Food Modelling Journal :
FSKX (Food Safety Knowledge)

Corresponding author: Esther M. Sundermann (esthermaria.sundermann@bfr.bund.de), Maarten Nauta (mjna@ssi.dk), Arno Swart (arno.swart@rivm.nl)
Academic editor: Matthias Filter
Received: 18 Jan 2021  Accepted: 27 Apr 2021  Published: 03 Jun 2021
© 2021 Esther M. Sundermann, Maarten Nauta, Arno Swart
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Sundermann EM, Nauta M, Swart A (2021) A readytouse doseresponse model of Campylobacter jejuni implemented in the FSKXstandard. Food Modelling Journal 2: e63309. https://doi.org/10.3897/fmj.2.63309

Doseresponse models are an important part of quantitative microbiological risk assessments. In this paper, we present a transparent and readytouse version of a published doseresponse model that estimates the probability of infection and illness after the consumption of a meal that is contaminated with the pathogen Campylobacter jejuni. To this end, model and metadata are implemented in the fskxstandard. The model parameter values are based on data from a set of different studies on the infectivity and pathogenicity of Campylobacter jejuni. Both, challenge studies and outbreaks are considered, users can decide which of these is most suitable for their purpose. We present examples of results for typical ingested doses and demonstrate the utility of our readytouse model reimplementation by supplying an executable model embedded in this manuscript.
exchange format, mathematical modelling, infection probability, illness probability, campylobacteriosis, food safety, executable document
Thermotolerant Campylobacter is the most commonly reported zoonotic disease in the EU (
After an earlier reconsideration of the "classic" DRM (
In this paper, we provide the DRM developed by
The model metadata are a schema to annotate the model in a harmonised way. It is part of the FSKXfile (see Suppl. material
Source: PUBLISHED SCIENTIFIC STUDIES
Identifier: CampylobacterDRTeunis2018
Rights: Creative Commons Attribution 4.0 (CC BY 4.0)
Availability: Open access
Language: English
Software: FSKLab
Language Written In: R
Objective: The objective of the model is to estimate the probability of infection and illness after ingestion of a dose of Campylobacter jejuni.
Name: Any product
Description: Any product
Hazard type: Microorganisms
Hazard name: Campylobacter jejuni
Hazard unit: Colony forming unit (CFU)
Adverse Effect: Asymptomatic or symptomatic infection with Campylobacter jejuni (campylobacteriosis)
Name: General population or outbreaks
Target Population: Two target populations are defined: the general population and groups involved in a foodborne outbreak.
The doseresponse model provides the probability of infection and illness as a function of the exposure, i.e., the ingested dose of Campylobacter jejuni. Model parameters are based on datasets from human and primate challenge studies and outbreaks.
Study Title: Acute illness from Campylobacter jejuni may require high doses while infection occurs at low doses.
Study Description: Data from a set of different studies on the infectivity and pathogenicity of Campylobacter jejuni were analysed with a multilevel model. This allowed us to include effects of host species (nonhuman primates and humans), different strains of the pathogen, and differentiation between outbreak and nonoutbreak settings. To this end, three groups of studies were included: (1) four controlled human infection studies (challenge studies) involving three distinct strains (81176, CG8421, and A3249), (2) four studies on outbreaks of unknown strains and, in one case, strain 81176, and (3) five challenge studies in three species of nonhuman primates of strains 81176, 7837, and V212X. All studies recorded both asymptomatic infection and illness as endpoints. The data are used to parameterise the doseresponse model; see Section "Material and methods" and
Doseresponse models for infection are usually based on a limited number of biologically motivated axioms (
\(P_{inf} = 1 (1r)^n\) (Equ. 1)
With this expression as a basis, several extensions can be made by assuming variability distributions for r (heterogeneity in infectivity or susceptibility) or n (heterogeneity in the doses received). In
\(P_{{inf}} = 1 \sideset{_1}{_1}F(a,a+b,D)\) (Equ. 2),
where _{ 1}F_{1 } is the Kummer confluent hypergeometric function. The model to describe the probability for illness among infected subjects (P_{illinf}, Equ. 3) is based on other principles. It is no longer a matter of a single organism initiating infection, but rather the resulting growth of the population of organisms that should "outrun" the defensive measures of the immune system.
