Modeling strain variability in Campylobacter jejuni thermal inactivation by quantifying the number of strains required.

There is a limited understanding of the survival responses of Campylobacter jejuni during thermal processing, which must be investigated for appropriate risk assessment and processing. Therefore, we aimed to elucidate the survival response of C. jejuni and develop a predictive model considering strain variability and uncertainty, which are important for quantitative microbial risk assessment (QMRA) or risk-based processing control measures. We employed the most probable curve (MPC) method to consider the uncertainty in cell concentrations. Further, the multivariate normal (MVN) distribution served as a model for strain variability in bacterial survival behavior. The prediction curves from the MVN successfully captured the parameter variability of the most probable curves of each strain. More than ten reference strains effectively described the strain variability in parameters using the MVN distribution. The findings indicated that, with sufficient strain data, the MVN could estimate the strain variability, including unknown strains. The multi-level model for strain variability can potentially become a specialized tool for QMRA and risk-based processing controls. The combined approach of MPC and MVN provides valuable insights into strain variability, emphasizing the importance of accounting for variability and uncertainty in predictive models for QMRA and risk-based processing control measures.

Testing a frailty prevention program for older men during COVID-19: A 2-year mixed-methods pilot study.

BACKGROUND: Frailty is a syndrome related to declining functioning attributed to aging. As a reversible, often improved condition, preventive measures for frailty can be effective. OBJECTIVE: This study aimed to evaluate a frailty prevention program for older men comprising face-to-face meetings and an original social mobile application. We also examined the effect of COVID-19-associated social isolation on the implementation of this program. METHODS: We conducted a mixed-methods pilot study featuring a single group before and after comparison of 11 man participants, ≥65 years, living in Japanese cities with a spouse or relatives. Program outcome measures included frailty, loneliness, grip strength, step count and mental health status. Process evaluation considered the experience of participants through a semi-structured interview. RESULTS: The intervention period included an interval of self-isolation owing to the spread of COVID-19. Among the outcomes, grip strength decreased after intervention. No significant negative changes were observed in other items. Themes emerging from participant experiences with the program included 'Cooperation with researchers and contributing to research', 'Greater awareness of health', 'Interest in and experience of "newness"', 'Hesitation over active engagement', 'Casual ties with members' and 'Relationships that do not breach personal boundaries'. CONCLUSIONS: Although the COVID-19 pandemic overlapped with the intervention, participants maintained their mental health. The program was a novel, stimulating experience for older men and demonstrated the usefulness of information and communication technology in supporting their social activities. IMPLICATIONS FOR PRACTICE: As a community health nursing initiative for older people, we propose activities that combine group and online support. Frailty prevention programs for older men must contain content that stimulates their interests, such as 'health' and 'newness'.

Verification of the Effectiveness of a Communication Application in Improving Social Connectedness and Physical Health among Unacquainted Older Men: A Mixed-Methods Pilot Study.

This study aimed to verify the effectiveness of an application (app) in establishing social connectedness among unacquainted older men, as well as improving their physical health. The nine participants were men aged 65 and older in the subarctic zone of Hokkaido, Japan. A mix of quantitative and qualitative methods were adopted as the study design. A questionnaire survey was completed before and after the intervention, and a semi-structured interview was conducted after the intervention. An app-installed smartphone was loaned to the participants, which allowed them to share pictures, voice recordings, and their step count. Quantitative data were analyzed using descriptive statistics and the Wilcoxon signed-rank test, and qualitative data were analyzed using qualitative descriptive analysis to generate categories. The average age of the participants was 77.7 years. The relationship between participants who were interacting for the first time through the app advanced as their understanding of each other's personalities deepened. The average step count during the third and fourth months was significantly higher than in the first two months. By using the app, older men were able to build relationships with one another. In addition, visualizing the number of steps on the app was effective in improving the number of steps.

In vitro study on the partitioning of red blood cells using a microchannel network.

To investigate the partitioning properties of red blood cells (RBCs) in the bifurcating capillary vessels, an in vitro experiment was performed to perfuse human RBC suspensions into the microfluidic channels with a width of <10 µm. Two types of microchannel geometries were established. One is a single model comprising one parent and two daughter channels with different widths, and the other is a network model that had a symmetric geometry with four consecutive divergences and convergences. In addition to the fractional RBC flux at each bifurcation, changes in hematocrit levels and flow velocity before and after the bifurcation were investigated. In the single model, non-uniform partitioning of RBCs was observed, and this result was in good agreement with that of the empirical model. Furthermore, in the network model, the RBC distribution in the cross-section before the bifurcation significantly affected RBC partitioning in the two channels after the bifurcation. Hence, there was a large RBC heterogeneity in the capillary network. The hematocrit levels between the channels differed for more than one order of magnitude. Therefore, the findings of the current research could facilitate a better understanding of RBC partitioning properties in the microcirculatory system.

