# Dairy goat demography and Q fever infection dynamics.

Lenny Hogerwerf, Aurélie Courcoul, Don Klinkenberg, François Beaudeau, Elisabeta Vergu, Mirjam Nielen

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Lenny Hogerwerf, Aurélie Courcoul, Don Klinkenberg, François Beaudeau, Elisabeta Vergu, et al. Dairy goat demography and Q fever infection dynamics. Veterinary Research, 2013, 44, pp.13. 10.1186/1297-9716-44-28. hal-02650291

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# Dairy goat demography and Q fever infection dynamics

Lenny Hogerwerf<fnref n="1" />*, Aurélie Courcoul²,³,⁴, Don Klinkenberg<fnref n="1" />, François Be)audeu²,³, Elisabeta Vergu⁵
and Mirjam Nielen<fnref n="1" />

## Abstract

Between 2007 and 2009, the largest human Q fever epidemic ever described occurred in the Netherlands. The source was traced back to dairy goat farms, where abortion storms had been observed since 2005. Since one putative cause of these abortion storms is the intensive husbandry systems in which the goats are kept, the objective of this study was to assess whether these could be explained by herd size, reproductive pattern and other demographic aspects of Dutch dairy goat herds alone. We adapted an existing, fully parameterized simulation model for Q fever transmission in French dairy cattle herds to represent the demographics typical for Dutch dairy goat herds. The original model represents the infection dynamics in a herd of 50 dairy cows after introduction of a single infected animal; the adapted model has 770 dairy goats. For a full comparison, herds of 770 cows and 50 goats were also modeled. The effects of herd size and goat versus cattle demographics on the probability of and time to extinction of the infection, environmental bacterial load and abortion rate were studied by simulation. The abortion storms could not be fully explained by demographics alone. Adequate data were lacking at the moment to attribute the difference to characteristics of the pathogen, host, within-herd environment, or a combination thereof. The probability of extinction was higher in goat herds than in cattle herds of the same size. The environmental contamination was highest within cattle herds, which may be taken into account when enlarging cattle farming systems.

## Introduction

Q fever, a zoonotic disease caused by the bacterium *Coxiella burnetii*, has been detected in many host species, with ruminants considered to be the main reservoir [1,2]. In most cases the infection in ruminants is asymptomatic, but occasionally abortions occur, which leads to the shedding of large quantities of bacteria in placentas and birth fluids [3]. Transmission between animals and from animals to humans is believed to occur mainly from the environment, through inhalation of contaminated aerosols [1,2]. Most human clinical infections occur in people handling animals or their products and this was generally not perceived as a major public health problem until 2007, when the Netherlands experienced the largest human Q fever epidemic ever described [4,5]. The number of reported human cases was 168 in 2007, 1000 in 2008, 2354 in 2009, 504 in 2010 and 81 in 2011 [6]. The source

of the human epidemic was traced back to dairy goat herds where, within subgroups of several herds during 2005–2009, waves of abortions with an incidence of up to 80% had occurred [5,7-9]. Further details on the abortion patterns in these herds are sparse. Intervention measures included vaccination of dairy goats, followed by culling of all pregnant animals from infected dairy goat herds early 2010 to prevent further shedding into the environment during the following kidding season and thus minimizing human exposure [5,10]. In 2010 and the following years, the number of human cases sharply decreased, suggesting that the intervention measures were effective.

In order to prevent and control future problems with Q fever on goat farms and in humans living close to goat farms, an understanding of the mechanisms driving the abortion storms in goat herds is crucial. Much research has been conducted on Q fever dynamics on cattle farms [11-15], but the Q fever dynamics on goat farms are still poorly understood. In broad terms, while there is some evidence to indicate pathophysiological differences between

<footnote>* Correspondence: l.hogerwerf@uu.nl</footnote>

<footnote n="1">¹Department of Farm Animal Health, Faculty of Veterinary Medicine, Utrecht University, Yalelaan 7, Utrecht 3584 CL, The Netherlands</footnote>

<footnote>Full list of author information is available at the end of the article</footnote>
goats and cattle, the pathogenesis in individual cattle and goats is similar (i.e. reproductive disorders are the main clinical sign, the infection is usually asymptomatic, bacterial shedding occurs mainly through birth products and also through milk, faeces, and other various routes) [16]. Thus while there may be differences in the relative proportion of each shedding route in the whole bacterial shedding, the shedding routes are qualitatively similar. Further, while the rate of abortion may be higher in goats than in cattle, in both species reproductive disorders are the main clinical sign [16]. Therefore, it could well be that the known difference between cattle and goat *C. burnetii* dynamics at the herd level, such as the occurrence of abortion storms solely in goat herds, mainly lies in the population dynamics and farm structure, and not so much the manifestation of the infection in individual cows versus goats. In that case, novel options for Q fever prevention and control might target the host population demographics.

If differences in Q fever abortion patterns for goat and cattle herds are indeed mainly driven by host demographics, the occurrence of abortion waves with large numbers of goats aborting due to Q-fever could result from the fact that goat farms are much larger than cattle farms, and that kidding in goat farms is concentrated in the spring rather than continuous throughout the year. The fact that the abortion waves are such a recent phenomenon in the Netherlands could then be explained by the recent (since the 1990s) major intensification of Dutch goat farming. In 1995, 76 000 goats were housed in the Netherlands, of which 56% stayed in professional dairy goat farms. In 2009, 375 000 goats were housed in the Netherlands, of which 80% stayed on ~350 professional farms with 200–10 000 adult goats each [17,18]. These farms are mainly located in the densely populated province of Noord-Brabant, the province where most human cases were reported. Hence, one of the putative causes of the emergence of Q fever in goats in the Netherlands is the intensive husbandry system in which the goats are kept. However, this has never been investigated.

In this paper we address the question whether the abor-
tion waves in the Dutch dairy goat herds and the differ-
ence with Q-fever abortion patterns in cattle herds can be
explained by herd demographics alone, rather than by a
species specific manifestation of the infection. To this end,
we adapted an existing and fully parameterized simulation
model for within-herd *C. burnetii* transmission in dairy
cattle herds in western France. While keeping disease-
related parameters fixed, we changed only the farm size,
the yearly kidding pattern, and other demographic aspects
to match Dutch goat farms to determine whether abortion
waves as observed in the Netherlands could be repro-
duced. In addition, a sensitivity analysis of the model
outcomes was performed to identify additional factors that
may also in part explain the observed abortion patterns.