\(P_{illinf}=1(1+D/\eta) ^{r}\) (Equ. 3)
Like a and b, the parameters r and \(\eta\) are parameters that were estimated from data (see Subsection "Parameter estimation" for details). To determine the probability of illness or illness given infection, the corresponding equations are used and parameterised with the uncertainty distributions for a, b, r, and \(\eta\) . The user may supply the Poissonmean dose D. The unconditional probability of illness is calculated by multiplying the conditional probability for illness (P_{illinf}, Equ. 3) and the probability of infection (P_{inf}, Equ. 2):
\(P_{ill} = P_{illinf} P_{inf}\) (Equ. 4)
Note that the probability of illness is for the exposed population only. The
fraction of the population that is exposed should be derived from an exposure assessment. This assessment is part of a full QMRA.The parameters a and b (used to describe P_{inf}, Equ. 2) as well as the parameters r and \(\eta\) (used to calculate P_{illinf}, Equ. 3) were estimated from the data from the challenge studies and outbreak studies as performed in
Description of the model parameters of the doseresponse model of Campylobacter jejuni.
Id  dose 
Classification  INPUT 
Name  Doses 
Description  A range (vector) of mean doses of Campylobacter jejuni 
Unit  CFU 
Data Type  DOUBLE 
Source  Article 
Value  rep(1,10000) 
Min Value  0 
Id  n_sim 
Classification  INPUT 
Name  Number of parameter simulations 
Description  Number of simulations 
Unit  [] 
Data Type  INTEGER 
Source  Article 
Value  50 
Min Value  1 
Id  Pexp 
Classification  INPUT 
Name  Probability of exposure 
Description  In exposure models, the Pexp is often called the prevalence. 
Unit  [Probability] 
Data Type  DOUBLE 
Source  User supplied 
Value  1 
Min Value  0 
Max Value  1 
Id  challenge 
Classification  INPUT 
Name  Analysis done on the basis of challenge study data or outbreak data 
Description  TRUE if challenge, FALSE if outbreak 
Unit  [] 
Data Type  BOOLEAN 
Source  Data 
Value  TRUE 
Id  mean_w_inf_ch 
Classification  INPUT 
Name  Mean of w1 
Description  w1 is a measure of infectivity (location). Value of the challengescenario. 
Unit  [] 
Data Type  DOUBLE 
Source  Article 
Value  0.177 
Id  mean_z_inf_ch 
Classification  INPUT 
Name  Mean of z1 
Description  z1 is a measure of variation in infectivity (spread). Value of the challengescenario. 
Unit  [] 
Data Type  DOUBLE 
Source  Article 
Value  0.054 
Id  var_w_inf_ch 
Classification  INPUT 
Name  Variance of w1 
Description  w1 is a measure of infectivity (location). Value of the challengescenario. 
Unit  [] 
Data Type  DOUBLE 
Source  Article 
Value  1.303 
Id  var_z_inf_ch 
Classification  INPUT 
Name  Variance of z1 
Description  z1 is a measure of variation in infectivity (spread). Value of the challengescenario. 
Unit  [] 
Data Type  DOUBLE 
Source  Article 
Value  1.07 
Id  cov_wz_inf_ch 
Classification  INPUT 
Name  Covariance of (w1,z1) 
Description  w1 is a measure of infectivity (location) and z1 is a measure of variation in infectivity (spread). Value of the challengescenario. 
Unit  [] 
Data Type  DOUBLE 
Source  Article 
Value  0.041 
Id  mean_w_ill_ch 
Classification  INPUT 
Name  Mean of w2 
Description  w2 is a location parameter. Value of the challengescenario. 
Unit  [] 
Data Type  DOUBLE 
Source  Article 
Value  2.744 
Id  mean_z_ill_ch 
Classification  INPUT 
Name  Mean of z2 
Description  z2 is a spread parameter. Value of the challengescenario. 
Unit  [] 
Data Type  DOUBLE 
Source  Article 
Value  0.00489 
Id  var_w_ill_ch 
Classification  INPUT 
Name  Variance of w2 
Description  w2 is a location parameter. Value of the challengescenario. 
Unit  [] 
Data Type  DOUBLE 
Source  Article 
Value  1.337 
Id  var_z_ill_ch 
Classification  INPUT 
Name  Variance of z2 
Description  z2 is a spread parameter. Value of the challengescenario. 
Unit  [] 
Data Type  DOUBLE 
Source  Article 
Value  0.993 
Id  cov_wz_ill_ch 
Classification  INPUT 
Name  Covariance of (w2,z2) 
Description  w2 is a location parameter and z2 is a spread parameter. Value of the challengescenario. 