Experimentally observed Campylobacter jejuni survival kinetics in chicken meat products during model gastric digestion tended to be lower than model predictions.

Campylobacter jejuni-related foodborne diseases are mainly attributed to the consumption of undercooked chicken meat and cross-contaminated produce. This study aimed to develop a survival kinetics model, based on the Weibull model, for predicting foodborne C. jejuni survival during gastric digestion in a model stomach. We previously confirmed that C. jejuni can survive temperatures up to 62 °C; therefore, certain types of grilled chicken skewers (yakitori) were examined for C. jejuni survival during simulated gastric digestion. C. jejuni survival on a chicken thigh following grilling was examined to confirm the foods for digestion experiments. Further, C. jejuni survival during model digestion was investigated through simultaneous digestion of raw chicken and cross-contaminated iceberg lettuce. The model stomach pH increased from 1.5 to 6.0 immediately after yakitori ingestion and did not decrease below 4.0 within 3 h of digestion. Gastric digestion did not significantly contribute to C. jejuni inactivation (<1.5 log reduction after 3 h digestion). Our model could predict C. jejuni survival kinetics in simulated gastric fluid under varying pH during model digestion. This approach can be used to predict C. jejuni survival rates following digestion to improve food safety and reduce Campylobacter-related disease outbreaks.

Older rural people's perception of connectedness through a communication application: A qualitative descriptive study.

Connectedness among older people is essential for healthy communities, especially among rural populations where limited social interaction and associated health effects may be cause for concern. In this qualitative descriptive study, we explored older rural people's perception of connectedness through a communication application. The study assessed 10 participants (mean age = 76.2 years) living in rural Japan who regularly participated in a senior citizens' club. From July 2019 to January 2020, the participants used a social media application developed by our research team to meet the needs of older people. Semi-structured interviews were conducted. Six themes representing older rural people's perception of connectedness were identified: (1) thoughtful consideration for members strengthened even without them meeting face-to-face, (2) encouragement received from familiar members, (3) joy in sharing daily routine with neighbors, (4) courage to advance through face-to-face interaction, (5) willingness to continue club membership, and (6) fear of disrupting club's harmony. Participants who used the application felt compensated for the lack of social interaction opportunities in rural settings and strengthened their existing relationships.

Competitive growth kinetics of Campylobacter jejuni, Escherichia coli O157:H7 and Listeria monocytogenes with enteric microflora in a small-intestine model.

AIMS: The biological events occurring during human digestion help to understand the mechanisms underlying the dose-response relationships of enteric bacterial pathogens. To better understand these events, we investigated the growth and reduction behaviour of bacterial pathogens in an in vitro model simulating the environment of the small intestine. METHODS AND RESULTS: The foodborne pathogens Campylobacter jejuni, Listeria monocytogenes and Escherichia coli O157:H7 were cultured with multiple competing enteric bacteria. Differences in the pathogen's growth kinetics due to the relative amount of competing enteric bacteria were investigated. These growth differences were described using a mathematical model based on Bayesian inference. When pathogenic and enteric bacteria were inoculated at 1 log CFU per ml and 9 log CFU per ml, respectively, L. monocytogenes was inactivated over time, while C. jejuni and E. coli O157:H7 survived without multiplying. However, as pathogen inocula were increased, its inhibition by enteric bacteria also decreased. CONCLUSIONS: Although the growth of pathogenic species was inhibited by enteric bacteria, the pathogens still survived. SIGNIFICANCE AND IMPACT OF THE STUDY: Competition experiments in a small-intestine model have enhanced understanding of the infection risk in the intestine and provide insights for evaluating dose-response relationships.

A New Dose-Response Model for Estimating the Infection Probability of Campylobacter jejuni Based on the Key Events Dose-Response Framework.