**Materials and methods**

A model for the infection dynamics of *C. burnetii* in a French cattle herd developed by A. Courcoul et al. [15] was adjusted to represent the population size, seasonal kidding and other characteristics related to the population dynamics of typical Dutch dairy goat herds and to simulate bacterial spread within the herd.

The original model for cattle herds in western France

The original model, representing the dynamics of *C. burnetii* transmission in French dairy cattle herds, is a stochastic, individual based model with one-week time steps. This model consists of two parts: (i) an epidemiological model, with a compartmental SIR-like structure, coupled with (ii) a population dynamics model, representing introductions of new animals, culling, lactation, and gestation. Both parts of the model are based on data from western France, on endemically infected dairy cattle herds without clinical signs.

The epidemiological part of the model is based on a
standard SIR-like model (susceptible, infectious, recovered),
with added complexity to represent several aspects of *C.
burnetii* transmission and shedding patterns that were
observed in the field. For a full description of the model see
Courcoul et al. [15]. A flow diagram describing the modeled
within-herd spread of *C. burnetii* is provided in Figure 1. In
brief, susceptible animals (in state *S*) can become infected
from the environment (*E*) and move to *I*₁. From *I*₁, the
animals can eliminate the bacterium (go back to *S*) or
become chronically infected, either without (*I*₂) or with (*I*₃)
persistent shedding in milk. In infection states *I*₁, *I*₂, and *I*₃,
shedding occurs through different routes (milk and/or
mucus/faeces) in different quantities (low, mid, high), which
can change from week to week. From *I*₂ and *I*₃, an intermit-
tent shedding pattern can begin by moving to *C*₁ (non-
shedding but still infected individuals) and then between *I*₂
and *C*₁. From *C*₁ the animals can eliminate the bacterium
and move to *C*₂. From *C*₂, reinfection can take place upon
which animals go to *I*₂. During three weeks following infec-
tion, reinfection or resumption of shedding of a pregnant
animal (i.e. *S*→*I*₁, *C*₁→*I*₂ and *C*₂→*I*₂ transitions), abortion may
occur, resulting in temporarily high shedding. Each animal
can abort only once in her life. Of all bacteria shed, which
are expressed in dimensionless units, a proportion that is
dependent on the shedding route enters the environment
and thereby contributes to the environmental contami-
nation level *E*. The decay rate of *C. burnetii* in the environ-
ment, *μ*, includes the natural mortality of the bacterium
and its removal in relation to the periodic cleaning of the
barn. All parameters of the epidemiological model with
their definitions, values and sources are provided in
Additional file 1.

In the population dynamics model, information is rep-
resented on the age of the animals, stage of gestation,
<figure><img src="image_3.png" /></figure>

**Figure 1** Flow diagram describing the modeled within-herd spread of *C. burnetii*. Flow diagram adapted from Courcoul et al. [15], describing the modeled within-herd spread of *C. burnetii*. The health states are the following: *S*, nonshedder apparently susceptible animal, *I*₁, shedder which still has the possibility to eliminate the bacterium and to become *S* again, *I*₂, shedder which no longer has the possibility to become *S* again, *I*₃, shedder which no longer has the possibility to become *S* again and sheds in milk in a persistent way, *C*₁, non-shedder but still infected individual and *C*₂, non-shedder which was *C*₁ in the past but eliminated the bacterium. *I* animals are in the subcategory *m* if they shed in milk only, *mf* if they shed in vaginal mucus/faeces only and *mmf* if they shed in milk and vaginal mucus/faeces. *Environment* represents the environmental bacterial load expressed in dimensionless units, and *p*, the probability of infection or reinfection, is equal to 1 - exp(-*E*̄(*t*)/N). *ε*₁, *ε*₂, and *ε*₃ are the quantities of bacteria shed during a time step by an individual *I*₁, *I*₂, and *I*₃ respectively and contaminating the environment. For any shedder, *ε* represents the sum, for each shedding route, of the quantity of bacteria released, *Qty*, times *p*, its fraction reaching the herd environment. The definitions, values and sources of all parameters in the epidemiological model can be found in Additional file 1.

lactation number and stage of lactation, moment of parturition, moment of introduction into and removal from the herd, for each animal in the herd and for each time step. A description of the model parameters for the herd demography and their values is provided in Table 1.

## Adaptation of population dynamics to goat farms in The Netherlands

Goat population dynamics were modeled based on a mean herd, derived from a questionnaire survey, in 2007 in The Netherlands, of 163 goat herds [19]. In the model, it is assumed that every year, 217 new goats are added to the population at uniform random times during a 12-week kidding season. After birth, goats can leave the herd by age-dependent culling rates (Table 1). The yearly new additions of goats and culling rates result in a goat farm of 770 animals on average, with a realistic age distribution and a yearly 30% replacement rate. Pregnancies and resulting deliveries or abortions (related to *C. burnetii* shedding) are modeled independently of the new additions, through “deliveries” that take place in the same 12-week kidding season. This is done for practical reasons, to keep the herd size constant and not to have to simulate birth of males and females and management decision on which females to sell. A “worst case scenario” was chosen for pregnancies and lactation schemes by letting all goats get pregnant every year (maximum potential for bacterial

shedding around abortion or parturition) and stay in lactation for the rest of their lives after they have their first parturition, regardless of their gestation stage (maximum potential for shedding in milk). The goats get pregnant at uniform random times during a 12-week mating season, and have a gestation period of 21 weeks. Dutch dairy goats from intensive husbandry systems are kept inside the barn year round (non-grazing system), whilst dairy cattle in western France go outside part of the year (pasture based system). For the model, this has two implications. First, the pasture is not included in the goat model, which means the model has only one environment instead of two (as represented in the cattle model). Second, youngstock are included in the goat model. Young animals are usually kept under the same roof as the lactating goats. Further, since *C. burnetii* has been detected inside the uterus of nulliparous goats from infected Dutch herds [10], this age group is likely to play a role in within-herd transmission dynamics of *C. burnetii*. Because dairy youngstock are usually kept separately from the lactating animals in dairy cattle herds in western France, they were not included in the original model.