Unit  [] 
Data Type  DOUBLE 
Source  Article 
Value  0.01 
Id  mean_w_inf_ob 
Classification  INPUT 
Name  Mean of w1 
Description  w1 is a measure of infectivity (location). Value of the outbreak scenario. 
Unit  [] 
Data Type  DOUBLE 
Source  Article 
Value  0.226 
Id  mean_z_inf_ob 
Classification  INPUT 
Name  Mean of z1 
Description  z1 is a measure of variation in infectivity (spread). Value of the outbreakscenario. 
Unit  [] 
Data Type  DOUBLE 
Source  Article 
Value  0.017 
Id  var_w_inf_ob 
Classification  INPUT 
Name  Variance of w1 
Description  w1 is a measure of infectivity (location). Value of the outbreakscenario. 
Unit  [] 
Data Type  DOUBLE 
Source  Article 
Value  1.404 
Id  var_z_inf_ob 
Classification  INPUT 
Name  Variance of z1 
Description  z1 is a measure of variation in infectivity (spread). Value of the outbreakscenario. 
Unit  [] 
Data Type  DOUBLE 
Source  Article 
Value  1.003 
Id  cov_wz_inf_ob 
Classification  INPUT 
Name  Covariance of (w1,z1) 
Description  w1 is a measure of infectivity (location) and z1 is a measure of variation in infectivity (spread). Value of the outbreakscenario. 
Unit  [] 
Data Type  DOUBLE 
Source  Article 
Value  0.053 
Id  mean_w_ill_ob 
Classification  INPUT 
Name  Mean of w2 
Description  w2 is a location parameter. Value of the outbreakscenario. 
Unit  [] 
Data Type  DOUBLE 
Source  Article 
Value  6.241 
Id  mean_z_ill_ob 
Classification  INPUT 
Name  Mean of z2 
Description  z2 is a spread parameter. Value of the outbreakscenario. 
Unit  [] 
Data Type  DOUBLE 
Source  Article 
Value  0.0086 
Id  var_w_ill_ob 
Classification  INPUT 
Name  Variance of w2 
Description  w2 is a location parameter. Value of the outbreakscenario. 
Unit  [] 
Data Type  DOUBLE 
Source  Article 
Value  40.99 
Id  var_z_ill_ob 
Classification  INPUT 
Name  Variance of z2 
Description  z2 is a spread parameter. Value of the outbreakscenario. 
Unit  [] 
Data Type  DOUBLE 
Source  Article 
Value  0.995 
Id  cov_wz_ill_ob 
Classification  INPUT 
Name  Covariance of (w2,z2) 
Description  w2 is a location parameter and z2 is a spread parameter. Value of the outbreakscenario. 
Unit  [] 
Data Type  DOUBLE 
Source  Article 
Value  0.184 
Id  Qillmean 
Classification  OUTPUT 
Name  Mean probability of illness for each simulation over all doses 
Description  
Unit  [Probability] 
Data Type  VECTOROFNUMBERS 
Min Value  0 
Max Value  1 
Id  Qinfmean 
Classification  OUTPUT 
Name  Mean probability of infection for each simulation over all doses 
Description  
Unit  [Probability] 
Data Type  VECTOROFNUMBERS 
Min Value  0 
Max Value  1 
The simulation settings for the doseresponse model. The settings specify the parameter names and the values (see Table
defaultSimulation  
dose  rep(1,10000) 
n_sim  50 
Pexp  1 
challenge  TRUE 
mean_w_inf_ch  0.177 
mean_z_inf_ch  0.054 
var_w_inf_ch  1.303 
var_z_inf_ch  1.07 
cov_wz_inf_ch  0.041 
mean_w_ill_ch  2.744 
mean_z_ill_ch  0.00489 
var_w_ill_ch  1.337 
var_z_ill_ch  0.993 
cov_wz_ill_ch  0.01 
mean_w_inf_ob  0.226 
mean_z_inf_ob  0.017 
var_w_inf_ob  1.404 
var_z_inf_ob  1.003 
cov_wz_inf_ob  0.053 
mean_w_ill_ob  6.241 
mean_z_ill_ob  0.0086 
var_w_ill_ob  40.99 
var_z_ill_ob  0.995 
cov_wz_ill_ob  0.184 
Outbreak  
dose  rep(1,10000) 
n_sim  50 
Pexp  1 
challenge  FALSE 
