### Abstract

- Top of page
- Abstract
- 1. INTRODUCTION
- 2. FRAMEWORK, MODEL, AND DATA
- 3. RESULTS
- 4. DISCUSSION
- 5. CONCLUSIONS
- ACKNOWLEDGMENTS
- APPENDIX
- REFERENCES

Evaluations of *Listeria monocytogenes* dose-response relationships are crucially important for risk assessment and risk management, but are complicated by considerable variability across population subgroups and *L. monocytogenes* strains. Despite difficulties associated with the collection of adequate data from outbreak investigations or sporadic cases, the limitations of currently available animal models, and the inability to conduct human volunteer studies, some of the available data now allow refinements of the well-established exponential *L. monocytogenes* dose response to more adequately represent extremely susceptible population subgroups and highly virulent *L. monocytogenes* strains. Here, a model incorporating adjustments for variability in *L. monocytogenes* strain virulence and host susceptibility was derived for 11 population subgroups with similar underlying comorbidities using data from multiple sources, including human surveillance and food survey data. In light of the unique inherent properties of *L. monocytogenes* dose response, a lognormal-Poisson dose-response model was chosen, and proved able to reconcile dose-response relationships developed based on surveillance data with outbreak data. This model was compared to a classical beta-Poisson dose-response model, which was insufficiently flexible for modeling the specific case of *L. monocytogenes* dose-response relationships, especially in outbreak situations. Overall, the modeling results suggest that most listeriosis cases are linked to the ingestion of food contaminated with medium to high concentrations of *L. monocytogenes*. While additional data are needed to refine the derived model and to better characterize and quantify the variability in *L. monocytogenes* strain virulence and individual host susceptibility, the framework derived here represents a promising approach to more adequately characterize the risk of listeriosis in highly susceptible population subgroups.

### 1. INTRODUCTION

- Top of page
- Abstract
- 1. INTRODUCTION
- 2. FRAMEWORK, MODEL, AND DATA
- 3. RESULTS
- 4. DISCUSSION
- 5. CONCLUSIONS
- ACKNOWLEDGMENTS
- APPENDIX
- REFERENCES

*Listeria* monocytogenes is one of the leading causes of hospitalization, fetal loss, and death due to foodborne illnesses in the United States.[1] Derivations of *L. monocytogenes* dose-response relationships, though crucially important for risk assessment and risk management, are impaired by the difficulties of collecting adequate data from outbreak investigations or sporadic cases, by the lack of appropriate animal models, and by the inability to use volunteer studies due to ethical and practical concerns.[2, 3]

Two well-accepted *L. monocytogenes* dose-response models have been developed by U.S. agencies[4] and an international expert panel,[5] both scaled to epidemiological data. In 2003, the Food and Drug Administration (FDA) of the U.S. Department of Health and Human Services and the Food Safety and Inspection Service (FSIS) of the U.S. Department of Agriculture published a joint risk assessment for *L. monocytogenes* in 23 selected categories of ready-to-eat (RTE) foods.[4] The risk assessment evaluated the risk of invasive listeriosis and death due to listeriosis for the total U.S. population as well as for three separate population subgroups: (i) neonates infected in utero through contaminated food consumed by their mothers; (ii) the intermediate-age population; and (iii) older adults. One dose-response relationship (i.e., modeling mortality in humans following the ingestion of *L. monocytogenes)* was initially developed and different multipliers were subsequently applied to generate models for invasive listeriosis for each of the population subgroups. To derive the dose-response relationship for mortality in humans, five dose-response models (i.e., probit, exponential, logistic, multihit, and Gompertz-log) were initially fitted to data obtained in mice challenged with a single *L. monocytogenes* strain. These models were weighted and used simultaneously to characterize uncertainty in the shape of the dose-response curve, with the best-fitting exponential model receiving the greatest weight. A distribution of median lethal dose values (LD_{50}) observed in mice challenged with different *L. monocytogenes* strains was subsequently incorporated in the dose-response model to characterize *L. monocytogenes* strain variability in virulence and its uncertainty. Variability and uncertainty in host susceptibility within the three population subgroups were estimated based on observations in mice and epidemiological data, and incorporated in the dose-response model as well. Finally, because the derived model considerably overestimated the expected number of invasive listeriosis cases, surveillance data on the incidence of listeriosis in the United States were used to scale the dose-response relationship to reflect differences in susceptibility between humans and mice.[4]

In 2004, an international expert panel of the Food and Agriculture Organization of the United Nations (FAO)/World Health Organization (WHO) developed another dose-response model based on a data subset extracted from the exposure estimates and the estimated annual number of cases used to derive the draft FDA/FSIS dose-response model published in 2001. The FAO/WHO dose-response model for invasive listeriosis is an exponential dose-response model.[6] The exponential dose-response model is a “single-hit” model:[6, 7] it assumes that the probability of a given bacterial cell causing the adverse effect is independent of the number or characteristics of other ingested pathogens, so that a single ingested microorganism is sufficient to cause the adverse effect with some probability greater than zero. The exponential dose-response model further assumes that the bacterial cells are randomly distributed in the food, hence the dose per portion follows a Poisson distribution, and that the average probability, *r*, that one pathogen, within a given exposure of a particular consumer to a specific population of pathogens, will survive the host-pathogen interaction to initiate infection and cause illness is constant.[8]