## Scaling of transmission rate and abortion rate

A first scaling adjustment had to be made to adjust for the effect of herd size on the probability of infection from the environment (*p*). In the original model, the per
<table><caption>**Table 1** Adaptations made to the original cow model to obtain the goat model</caption><thead><tr><th>Characteristic</th><th>Cow model</th><th>Goat model</th></tr></thead><tbody><tr><td>Herd size</td><td>50</td><td>770</td></tr><tr><td>Birth-birth interval</td><td>55 weeks</td><td>52 weeks</td></tr><tr><td>Birth season</td><td>year-round</td><td>12 weeks</td></tr><tr><td>Gestation period</td><td>40 weeks</td><td>21 weeks</td></tr><tr><td>Non-gestation period</td><td>15 weeks</td><td>31 weeks</td></tr><tr><td>Dry period</td><td>8 weeks</td><td>-</td></tr><tr><td>Young animals</td><td>no heifers in the model</td><td>includes youngstock</td></tr><tr><td>Environment</td><td>2 environments</td><td>1 environment</td></tr><tr><td>Replacement rate (year<sup>-1</sup>)</td><td>0.355</td><td>0.305</td></tr><tr><td>Culling rate (week<sup>-1</sup>)</td><td></td><td></td></tr><tr><td>Lactation or age 1</td><td>0.0057</td><td>0.0029</td></tr><tr><td>Lactation or age 2</td><td>0.0052</td><td>0.0029</td></tr><tr><td>Lactation or age 3</td><td>0.0065</td><td>0.0029</td></tr><tr><td>Lactation or age 4</td><td>0.0067</td><td>0.0136</td></tr><tr><td>Lactation or age 5&amp;6</td><td>0.0161</td><td>0.0136</td></tr><tr><td>Lactation or age 7&amp;8</td><td>NA</td><td>0.0136</td></tr><tr><td>Probability distribution of the lactation numbers (for cows) or age (for goats) at the start of simulation</td><td></td><td></td></tr><tr><td>Lactation or age 1</td><td>0.337</td><td>0.285</td></tr><tr><td>Lactation or age 2</td><td>0.252</td><td>0.245</td></tr><tr><td>Lactation or age 3</td><td>0.173</td><td>0.211</td></tr><tr><td>Lactation or age 4</td><td>0.11</td><td>0.136</td></tr><tr><td>Lactation or age 5</td><td>0.088</td><td>0.067</td></tr><tr><td>Lactation or age 6</td><td>0.04</td><td>0.033</td></tr><tr><td>Lactation or age 7</td><td>NA</td><td>0.016</td></tr><tr><td>Lactation or age 8</td><td>NA</td><td>0.008</td></tr><tr><td>Infection from the environment</td><td>p = 1 - exp(-E(t))</td><td>p = 1 - exp(-Ê(t)/N)</td></tr><tr><td>Quantity of bacteria released by shedders in low, mid and high levels respectively, expressed in dimensionless units.</td><td>1, 1/30, or 1/3000</td><td>1*50, (1/30)*50, or (1/3000)*50</td></tr><tr><td>Probability of abortion</td><td>0.02</td><td>0.02*(40/21)</td></tr></tbody></table>

Description of the model parameters that were adapted in the original cattle model to obtain the default goat model. Parameter definitions and values for the epidemiological model can be found in Additional file 1.

capita infection probability in week t, $p(t)$ is directly related to the amount of bacteria present in the environment by $p = 1 - \exp(-E(t))$, where $E(t)$ reflects the quantity of bacteria in the environment at time t, expressed in dimensionless units [15]. This so called “one hit” Poisson dose response relation assumes every unit of the environment makes an independent contribution to the force of infection, which matches the existing evidence that the infectious dose of *C. burnetii* is likely one bacterium and that animals are exposed via inhalation [20]. Increasing the herd size would result in larger environmental contamination, with $p$ increasing up to the point where it reaches the maximum value 1, at which all susceptible animals are infected at each time step. However, the likelihood of infection is not only related to the total amount of bacteria shed into the environment by the animals in the herd. It is also likely to depend on the area that the animals share over which the bacteria are distributed (a larger herd will have a larger area, but not necessarily proportional to the number of animals), and on how easily the bacteria that are present in the environment become available to the animals (possibly depending on the texture of the manure and other factors). There are no data to suggest that for a given prevalence of shedders, a goat in a large herd of goats has a different probability of infection than a cow in a herd of 50 cows. Therefore we rescaled the original per capita environmental contamination level $E(t)$, and defined a new variable $\hat{E}(t)$ as the total environmental contamination: $\hat{E}(t) = 50 \times E(t)$, where 50 represents the mean number of animals in the original (cow) herd over the simulation period. Thus, the probability of infection $p$ becomes $1 - \exp(-\hat{E}(t)/N)$, where $N$ represents the mean number of animals in the modeled cattle or goat herd. Further, the rescaling of the environmental contamination implied that the shedding levels had to be changed accordingly, so they were multiplied by 50 as well.

A second scaling adjustment was needed to accommodate the shorter gestation period of goats. In the model, the abortion rate is a weekly rate, which was calibrated to match field data and expert opinion on abortion rates in dairy cattle in western France, resulting in a certain probability of abortion per pregnancy. In order to have a similar abortion probability per pregnant goat, with a gestation period of 21 instead of 40 weeks, the abortion rate in goats was multiplied by 40/21. An overview of the model adaptations is provided in Table 1.

## Model simulations

Four versions of the model were each run 100 times (100 iterations or herds) over a simulation period of 10 years, as in the original model. In the default version, herd size was 770 goats. The second version used a herd of 50 goats and a yearly addition of 14 individuals to
investigate the effect of herd size on within-herd transmission dynamics of *C. burnetii*. The third version was run for 50 cows (the original model), and the fourth for 770 cows, to investigate the effect of seasonal kidding and other goat characteristics.

In addition to these four versions of the model, a sensitivity analysis was performed on the default goat model. For this sensitivity analysis, three elements of the infection dynamics were altered in five scenarios, and one element of the population dynamics was altered in a sixth scenario. The details of these six scenarios are provided below. An overview of the four versions of the model and the six scenarios for the sensitivity analysis of the default model is given in Table 2.

In scenarios one and two of the sensitivity analysis, the moment of introduction of infection was varied. In both the original cow model as well as the default goat model, the simulations start with the introduction of an infected goat that just kidded (t = 1), initiating the transmission process. However, in the goat model the moment of introduction of an infected animal is set as the first day of the mating season, rather than at a random time during the year. In this way each simulation year started at the first day of the mating season and included a complete reproductive season, eliminating a possible source of variation, in that the timing of the introduction of an infected animal may influence the likelihood that the infection catches on in the population and the subsequent infection dynamics. To learn more about the effects of timing, in the first scenario both the introduction as well as the parturition of the infected animal were timed in the middle of the 12-week kidding season (at t = 27, six months after the start of the simulation).

