 2) and >2 years old (age category 3). For the two species considered, it is assumed that sexual maturity occurs at over 2 years old (MacDonald and Barrett, 1993). Hunting is assumed to be the main cause of mortality in both modelled populations. Because of the specific topography of the modelled area (the forest studied is completely bounded by the Seine River and by a highway), emigration and immigration are considered negligible.

Let At(y, z) denote the number of animals of species A (RD or WB) in age category y (1, 2 or 3) that are in health state z (S, E or I) at time t. The dynamics for a population of species A is described by the Equations 1 and 2 for age category 1, Equations 3–5 for age category 2 and Equations 6–8 for age category 3.


These equations incorporate both demographic and infectious processes.

Demographic processes involve the birth of the animals at the beginning of each time period, their ageing and also their death during the hunting season at the end of each time step: λAt denotes the birth rate for species A (number of offspring per reproductive female for year t), which varies with time, and μΑ(y) denotes the age- and species-specific mortality rate, for species A and age category y. Sex ratio is assumed to be 1 : 1; thus, half of the animals of age category 3 are breeding females.

Infectious processes result from three contagion modes: pseudo-vertical, direct and indirect contagion. Pseudo-vertical contagion represents contamination of young animals through contaminated milk or through close contact with their mother. It is dependent on a species-specific transmission parameter denoted νA and on the proportion of infectious breeding females denoted VAt:


where inline image represents the total number of age category 3 animals, summed over all the health states (similarly, in the equations below, summation indices will be replaced by dots). Horizontal transmission represents direct transmission of M. bovis between two animals of the same species (for behavioural reasons, direct transmission between two animals of different species is disregarded). It is dependent on a species-specific transmission parameter denoted βA and on the proportion of infectious animals in the population denoted HAt:


Indirect contagion occurs when live animals come into contact with dead animals or with infected offal left by hunters, through scavenging (WB) or exploratory behaviour (RD). Contamination of animals of species A by contact with infected offal from species X (X being either the same species A or the second species B) is dependent on a transmission parameter specific to the pair of species considered (ϕXA) and on the proportion of infectious animals (JXt) among the dead animals of species X:


In Equations 1–8, force of infection depends on the contagion modes to which animals are exposed. As animals ≤1 year old (category 1) are exposed to the three contagion modes, the corresponding force of infection, rAt, in Equations 1 and 2, is:


Animals >1 year old (age categories 1 and 2) are not exposed to pseudo-vertical transmission; in Equations 3–8, the force of infection is thus:



Population dynamics

As no reliable data on RD and WB population sizes were available, RD and WB populations were assumed to be at demographic equilibrium before the introduction of M. bovis. In this case, the number of animals born each year compensates for the number of animals killed each year during the hunting season (see details in Appendix).

Infection dynamics

As the molecular profile of the corresponding strain was first identified in 1995 in cattle, three possible dates of M. bovis introduction in the RD population were considered: 1985, 1990 and 1995. Previous introduction dates would have led to its earlier detection considering that RD are not very resistant to M. bovis (Clifton-Hadley and Wilesmith, 1991) and that even very young animals show visible lesions. The model was thus run from the date of M. bovis introduction until 2006, the initial situation being demographic equilibrium with a single infectious RD (>2 years old, age category 3).

Until the date of implementation of control measures (2002–2003), mortality rate values estimated for demographic equilibrium were applied. From 2002–2003 to 2006–2007, the real number of animals hunted was used, and the efficacy of offal harvest implementation was taken into account by reducing the transmission rates from dead animals ϕAB by a coefficient ϕmin. Two values were considered for this parameter: 0.01 and 0.1.

The model incorporates eight transmission parameters according to the mode of contagion and the species: one direct transmission parameter and one pseudo-vertical transmission parameter per species, and four transmission parameters from offal, as transmission can occur through contact with infected offal from animals of the same species or other species. To estimate these parameters, we defined links between homologous parameters in the two species considered. Links between parameters related to contagiousness were defined first, given that contagiousness differs from species to species (Zanella et al., 2008b). The ratio of WB to RD contagiousness was therefore assumed to be constant:


Links between parameters related to exposure differences were also defined, considering that behavioural differences between RD and WB should lead to differences in exposure to M. bovis. As for contagiousness, the ratio of susceptibility to offal infection for WB and RD was thus assumed to be constant:


Five parameters were thus estimated from epidemiological data (βRD,νRD, ϕRD-RD, k1 and k2). The R function nlminb (GNU project, Free Software Foundation) was used to minimize the sum of squared deviations between the observed and predicted prevalence values for the 2001–2002, 2005–2006 and 2006–2007 hunting seasons (Table 1).

Model exploitation

The model was used to investigate the progression of the epidemiological situation from 2007 to 2008 based on scenarios about mortality rates and offal harvesting.