If the virulence of pathogens or the susceptibility of consumers varies from exposure to exposure, then *r* may vary and may be represented by a random variable with distribution *f*(*r*). [8] Challenges remain regarding how best to quantify the distribution of *r* in relation to the host, the bacterial strain, and the exposure scenario. To account for differences in host susceptibility for *L. monocytogenes*, the FAO/WHO group of experts assumed the existence of two distinct values for *r*, applicable to the general population and population subgroups with increased susceptibility, respectively. The two *r* parameters (i.e., one value for each of the two population subgroups) were estimated from epidemiological[9] and food exposure[10] data obtained in the United States. The estimated *r* parameters were extremely low (i.e., approximately 10^{−12}–10^{−13} for the population with increased susceptibility and 10^{−13}–10^{−15} for the general population), translating into a very low probability of illness following the ingestion of a low dose of bacteria. This dose-response model or some adaptations of the model have been used in various risk assessments.^{(11-14)}

Since 2004, new scientific data have become available, demonstrating the considerable variability in virulence among *L. monocytogenes* strains and molecular subtypes.[15-18] New data have, for example, shown that the entry of *L. monocytogenes* into certain human epithelial cells is primarily receptor mediated, depending on specific interactions between internalins on the bacterial surface and their respective host cell receptors.[19-22] Therefore, point mutations in the *inlA* gene can lead to virulence attenuation of *L. monocytogenes* strains.[16, 23, 24] New data are also available regarding the variability in susceptibility among individuals with different predisposing conditions such as pregnancy, old age, or other underlying conditions.[25-28] The relative risk of listeriosis for pregnant women, for example, has been estimated to be approximately 100 times higher than that for nonpregnant women.[25-27] Relative risks higher than 1,000 have been reported for individuals with chronic lymphocytic leukemia when compared to a reference population of individuals <65-year old without any known underlying conditions.[26]

Because of the challenges in developing adequate dose-response models of listeriosis, an interagency expert workshop was held in the United States in 2011, with the goal of identifying new data, strategies, and insights for *L. monocytogenes* dose-response modeling. Short-term strategies identified during this workshop included updating the dose-response model developed by FDA/FSIS[4] by incorporating new data and insights about differences in strain virulence and *L. monocytogenes* pathophysiology. A key-events approach to dose-response modeling[29] was identified as a promising though extremely challenging, data-intensive, and potentially unachievable framework for future microbial dose-response models.[2]

Current dose-response models linked to epidemiological data tend to agree that a low dose of *L. monocytogenes* leads to an average low probability of invasive listeriosis in the general population as well as in broadly defined populations with heightened susceptibility.[4, 5, 30] However, a more nuanced evaluation of *L. monocytogenes* dose response for *L. monocytogenes* strains with different virulence and for different human population subgroups at heightened risk of listeriosis is needed to adequately characterize the listeriosis risk in different population subgroups, including those with highest susceptibility. Such nuanced models would allow for more in-depth inference about the listeriosis risk posed to highly susceptible population subgroups by highly virulent *L. monocytogenes* strains, and may become instrumental for evaluating key risk management issues such as the potential public health threat associated with the ingestion of a given dose of *L. monocytogenes*.

In this article, the existing exponential *L. monocytogenes* dose-response model[5] for invasive listeriosis is being revisited. A mathematical framework for considering variability in *L. monocytogenes* virulence and in host susceptibility is derived and applied to currently available epidemiological data, including data from one well-documented listeriosis outbreak.[4, 5, 31] Unlike other foodborne pathogens such as *Salmonella*,[32-34] *Campylobacter*,[35] or norovirus,[36, 37] *L. monocytogenes* is characterized by an extremely low probability of illness at low exposure doses when averaging across the total population or broadly defined population subgroups[4, 5, 30] and by extreme variability in the probability of infection among population subgroups with different predisposing risk factors.[5, 26, 27, 38] Two dose-response models are evaluated and compared here in light of the unique challenges associated with modeling *L. monocytogenes* dose response.[2, 4, 5, 29] The first evaluated model uses beta distributions to characterize variability in *r* from exposure to exposure, resulting in an “exact beta-Poisson” dose-response relation[6] (also known as “hypergeometric”[7] or “actual beta-Poisson”[8] dose-response relation), which may be simplified to an approximate “beta-Poisson” model if certain conditions are met.[7, 39] The second model, a newly developed “lognormal-Poisson” model, characterizes variability in *r* due to variability in strain virulence and host susceptibility using lognormal distributions. As will be illustrated in this article, the lognormal distribution was found appropriate and useful for modeling the special case of *L. monocytogenes* dose response whereas the beta-Poisson model showed insufficient flexibility to adequately model one of the well-described *L. monocytogenes* outbreaks.

### 5. CONCLUSIONS

- Top of page
- Abstract
- 1. INTRODUCTION
- 2. FRAMEWORK, MODEL, AND DATA
- 3. RESULTS
- 4. DISCUSSION
- 5. CONCLUSIONS
- ACKNOWLEDGMENTS
- APPENDIX
- REFERENCES

The exponential model has the oversimplifying assumption of a constant probability of infection following the ingestion of *L. monocytogenes* in a given population. This study incorporates variability in strain virulence and host susceptibility into the dose-response relationships. Additional data are needed to better understand and model the process from the ingestion of *L. monocytogenes* cells to the development of invasive listeriosis. However, several general conclusions can be made based on the available data. Overall, our model predicts the expected number of cases linked to the consumption of 10,000 cfu or less in 55 out of 1,591 cases, i.e., 3.5% of cases. Notably, these servings are expected to represent 99.96% of all RTE servings, indicating that most cases are expected to be caused by highly contaminated food items. Importantly, however, most of these cases attributable to low contamination doses are predicted to occur in the most highly susceptible population subgroups, including, for example, pregnant women. Using the model and assumptions discussed above led to the conclusion that, while most of the cases are linked to a medium to high exposure doses to *L. monocytogenes*, those at greatest risk of developing listeriosis are also at a measurable risk of illness when consuming food contaminated with relatively low doses of *L. monocytogenes*, especially if highly virulent bacterial strains are involved.