In this scenario the infection was not present in the herd during the six months between t = 1 and t = 27. In scenario two, the moment of introduction of the infected animal was kept at t = 1, but the parturition of the introduced infected animal was at t=27, unless by chance abortion due to *C. burnetii* occurred before that time.

In scenarios three and four, the probability of abortion due to Q fever (after a transition S to $I_1$, $C_1$ to $I_2$ and $C_2$ to $I_2$) was adjusted. In scenario three, the abortion rate increased 10 fold, from 0.038 to 0.38, as it has been suggested in the literature that the abortion rate in individual goats may be higher than in cows [16]. In scenario four, the abortion rate decreased to 0.02, to exactly match the abortion rate in the cattle models. This scenario was used to investigate the sensitivity of the model to the scaling of the abortion rate that was applied due to the short gestation period of goats.

In scenario five, the probability p of infection (transition from S to $I_1$ or from $C_2$ to $I_2$) was based on 10x the environmental load (instead of 1x the environmental load), according to $1 - \exp(-10*\hat{E}(t)/N)$. With this scenario, the sensitivity of the model was tested with regards to the scaling of the transmission rate. It can also be viewed as a potential scenario for currently unknown differences in the infection rate or in bacterial shedding levels in goats versus cows, since some differences in the relative proportion of each shedding route in the whole bacterial shedding have been reported [16].

In scenario six, youngstock were excluded from the model. The total herd size and age dependent culling rates remained unchanged. As in the cattle model, every year 282 uninfected goats that just kidded for the first time were introduced into the herd at random uniform

<table><caption>Table 2 Description of model variations and sensitivity analyses</caption><thead><tr><th>Model</th><th>Model code</th><th>Species</th><th>Herd size</th><th>Young animals</th><th>Time introduction<br>infected animal</th><th>Time kidding introduced<br>infected animal</th><th>Prob.<br>to abort</th><th>Prob. of<br>infection</th></tr></thead><tbody><tr><td colspan="9">Variations of the model</td></tr><tr><td>m1</td><td>770 goats</td><td>Goats</td><td>770</td><td>Yes</td><td>1</td><td>1</td><td>0.038</td><td>1-<i>exp</i>(-&#x0302;(t)/N)</td></tr><tr><td>m2</td><td>50 goats</td><td>Goats</td><td><b>50</b></td><td>Yes</td><td>1</td><td>1</td><td>0.038</td><td>1-<i>exp</i>(-&#x0302;(t)/N)</td></tr><tr><td>m3</td><td>770 cows</td><td><b>Cows</b></td><td>770</td><td>Yes</td><td>1</td><td>1</td><td><b>0.02</b></td><td>1-<i>exp</i>(-&#x0302;(t)/N)</td></tr><tr><td>m4</td><td>50 cows</td><td><b>Cows</b></td><td><b>50</b></td><td>Yes</td><td>1</td><td>1</td><td><b>0.02</b></td><td>1-<i>exp</i>(-&#x0302;(t)/N)</td></tr><tr><td colspan="9">Scenarios of sensitivity analysis</td></tr><tr><td>s1</td><td>TimeIntro</td><td>Goats</td><td>770</td><td>Yes</td><td><b>27</b></td><td><b>27</b></td><td>0.038</td><td>1-<i>exp</i>(-&#x0302;(t)/N)</td></tr><tr><td>s2</td><td>TimeBirth</td><td>Goats</td><td>770</td><td>Yes</td><td>1</td><td><b>27</b></td><td>0.038</td><td>1-<i>exp</i>(-&#x0302;(t)/N)</td></tr><tr><td>s3</td><td>ProbAbUp</td><td>Goats</td><td>770</td><td>Yes</td><td>1</td><td>1</td><td><b>0.38</b></td><td>1-<i>exp</i>(-&#x0302;(t)/N)</td></tr><tr><td>s4</td><td>ProbAbLow</td><td>Goats</td><td>770</td><td>Yes</td><td>1</td><td>1</td><td><b>0.02</b></td><td>1-<i>exp</i>(-&#x0302;(t)/N)</td></tr><tr><td>s5</td><td>ProbInfUp</td><td>Goats</td><td>770</td><td>Yes</td><td>1</td><td>1</td><td>0.038</td><td>1-<i>exp</i>(-10*&#x0302;(t)/N)</td></tr><tr><td>s6</td><td>NoYoung</td><td>Goats</td><td>770</td><td><b>No</b></td><td>1</td><td>1</td><td>0.038</td><td>1-<i>exp</i>(-&#x0302;(t)/N)</td></tr></tbody></table>

Overview of model parameters that have been varied in the 4 variations of the model and 6 scenarios of the sensitivity analysis. Bold font indicates a change relative to the default model of 770 goats.
times during the kidding season. With this scenario, the sensitivity to the addition of youngstock in the model was assessed.

## Model outputs

The four main outputs of interest of the model were, in short, (i) abortion patterns, expressed as annual incidence of abortions and rolling monthly incidence of abortions, (ii) environmental bacterial load, (iii) extinction of the infection, and (iv) the prevalence of shedders. A detailed description of these model outputs and the relation to the “real world” is given below.

From 2005–2009, unusually high numbers of abortions were observed in 28 commercial dairy goat herds in the Netherlands [9]. On 12 June 2008, abortion problems due to Q fever in dairy goat and dairy sheep herds in the Netherlands became notifiable. Abortion problems were defined as abortions in at least 5% of pregnant animals in large herds or in more than 3 animals in small herds (< 100 animals) within a period of 30 days [5]. In cattle, abortion storms featuring a high incidence of abortions during a short period of time have not been described. To investigate whether the difference in abortion patterns between cattle herds and dairy goat herds can be explained by differences in demographics, two measures for the abortion dynamics were computed: the annual incidence of abortions and a rolling monthly incidence of abortions. The annual incidence of abortions was defined as the annual cumulative number of abortions divided by the average herd size over a year, with the assumption that on average all animals in the herd have one pregnancy each year. The rolling monthly incidence of abortions was defined as the number of abortions that occurred in the herd over a four-week period divided by the number of animals that were pregnant at the start of this four-week period. Because the model has time-steps of one week, 52 rolling monthly incidences were computed for each model year, with the exception of the first four weeks of the simulation period.