Three mortality hypotheses were considered:

  • 1 abandonment of over-hunting and return to normal hunting levels, corresponding to mortality rates of the population at equilibrium,
  • 2 total depopulation of RD and return to normal hunting levels for WB,
  • 3 over-hunting for the two species for 5 years (2006–2007 hunting level) and return to a normal hunting level thereafter.

Three offal harvesting levels were considered:

  • 1 perfect harvest (ϕmin = 0),
  • 2 the same harvest level as the one that best fitted the 2001–2002 to 2006–2007 data
  • 3 no offal harvesting (ϕmin = 1).

In total, nine prospective scenarios were thus studied (Table 3), with the time horizon being 2025.

Predicted infection prevalence at equilibrium was calculated, and disease eradication dates were estimated only for comparative purposes.


The set of transmission parameters that best fitted the prevalence data were those corresponding to an introduction of infection in 1995 and a parameter for offal harvesting of 0.1. Estimated transmission parameters indicate higher contagiousness in RD (k1 = 0.76) and a higher exposure of WB to M. bovis (k2 = 4.99). In WB, transmission from infected offal is largely predominant, followed by pseudo-vertical transmission and horizontal transmission (ϕRD-RD = 4.25 > νRD = 0.33 > βRD = 0.06) (Table 2). In RD, the same trend is observed, but the difference between the offal transmission parameters and the other two modes of transmission is less marked (ϕRD-RD =  0.65  >  νRD =  0.43 > βRD = 0.08). The parameter for between-species transmission from offal is much higher from dead RD to WB (3.23) than from dead WB to RD (0.85).

Table 2.   Estimated values of within- and between-species contagion parameters for pseudo-vertical, direct and indirect transmission of Mycobacterium bovis
  1. WB, wild boar; RD, red deer.

Red deer β RD Direct transmission0.08
ϕ RD-RD Transmission from offal of dead red deer0.65
ν RD Pseudo-vertical transmission0.43
WB β WB Direct transmission0.06
ϕ WB-WB Transmission from offal of dead WB4.25
ν WB Pseudo-vertical transmission0.33
Between-species ϕ RD-WB Transmission from offal of dead red deer to WB3.23
ϕ WB-RD Transmission from offal of dead WB to red deer0.85

Based on results for predicted prevalence (Table 1), the model fitted the prevalence data for RD in 2001–2002 and 2005–2006 reasonably well, while in 2006–2007, it overestimated the prevalence for this species. For WB, the predicted prevalence was in line with the observed prevalence.

According to scenario 1, the model predicts that with perfect offal harvest efficacy, the number of infected animals (latent + infectious) decreases in both species from 2008 to 2009 until 2025, when there are 49 infected RD and 10 infected WB (Table 3). When the offal harvest efficacy is the same as the 2001 to 2007 level (scenario 2), the number of infected animals in the RD population increases (108 in 2020), while steadily decreasing in the WB population until 2020 (326) and increasing again thereafter. The non-implementation of offal harvesting induces a progressive increase in the number of infected animals that reach very high levels in 2025 (scenario 3). In these three scenarios, where a hunting level at demographic equilibrium is applied to RD and WB, population sizes increase steadily but do not reach their equilibrium level by 2025.

Table 3.   Predicted population sizes in 2025, number of infected animals and Mycobacterium bovis infection prevalence, under nine prospective scenarios for red deer (RD) and wild boar (WB) Thumbnail image of

With the total depopulation of RD in 2007 and with a perfect offal harvesting (scenario 4), the number of infected WB decreases gradually until 2025. At this date, the number is the same as in scenario 1. It also decreases – but not so sharply (63 infected animals in 2020) – if the WB offal harvest is less effective (scenario 5). If harvesting is not implemented (scenario 6), the model predicts that infection may be maintained in the WB population: the number of infected animals increases to reach 917 in 2025. The WB population size in 2025 is the same as in scenarios 1, 2 and 3 because the hunting level at demographic equilibrium was applied.

If over-hunting of RD and WB is pursued for 5 years at the same level as in 2006–2007 (mortality rate of 0.41 for ≤1-year-old RD; 0.42 for >1-year-old RD and 0.66 for WB), the number of infected animals is very low in 2025 (11 RD and one WB) with a perfect offal harvest (scenario 7). When the harvest is not exhaustive (scenario 8) or is not carried out (scenario 9), the number of infected animals in both species decreases to low levels (17 RD and 40 WB in 2012 in scenario 8; 50 RD and 112 WB in scenario 9) and then begins to increase until 2025. Population sizes in these scenarios are low in 2025.

From the prevalence at equilibrium, we can see that in the long-term scenarios 1, 4, 5 and 7 would allow eradication of the infection; more rapidly for those scenarios that include total depopulation of RD.


Mathematical modelling helps to focus attention on elements that must be taken into account regarding disease transmission in a population (Smith et al., 1995; Barlow, 1996). The model that we developed thus considers the most important points shown by epidemiological surveys on tuberculosis transmission in RD and WB. Furthermore, simulations performed using mathematical models complement field data because they can be used to test the effects of control measures (Gormley and Collins, 2000). These predictions can then be verified in the field. We tested different control measures qualitatively with our model to show which ones could play a determinant role.

