Food Modelling Journal :
FSKX (Food Safety Knowledge)
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Corresponding author: Esther M. Sundermann (esther-maria.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 ready-to-use dose-response model of Campylobacter jejuni implemented in the FSKX-standard. Food Modelling Journal 2: e63309. https://doi.org/10.3897/fmj.2.63309
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Dose-response models are an important part of quantitative microbiological risk assessments. In this paper, we present a transparent and ready-to-use version of a published dose-response 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 fskx-standard. 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 ready-to-use model re-implementation 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 FSKX-file (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: FSK-Lab
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 food-borne outbreak.
The dose-response 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 (non-human primates and humans), different strains of the pathogen, and differentiation between outbreak and non-outbreak settings. To this end, three groups of studies were included: (1) four controlled human infection studies (challenge studies) involving three distinct strains (81-176, CG8421, and A3249), (2) four studies on outbreaks of unknown strains and, in one case, strain 81-176, and (3) five challenge studies in three species of non-human primates of strains 81-176, 78-37, and V212X. All studies recorded both asymptomatic infection and illness as endpoints. The data are used to parameterise the dose-response model; see Section "Material and methods" and
Dose-response models for infection are usually based on a limited number of biologically motivated axioms (
\(P_{inf} = 1- (1-r)^n\) (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 1F1 is the Kummer confluent hypergeometric function. The model to describe the probability for illness among infected subjects (Pill|inf, 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.
\(P_{ill|inf}=1-(1+D/\eta) ^{-r}\) (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 Poisson-mean dose D. The unconditional probability of illness is calculated by multiplying the conditional probability for illness (Pill|inf, Equ. 3) and the probability of infection (Pinf, Equ. 2):
\(P_{ill} = P_{ill|inf} P_{inf}\) (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 Pinf, Equ. 2) as well as the parameters r and \(\eta\) (used to calculate Pill|inf, Equ. 3) were estimated from the data from the challenge studies and outbreak studies as performed in
Description of the model parameters of the dose-response 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 challenge-scenario. |
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 challenge-scenario. |
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 challenge-scenario. |
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 challenge-scenario. |
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 challenge-scenario. |
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 challenge-scenario. |
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 challenge-scenario. |
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 challenge-scenario. |
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 challenge-scenario. |
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 challenge-scenario. |
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 outbreak-scenario. |
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 outbreak-scenario. |
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 outbreak-scenario. |
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 outbreak-scenario. |
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 outbreak-scenario. |
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 outbreak-scenario. |
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 outbreak-scenario. |
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 outbreak-scenario. |
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 outbreak-scenario. |
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 dose-response 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 FSKX-format.
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 jejuni-contaminated food. The dose-response model is applied using the challenge studies dataset and the outbreak studies dataset separately (
Figs
Figs
Dose-response 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 dose-response 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 fskx-model), 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