Seasonal peaks of acute human Q fever infection were observed in the Netherlands during 2007, 2008 and 2009. The incidence of human cases was the highest from late spring to early summer, following the seasonal peaks of kidding in dairy goat herds. Furthermore, the incidence of human cases was the highest in geographic areas with high densities of dairy goat farms, the epidemic genotype among humans was also dominant among goats [8], and *C. burnetii* DNA was detected in inhalable size dust fractions within and around infected dairy goat farms [21]. All together this suggests that environmental contamination could form a link between bacteria shed by individual dairy goats within farms and human exposure to these bacteria. Therefore, the within-farm environmental bacterial load (model compartment *E*) was considered a

main output of interest of the model. For each simulation, the area under the curve (AUC) of the environmental bacterial load was calculated over the 10 year simulation period by summing the environmental bacterial load at each time step ($t = 0$ until $t = 520$). For comparison between the different versions of the model, these AUC were expressed as a percentage of the mean AUC of the default model (770 goats), which was set to 100%.

Extinction of infection in goat herds versus cattle herds, relevant for the design of control measures, risk analyses and the formulation of policies are defined as the permanent absence of animals in states $I_1, I_2, I_3$ and $C_1$ for a period of at least 1 year. The mean time to extinction was calculated over all herds in which the infection had gone extinct.

The prevalence of shedders, which provides additional information relevant to the dynamics of abortions, environmental bacterial load, and extinction of the infection, was defined as the number of animals in $I_1 + I_2 + I_3$ divided by the total number of animals in the herd, and was calculated for each time step in the model.

All analyses were performed using R software [22].

## Results

### Results of the comparison of herds

#### Abortion patterns

The annual abortion incidence in the default model with 770 goats increased gradually up to a steady state of ~ 6 abortions per 100 animals per year. In the model with 770 cows, the steady state incidence was ~ 8 abortions per 100 animals per year and steady state was reached sooner, as can be seen in Figure 2. In the herds with 50 animals, the mean annual abortion incidence during the tenth simulation year was ~6% in goat herds, and ~7% in cattle herds. During simulations, as long as the annual abortion incidence had not exceeded 1%, the infection could still go extinct in herds with 770 animals. In herds of 50 animals, extinction of the infection could still occur after higher annual abortion incidences: up to 6% in goats and up to 8% in cattle. The variation in abortion incidence was larger in small herds than in large herds, and a steady state was reached faster in small herds than in large herds. The annual abortion incidences in the four models are displayed in Table 3 and Figure 2.

The rolling four-week abortion incidence in the model with 770 goats in nearly all cases did not exceed the 5% incidence that was notifiable in the Netherlands during the epidemic. The notification threshold was exceeded slightly in a few herds at the start or end of the kidding season, when only a limited number of animals were at risk to abort. In the herds with 770 cows, the rolling incidence stayed well below 5%. In small goat and cattle herds, the rolling abortion incidence was very variable, and rolling incidences higher than 5% were regularly
<figure><img src="image_4.png" /><figcaption>**Figure 2** (See legend on next page.)</figcaption></figure>
(See figure on previous page.)

**Figure 2 Abortion patterns in the four models.** Boxplots for the annual incidence of abortions (defined as the annual number of abortions divided by the average herd size) in herds with- and without extinction of the infection after 10 years simulation (A, C, E and G) and rolling monthly incidence of abortions (defined as the number of abortions over four weeks divided by the number of animals pregnant at start of a four week period) in herds without extinction (B, D, F and H). The red dotted line in the panels B, D, F and H indicate the 5% rolling monthly abortion incidence that was notifiable in the Netherlands during the epidemic. In the legends, the numbers in between brackets indicate the total number of herds which got rid of the infection over the 10 years of simulation, and the number of herds which did not. A, B) model with 770 goats; C, D) model with 50 goats; E, F) model with 770 cows; G, H) model with 50 cows.

observed. The four-week rolling abortion incidences of the four models are displayed in Figure 2. The four-week rolling abortion incidences of four individual simulations of the model with 770 goats are provided in Additional file 2.

## Environmental bacterial load

The environmental bacterial load AUC over a ten year simulation in non-extinct herds was larger in large herds than in small herds. When comparing herds of the same size, the environmental load was larger in cattle herds than in goat herds. In the goat herds, the environmental load showed seasonal peaks, while the environmental load in the cattle herds was relatively constant over time. In all modeled herds, the environmental bacterial load increased gradually over time until it reached a steady state, which was achieved more quickly in small herds than in large ones. The mean environmental bacterial load in the four models is presented in Figure 3.

The mean AUC after 10 years simulation of herds with 770 goats without extinction of the infection was set to 100%. For the other three models, the mean AUC

relative to the default model AUC were 10% for non-extinct herds with 50 goats, 269% for 770 cows, and 21% for 50 cows (Table 3).

## Extinction of the infection

Extinction of the infection occurred more often in small cattle herds than in large cattle herds. When comparing herds of the same size, extinction was more common in goat herds than in cattle herds. After 10 years simulation, the infection was extinct in 29% of herds with 770 goats, 32% of herds with 50 goats, 13% of herds with 770 cows, and in 21% of herds with 50 cows (Table 3). The mean time to extinction was 145 weeks in herds with 770 goats, 162 weeks in herds with 50 goats, 67 weeks in herds with 770 cows, and 102 weeks in herds with 50 cows (Table 3). The dynamics of extinction and persistence of the infection in the four models are shown in Figure 4.

## Prevalence of shedders

The prevalence of shedders in non-extinct herds increased faster in small herds than in large herds. In