We developed an original model that explores within- and between-species transmission of M. bovis in two wildlife populations, distinguishing direct transmission (horizontal and pseudo-vertical) and indirect transmission through contaminated offal. Three health states (SEI) and a 1-year stay in compartment E (exposed) instead of the 2 years proposed by McCarty and Miller (1998) for white-tailed deer seemed more appropriate to us in view of the pathogenesis of the disease in RD and WB.

The estimated ratio of WB to RD contagiousness (k1) was <1, which is in line with different patterns in tuberculosis lesions found in RD and WB in the field, suggesting that contagion spreads more easily from RD than from WB (Zanella et al., 2008b). Indeed, lesions in RD are encapsulated and their rupture can enhance contact with the viable M. bovis present in the case, while in WB, the overall predominance of calcified granulomatous lesions suggests an appropriate immune response. Thus, within-species transmission by direct contact seems to be more common among RD. For the same reason, indirect transmission through contact with infected offal would occur more frequently with RD offal than with WB offal.

Conversely, the estimated ratio (k2) of susceptibility to offal infection for WB and RD was much higher than one which is line with ethological characteristics of these species: WB should get contaminated more easily than RD because of their scavenging habits. The contamination of RD from this source is much less common but cannot be ruled out because of the animals’ exploratory behaviour that can expose them to contaminated carcasses or offal.

The main transmission route is predicted to be through infected offal for both species, as the highest value parameters correspond to transmission from offal. This is the first time that this mode of transmission, linked to hunting practices, has been highlighted in RD and WB by a mathematical model. Indirect transmission from contaminated food has been mentioned for white-tailed deer in Michigan (USA) (Schmitt et al., 1997). In our model, we did not consider this source of contamination but it is possible that it may have contributed to the within-species transmission in RD before the ban on supplemental feeding was implemented in 2002.

In both species, the pseudo-vertical transmission parameter is more than five times that of direct transmission, which is coherent with greater fawn exposure to infection through close contact with infected dams. The direct transmission parameter is estimated to be much lower than the values found by McCarty and Miller (1998) in their white-tailed deer tuberculosis transmission model (females = 0.5, males = 8.1). However, values are hardly comparable as their study did not consider indirect transmission from dead animals specifically.

The set of transmission parameters allowed an appropriate fit of the model to field data. For RD, the reduction in M. bovis prevalence predicted by the model is not as marked as the reduction observed from 2005–2006 to 2006–2007. It should be taken into account that, for 2006–2007, infection prevalence was indirectly estimated from macroscopic lesions in this species. This approach may have led to an underestimation of infection prevalence.

From a prospective point of view, our model allowed a qualitative appreciation of the effects of combining different modalities of two tuberculosis control measures with regard to hunting and offal harvesting. From the scenario results, we can conclude that offal harvesting is the factor that plays the major role in infection control. When harvesting is carried out perfectly, infection can always be controlled. This is not the case when offal harvesting is not strictly applied or is not implemented at all. The other factor that may influence the outcome is the total depopulation of RD. With this control measure, the infection may be eradicated even if offal harvesting is not carried out perfectly. This second possibility is more in accordance with field conditions.

The most realistic scenario combines the total depopulation of RD and an efficient application of the offal harvesting. RD eradication was implemented in the 2007–2008 hunting season. Natural boundaries that prevent RD immigration from other areas made this possible. Survey results from the 2007–2008 to 2009–2010 hunting seasons in the Brotonne and Mauny forests seem to confirm predictions of this scenario. Indeed, a decreasing trend in the prevalence of M. bovis in WB was observed. In the long term, an effort will have to be made to enforce offal harvesting for hunted WB. Even in this case, it might take a long time to eradicate infection in WB populations. A similar situation occurred in Australia where, 20 years after the eradication of the main wild reservoir of the disease (wild buffaloes), feral pigs were found to be infected at low prevalence (Corner et al., 1981; McInerney et al., 1995).

The epidemiological characteristics of the M. bovis outbreak in the Brotonne and Mauny forests are unique. Model predictions could therefore only be validated in that context by comparing them to future control measure effects on the progression of the disease. However, the model structure allows its use in similar contexts where transmission from dead animals plays an important role in disease transmission between two or more species.


We would like to thank hunters for submitting the animal carcasses and veterinarians from the National Hunting and Wildlife Agency (Office National de la Chasse et de la Faune sauvage) for performing necropsy examination and sampling. We also thank the technicians in the District Laboratories and in the Anses Animal Health Laboratory of Maisons-Alfort who performed the tests and the National Forests Agency (Office National des Forêts) for providing information on hunted red deer and wild boar in the Brotonne and Mauny forests. The study was funded by the French Ministry of Agriculture.

Conflicts of interest

The authors have declared that there are no conflicts of interest.