mean_w_inf_ch  0.177 
mean_z_inf_ch  0.054 
var_w_inf_ch  1.303 
var_z_inf_ch  1.07 
cov_wz_inf_ch  0.041 
mean_w_ill_ch  2.744 
mean_z_ill_ch  0.00489 
var_w_ill_ch  1.337 
var_z_ill_ch  0.993 
cov_wz_ill_ch  0.01 
mean_w_inf_ob  0.226 
mean_z_inf_ob  0.017 
var_w_inf_ob  1.404 
var_z_inf_ob  1.003 
cov_wz_inf_ob  0.053 
mean_w_ill_ob  6.241 
mean_z_ill_ob  0.0086 
var_w_ill_ob  40.99 
var_z_ill_ob  0.995 
cov_wz_ill_ob  0.184 
ChallengeVarMeanDoses  
dose  10^rnorm(1000, 1, 1.5 ) 
n_sim  50 
Pexp  1 
challenge  TRUE 
mean_w_inf_ch  0.177 
mean_z_inf_ch  0.054 
var_w_inf_ch  1.303 
var_z_inf_ch  1.07 
cov_wz_inf_ch  0.041 
mean_w_ill_ch  2.744 
mean_z_ill_ch  0.00489 
var_w_ill_ch  1.337 
var_z_ill_ch  0.993 
cov_wz_ill_ch  0.01 
mean_w_inf_ob  0.226 
mean_z_inf_ob  0.017 
var_w_inf_ob  1.404 
var_z_inf_ob  1.003 
cov_wz_inf_ob  0.053 
mean_w_ill_ob  6.241 
mean_z_ill_ob  0.0086 
var_w_ill_ob  40.99 
var_z_ill_ob  0.995 
cov_wz_ill_ob  0.184 
OutbreakVarMeanDoses  
dose  10^rnorm(1000, 1, 1.5 ) 
n_sim  50 
Pexp  1 
challenge  FALSE 
mean_w_inf_ch  0.177 
mean_z_inf_ch  0.054 
var_w_inf_ch  1.303 
var_z_inf_ch  1.07 
cov_wz_inf_ch  0.041 
mean_w_ill_ch  2.744 
mean_z_ill_ch  0.00489 
var_w_ill_ch  1.337 
var_z_ill_ch  0.993 
cov_wz_ill_ch  0.01 
mean_w_inf_ob  0.226 
mean_z_inf_ob  0.017 
var_w_inf_ob  1.404 
var_z_inf_ob  1.003 
cov_wz_inf_ob  0.053 
mean_w_ill_ob  6.241 
mean_z_ill_ob  0.0086 
var_w_ill_ob  40.99 
var_z_ill_ob  0.995 
cov_wz_ill_ob  0.184 
In the next section, we describe how to implement the model and run model simulations using FSKXformat.
All model parameters and their descriptions are presented in Table
In order to execute the model, please register at the virtual research environment.
Execute with default simulation parameters: execute
The default simulation runs for 1 minute 4 seconds on the virtual research environment.
Execute another simulation scenario or create a personalised simulation scenario: execute
Results are visualised as boxplots that show the probability of illness and infection for the human population that consumes Campylobacter jejunicontaminated food. The doseresponse model is applied using the challenge studies dataset and the outbreak studies dataset separately (
Figs
Figs
Doseresponse models, as part of the hazard characterisation, are an indispensable ingredient of any QMRA model (
In the current study, we focus on a recently published doseresponse model for Campylobacter jejuni (
We present the recent model of
We wish to acknowledge the original work of Peter F.M. Teunis, Axel Bonačić Marinović, David R. Tribble, Chad K. Porter, and Stylianos Georgiadis.
EMS is funded by the European Union’s Horizon 2020 research and innovation programme under grant agreement No 731001 and the JIP MATRIX within the One Health EJP. One Health EJP has received funding from the European Union Horizon 2020 research and innovation programme under grant agreement No 773830.
Esther M. Sundermann: Conceptualisation, Software (creation of the fskxmodel), Project administration, Visualisation, Data Curation, Writing  Original Draft, Writing  Review & Editing, Maarten Nauta: Writing  Original Draft, Writing  Review & Editing, Arno Swart: Methodology, Software (development of the model), Writing  Original Draft, Writing  Review & Editing