<table><caption>**Table 3 Overview of model outputs**</caption><thead><tr><th rowspan="2">Model</th><th rowspan="2">Model code</th><th colspan="2">Abortion incidence</th><th colspan="2">Environmental bacterial load</th><th rowspan="2">Extinction rate (%)</th><th colspan="2">Time to extinction (weeks)</th><th colspan="2">Prevalence of shedders (%)</th></tr><tr><th>mean</th><th>median, 5-95%</th><th>mean</th><th>median, 5-95%</th><th>mean</th><th>median, 5-95%</th><th>mean</th><th>median, 5-95%</th></tr></thead><tbody><tr><td colspan="11">Variations of the model for goat and cow farm infection</td></tr><tr><td>m1</td><td>770 goats</td><td>6.2</td><td>6.1, 4.4-8.1</td><td>100</td><td>99, 53-142</td><td>29</td><td>145</td><td>111, 18-296</td><td>30</td><td>30, 25-34</td></tr><tr><td>m2</td><td>50 goats</td><td>5.6</td><td>6.0, 0-12</td><td>10</td><td>10, 4-14</td><td>32</td><td>162</td><td>144, 21-366</td><td>26</td><td>26, 7-45</td></tr><tr><td>m3</td><td>770 cows</td><td>8.0</td><td>7.9, 6.6-9.8</td><td>269</td><td>277, 184-320</td><td>13</td><td>67</td><td>51, 16-156</td><td>44</td><td>45, 40-48</td></tr><tr><td>m4</td><td>50 cows</td><td>7.1</td><td>6.0, 2.0-14</td><td>21</td><td>20, 14-28</td><td>21</td><td>102</td><td>72, 27-225</td><td>43</td><td>42, 28-57</td></tr><tr><td colspan="11">Scenarios of sensitivity analysis of goat farm infection</td></tr><tr><td>s1</td><td>TimeIntro</td><td>6.1</td><td>6.4, 4.4-8.1</td><td>83</td><td>90, 40-119</td><td>40</td><td>102</td><td>99, 1-280</td><td>29</td><td>30, 23-34</td></tr><tr><td>s2</td><td>TimeBirth</td><td>6.2</td><td>6.2, 4.2-8.5</td><td>82</td><td>88, 23-116</td><td>50</td><td>74</td><td>37, 5-219</td><td>29</td><td>30, 24-34</td></tr><tr><td>s3</td><td>ProbAbUp</td><td>24.8</td><td>24.8, 22-27.3</td><td>229</td><td>231, 209-246</td><td>4</td><td>25</td><td>24, 7-44</td><td>33</td><td>33, 29-36</td></tr><tr><td>s4</td><td>ProbAbLow</td><td>3.5</td><td>3.5, 2.4-4.7</td><td>82</td><td>85, 22-126</td><td>34</td><td>128</td><td>106, 21-317</td><td>28</td><td>29, 21-34</td></tr><tr><td>s5</td><td>ProbInfUp</td><td>8.3</td><td>8.3, 6.8-10.1</td><td>267</td><td>267, 255-282</td><td>1</td><td>1</td><td>1</td><td>52</td><td>52, 49-55</td></tr><tr><td>s6</td><td>NoYoung</td><td>6.4</td><td>6.4, 3.6-8.3</td><td>86</td><td>92, 18-129</td><td>34</td><td>172</td><td>162, 42-333</td><td>28</td><td>29, 15-35</td></tr></tbody></table>

Abortion incidence: incidence of abortions during the 10th simulation year in non-extinct herds; Environmental load AUC: area under the curve of the environmental load over 10 years simulation in non-extinct herds, expressed as percentage of the mean AUC of model m1; Ext. rate (%): percentage of herds with extinction of infection after 10 years simulation; Time to extinction: the number of weeks from introduction of an infected animal in the herd until extinction of the infection; Prevalence of shedders: prevalence of shedders at t = 520 in non-extinct herds.
<figure><img src="image_5.png" /><figcaption>**Figure 3** Environmental bacterial load. Temporal dynamics of the mean environmental bacterial load in the four models.</figcaption></figure>

the steady state, the prevalence of shedders in goat herds showed seasonal fluctuations, while the prevalence in cattle herds stayed relatively constant. Overall, the prevalence of shedders was higher in cattle herds than in goat herds. At the last day of the simulation period (t = 520), the mean prevalence of shedders was 30% in herds with 770 goats, 26% in herds with 50 goats, 44% in herds with 770 cows, and 43% in herds with 50 cows, see Figure 5.

<figure><img src="image_6.png" /><figcaption>**Figure 4** Extinction of infection. Kaplan Meier curve for extinction of infection in the four models.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Figure 5** Prevalence of shedders. Temporal dynamics of the mean prevalence of shedders in the four models.</figcaption></figure>

## Results of the sensitivity analyses

Annual and rolling abortion incidences, environmental load dynamics, extinction curves and prevalence dynamics of all sensitivity analyses are shown in Additional files 3, 4, 5, 6 and 7.

### Sensitivity to changes in timing of introduction of infection into the herd

Introduction of infection in the middle of the kidding season (scenario 1 and 2 of the sensitivity analysis) instead of at the start of the mating season (default model) increased the likelihood of extinction of the infection. The likelihood of extinction was 29% in the default model, 40% when the infected animal was introduced and kidded at t = 27 (scenario 1), and 50% when the infected animal was introduced at t = 1 but kidded at t = 27 (scenario 2), see Table 3 and Additional file 3. Once a steady state of infection was reached, the rolling abortion incidences in scenarios one and two were similar to the default model (Additional file 4).

### Sensitivity to changes in the probability of abortion

When the probability of abortion was increased tenfold (scenario 3), the likelihood of extinction decreased from 29% to 4%. The annual incidence of abortions was increased, peaking in the second year, with a mean of 45 and a maximum of 62 abortions per 100 animals. After this peak, the annual abortion incidence decreased to a steady mean incidence of ~25% per year (Table 3 and Additional file 5). The mean four-week rolling abortion incidence was well above the 5% “notifiable” incidence during the first two kidding seasons, and remained little
over 5% during the remaining kidding seasons. In
individual simulations, peaks up to ~40% were observed in
the four-week rolling abortions incidence. High peak
incidences were usually followed by a steep decline the
following season (Additional file 2). The mean environmen-
tal bacterial load peaked during the first two years, and then
decreased to a steady state well above the steady state of
the default model (Additional file 6).

When the probability of abortion was decreased (scenario 4), the annual abortion incidence and the rolling abortion incidence increased very gradually over the years, up to a mean annual abortion incidence of 3.5% in the 10th year (Table 3 and Additional file 5).

Sensitivity to an increased probability of infection

When the infection rate was increased tenfold (scenario 5), the likelihood of extinction dropped to 1%. The prevalence of shedders was higher in this scenario than in all other model variants. It peaked up to a mean of 59% in the first year, and then slowly decreased to a mean of 52% after 10 years (Table 3 and Additional file 7). The annual incidence of abortions was ~ 8% during the entire simulation period (Additional file 5). The environmental bacterial load peaked in the second year (although not as high as in scenario 3) and fluctuated at a high level for the remaining years (Additional file 6).

Sensitivity to no youngstock in the herd

In the model without youngstock (scenario 6), the mean annual abortion incidence as well as the likelihood of extinction were fairly similar to the default model. However, the seasonally peaked nature of the environmental bacterial load and the prevalence of shedders was less pronounced than in the default model. Between the kidding seasons, the environmental bacterial load and prevalence of shedders were similar to the default model, while during kidding seasons, the peaks were lower than in the default model.

Discussion

In this study, we explored whether the emergence of Q
fever in goats in the Netherlands could be explained by
demographic characteristics of large intensive dairy goat
husbandry systems versus the demographics of small
cattle herds where no large epidemics have been
observed. Using a modeling approach, it was found that
the occurrence of “abortion storms” and the hetero-
geneity of the abortion patterns across herds in intensive
goat husbandry systems in the Netherlands could not be
explained by the demographics of Dutch dairy goat
herds alone, and most likely aspects of the manifestation
of the infection in the host are essential in explaining
the observed abortion patterns.

The annual incidence of abortions and the environ-
mental bacterial load were higher in cattle herds than in
goat herds of the same size, and the infection was more
likely to go extinct in goat herds than in cattle herds. In
small herds (50 animals), the likelihood of extinction of
the infection was greater than in larger herds (770
animals) of the same species. Provided that infection
persisted, a steady state of infection dynamics was reached
faster in small herds than in large herds.

In the model with 770 goats, which represented the
average Dutch dairy goat herd, the abortion patterns
seemed to reproduce the patterns observed in the majority
of Dutch infected herds fairly well. As in real life, the abor-
tions in the model occurred in waves due to the seasonal
reproduction patterns, and as in most infected Dutch dairy
goat herds, the modeled rolling abortion incidence over 4
weeks did not exceed the 5% level that was notifiable in the
Netherlands during the time of the epidemic. The annual
abortion incidence of ~ 6% in the steady state seemed a
bit high because such repeated abortion waves have not
been reported, but it may be within reasonable limits for
endemically infected herds. The “abortion storms” with
high abortion incidences observed within some herds and
the large variability in abortion patterns observed across
herds were not reproduced.

In the Netherlands 94 herds were classified as infected
between 2005 and mid-2010, and abortion problems
were reported in only 28 herds, with abortion incidences
that range from just over the notification threshold of
5% up to 80% in subgroups of herds [9,23]. The fact that
abortion storms were rare suggests a possible role of
stochasticity related to seasonal kidding. Indeed, in the
simulated goat herds the rolling abortion incidence has
higher peaks than in cattle herds of the same size
(Figure 2, upper green lines). However, the fact that goat
herds are much bigger than cattle herds results in lower
rolling abortion incidences since this reduces the effect
of stochasticity (Figure 2). One explanation for the
abortion storms observed in the field could be that the
environmental contamination is not equally distributed
over entire herds, but is clustered in subgroups within a
herd. In that case the model with fewer animals may be
more representative, and indeed the model with 50 goats
shows higher variability in the infection dynamics across
herds and rolling abortion incidences above the notifica-
tion threshold.

An alternative explanation for the absence of abortion
storms in the model is related to the result that the
environmental load and prevalence of shedders was
lower in goat than in cattle herds. The kidding pattern
of dairy goats appears to be the major driver of this
difference. Due to the seasonality and short gestation
period of goats, pregnant animals were not present in
the goat herds during 19 weeks of the year, and therefore
abortions with associated shedding of large quantities of
bacteria could not occur during those periods. Hence,
the environmental bacterial load gradually decreased
after each kidding season, and increased again during
the following kidding season. As observed in the simula-
tions, in cattle herds, the continuous presence of animals
at risk to abort kept the infection running at a higher
level than on seasonally kidding goat herds. In addition,
in the model it was assumed that all animals get
pregnant every year, while farmers commonly choose for
fewer pregnancies per goat, for instance once every two
years, as goats are capable of extended lactation without
a new delivery. The presence of fewer pregnant animals
in the herd would result in even lower infection levels.

In addition to the kidding pattern and herd size, also
the presence of youngstock in goat herds influences the
within-herd infection dynamics. In herds without young-
stock (scenario 6), a higher turnover of animals was
required to keep the average herd size at 770 animals.
This meant that without youngstock, more potentially
infected animals were removed, and more susceptible
animals were introduced annually, which resulted in a
'wash-out' of infected animals and thereby lower in-
fection levels. Indeed, in goat herds with youngstock
(default model) the prevalence of shedders has higher
peaks than in goat herds without youngstock (Additional
file 7). Thus, the presence of youngstock increases preva-
lence, but not sufficiently to explain the high rolling abor-
tion incidences observed in the field.

Thus, one of the main conclusions from our model is
that the “abortion storms” observed in intensive goat
husbandry systems in the Netherlands are not wholly
explained by the herd size, reproductive pattern,
presence of youngstock and other demographic charac-
teristics of dairy goats in the intensified husbandry
system in the Netherlands. Therefore it is most likely
that aspects of the manifestation of the infection in the
host are essential in explaining the observed abortion
storms.

One possibility may be that the model itself inaccur-
ately describes some crucial part of the infection, even
though it was constructed based on longitudinal field
observations on 5 cattle herds and the simulated infec-
tion dynamics are consistent with field data from dairy
cattle herds in western France [12]. For example, the
model assumed that animals have a risk to abort during
three weeks following each event of infection, reinfection
or resumption of shedding (i.e. S-I<sub>1</sub>, C<sub>1</sub>-I<sub>2</sub> and C<sub>2</sub>-I<sub>2</sub>
transitions) [15]. In reality this may be different, e.g.
abortions may occur much later or only after initial
infection, and although resumption of shedding is likely to
follow abortion, it may not necessarily lead to abortion.
Further, the gestation status (pregnant or non-pregnant)
and phase of gestation (e.g. early or late) at the time of

infection may influence the resulting manifestation of the
infection (e.g. probability of abortion, immunological
response, shedding pattern). The potential effect of timing
of infection relative to gestation on the manifestation of
the infection may play out differently at the herd level in
herds with synchronized reproduction cycles (i.e. goat
herds) versus herds with year-round pregnancies and
deliveries (cattle herds). Data on gestation-stage dependent
Q-fever infection dynamics in ruminants are sparse, and
therefore these dynamics were not included. If the reason
for the absence of abortion storms is indeed in the model
structure itself, it is not clear whether this points at a funda-
mental difference between cows and goats, or whether the
same aspects of the model structure are inaccurate for
cattle as well.

A second possibility is that the infection process in the
individual animals (i.e. the parameter values of the
epidemiological part of the model) is different in goats
than in cattle. In the model, the abortion and infection
rates were scaled based on assumptions of similarity.
When the probability of abortion was increased 10-fold
in the model, this resulted in a peak in the mean annual
abortion incidence during the second year after intro-
duction of the infection, followed by a decrease to a
steady 25% mean annual abortion incidence. In some
herds the four-week rolling abortion incidences peaked
up to ~40% followed by a steep decline the following
season (Additional file 2), more resembling real herds.
When the infection rate was increased 10-fold, this also
resulted in more abortions (Additional files 4 and 5).

If the abortion rate or infection rate is indeed different
between cattle and goats, several mechanisms might
explain this difference. From the model it cannot be
concluded whether such mechanisms are pathogen-
related (e.g. different strains, evolution of virulence), host-
related (e.g. host susceptibility, immunological response),
within-herd environment related (e.g. barn characteristics)
or a combination. For instance, available phylogenetic
evidence suggests that the Dutch epidemic was caused by
one dominant strain [8,9], which may have differed in
terms of abortion or infection rate from the strain circu-
lating in the cattle herds used to parameterize the model.
Host related explanations include that goats may be more
sensitive to abort due to Q fever than cattle, that the
Dutch dairy goat herds may have been fully immunologi-
cally naïve (unlike the endemically infected cattle herds
used to parameterize the model), or that goats show a
difference in their bacterial shedding pattern or shedding
levels during parturition and abortion that led to more
environmental contamination and thus higher infection
rates [16]. Environmental explanations include that the
infection rate may be higher in goats due to the density of
animals in the barn or to the deep litter boxes in which
goats are kept.
In conclusion, the abortion storms in Dutch dairy goat herds could not be fully explained by demographics alone. Although most likely aspects of the manifestation of the infection in the host are essential in explaining the observed abortion patterns, there are gaps in the current understanding of the drivers of Q fever abortion storms, and this may hamper the prevention of future problems on goat farms and in humans living close to goat farms. Our finding that cattle herds may have higher levels of within-herd environmental bacterial load than goat herds after introduction of infection into a fully susceptible herd may be taken into account when enlarging cattle farming systems.

## Additional files

**Additional file 1: Parameter definitions and values for the epidemiological model.** Table with definitions of the epidemiological model parameters and their values used for simulations [13,24,25].

**Additional file 2: Rolling abortion incidence for individual simulations.** Figure of the rolling monthly incidence of abortions in 4 individual simulations for the model with 770 goats and 4 individual simulations of the sensitivity analysis for an increased probability of abortion. Rolling monthly incidence of abortions (defined as the number of abortions over four weeks divided by the number of animals pregnant at start of four week period) in 4 individual simulations of the model with 770 goats (**A** – **D**) and 4 individual simulations of the sensitivity analysis for an increased probability of abortion (**E** – **H**). The red dotted lines indicate the 5% rolling monthly abortion incidence that was notifiable in the Netherlands during the epidemic. The individual runs were selected to display the most extreme peaks in rolling abortion incidence (**A**, **E** & **F**) as well as a variety of more common abortion incidence patterns (**B**, **C**, **D**, **G** & **H**).

**Additional file 3: Extinction of infection in the sensitivity analyses.** Kaplan Meier curve for extinction of infection in the default model and six sensitivity analyses.

**Additional file 4: Rolling abortion incidence in the sensitivity analyses.** Figure of the rolling monthly incidence of abortions for the 6 scenarios of the sensitivity analysis. Rolling monthly incidence of abortions (defined as the number of abortions over four weeks divided by the number of animals pregnant at start of four week period) in herds without extinction for the 6 scenarios of the sensitivity analysis. The red dotted lines indicate the 5% rolling monthly abortion incidence that was notifiable in the Netherlands during the epidemic.

**Additional file 5: Annual abortion incidence in the sensitivity analyses.** Figure of the annual incidence of abortions for the 6 scenarios of the sensitivity analysis. Boxplots for the annual incidence of abortions (defined as the annual number of abortions divided by the average herd size) in herds with- and without extinction of the infection for the 6 scenarios of the sensitivity analysis.

**Additional file 6: Environmental bacterial load in the sensitivity analyses.** Figure of the temporal dynamics of the mean environmental bacterial load in the default model and six sensitivity analyses.

**Additional file 7: Prevalence of shedders in the sensitivity analyses.** Figure of the temporal dynamics of the mean prevalence of shedders in the default model and six sensitivity analyses.

## Competing interests

The authors declare that they have no competing interests.

## Authors' contributions

LH participated in the design of the study, carried out the model adjustments and analyses, and drafted the manuscript. AC, FB and EV

participated in the design of the study, and helped to draft the manuscript. DK and MN participated in the design and coordination of the study and helped to draft the manuscript. All authors read and approved the final manuscript.

## Acknowledgements

The authors would like to thank Raphael Guatteo, Hans Heesterbeek, Piet Vellema, Hendrik-Jan Roest, Daniel Bontje, Jan Slingenbergh, Anneke Engering and Linda McPhee for their useful comments and suggestions, and are grateful to Gerrit Koop for providing questionnaire data on dairy Dutch goat herd demography. The collaboration between the Faculty of Veterinary Medicine of Utrecht and the French National Institute for Agricultural Research (INRA) was financially supported by the Netherlands Organisation for Scientific Research (NWO) and the French Ministry of Foreign and European Affairs through the Van Gogh Programme.

## Author details

¹Department of Farm Animal Health, Faculty of Veterinary Medicine, Utrecht University, Yalelaan 7, Utrecht 3584 CL, The Netherlands. ²INRA, UMR1300 Biologie, Epidémiologie et Analyse de Risque en santé animale, BP 40706, Nantes F-44307, France. ³Ecole nationale vétérinaire, agroalimentaire et de l'alimentation Nantes-Atlantique, UMR BioEpAR, LUNAM Université, Oniris, Nantes F-44307, France. ⁴Present address: Anses, Laboratoire de Santé Animale, Unité EPI, 23, avenue du Général de Gaulle, Maisons-Alfort 94706, France. ⁵INRA, UR341 Mathématiques et Informatique Appliquées, Domaine de Vilvert, Jouy-en-Josas 78350, France.

Received: 12 September 2012 Accepted: 27 March 2013

Published: 26 April 2013

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doi:10.1186/1297-9716-44-28

Cite this article as: Hogerwerf et al.: Dairy goat demography and Q fever infection dynamics. *Veterinary Research* 2013 **44**:28.

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