Understanding the dose-response relationship between ingested pathogenic bacteria and infection probability is a key factor for appropriate risk assessment of foodborne pathogens. The objectives of this study were to develop and validate a novel mechanistic dose-response model for Campylobacter jejuni and simulate the underlying mechanism of foodborne illness during digestion. Bacterial behavior in the human gastrointestinal environment, including survival at low pH in the gastric environment after meals, transition to intestines, and invasion to intestinal tissues, was described using a Bayesian statistical model based on the reported experimental results of each process while considering physical food types (liquid versus solid) and host age (young adult versus elderly). Combining the models in each process, the relationship between pathogen intake and the infection probability of C. jejuni was estimated and compared with reported epidemiological dose-response relationships. Taking food types and host age into account, the prediction range of the infection probability of C. jejuni successfully covered the reported dose-response relationships from actual C. jejuni outbreaks. According to sensitivity analysis of predicted infection probabilities, the host age factor and the food type factor have relatively higher relevance than other factors. Thus, the developed "key events dose-response framework" can derive novel information for quantitative microbiological risk assessment in addition to dose-response relationship. The framework is potentially applicable to other pathogens to quantify the dose-response relationship from experimental data obtained from digestion. IMPORTANCE Based on the mechanistic approach called the key events dose-response framework (KEDRF), an alternative to previous nonmechanistic approaches, the dose-response models for infection probability of C. jejuni were developed considering with age of people who ingest pathogen and food type. The developed predictive framework illustrates highly accurate prediction of dose (minimum difference 0.21 log CFU) for a certain infection probability compared with the previously reported dose-response relationship. In addition, the developed prediction procedure revealed that the dose-response relationship strongly depends on food type as well as host age. The implementation of the key events dose-response framework will mechanistically and logically reveal the dose-response relationship and provide useful information with quantitative microbiological risk assessment of C. jejuni on foods.

Bayesian Generalized Linear Model for Simulating Bacterial Inactivation/Growth Considering Variability and Uncertainty.

Conventional regression analysis using the least-squares method has been applied to describe bacterial behavior logarithmically. However, only the normal distribution is used as the error distribution in the least-squares method, and the variability and uncertainty related to bacterial behavior are not considered. In this paper, we propose Bayesian statistical modeling based on a generalized linear model (GLM) that considers variability and uncertainty while fitting the model to colony count data. We investigated the inactivation kinetic data of Bacillus simplex with an initial cell count of 105 and the growth kinetic data of Listeria monocytogenes with an initial cell count of 104. The residual of the GLM was described using a Poisson distribution for the initial cell number and inactivation process and using a negative binomial distribution for the cell number variation during growth. The model parameters could be obtained considering the uncertainty by Bayesian inference. The Bayesian GLM successfully described the results of over 50 replications of bacterial inactivation with average of initial cell numbers of 101, 102, and 103 and growth with average of initial cell numbers of 10-1, 100, and 101. The accuracy of the developed model revealed that more than 90% of the observed cell numbers except for growth with initial cell numbers of 101 were within the 95% prediction interval. In addition, parameter uncertainty could be expressed as an arbitrary probability distribution. The analysis procedures can be consistently applied to the simulation process through fitting. The Bayesian inference method based on the GLM clearly explains the variability and uncertainty in bacterial population behavior, which can serve as useful information for risk assessment related to food borne pathogens.

Evaluation of Strain Variability in Inactivation of Campylobacter jejuni in Simulated Gastric Fluid by Using Hierarchical Bayesian Modeling.

This study was conducted to quantitatively evaluate the variability of stress resistance in different strains of Campylobacter jejuni and the uncertainty of such strain variability. We developed Bayesian statistical models with multilevel analysis to quantify variability within a strain, variability between different strains, and the uncertainty associated with these estimates. Furthermore, we measured the inactivation of 11 strains of C. jejuni in simulated gastric fluid with low pH, using the Weibullian survival model. The model was first developed for separate pH conditions and then analyzed over a range of pH levels. We found that the model parameters developed under separate pH conditions exhibited a clear dependence of survival on pH. In addition, the uncertainty of the variability between different strains could be described as the joint distribution of the model parameters. The latter model, including pH dependency, accurately predicted the number of surviving cells in individual as well as multiple strains. In conclusion, variabilities and uncertainties in inactivation could be simultaneously evaluated and interpreted via a probabilistic approach based on Bayesian theory. Such hierarchical Bayesian models could be useful for understanding individual-strain variability in quantitative microbial risk assessment. IMPORTANCE Since microbial strains vary in their growth and inactivation patterns in food materials, it is important to accurately predict these patterns for quantitative microbial risk assessment. However, most previous studies in this area have used highly resistant strains, which could lead to inaccurate predictions. Moreover, variability, including measurement errors and variability within a strain and between different strains, can contribute to predicted individual-level outcomes. Therefore, a multilevel framework is required to resolve these levels of variability and estimate their uncertainties. We developed a Bayesian predictive model for the survival of Campylobacter jejuni under simulated gastric conditions taking into account the variabilities and uncertainties. We demonstrated a high correspondence between predictions from the model and empirical measurements. The modeling procedure proposed in this study recommends a novel framework for predicting pathogen behavior, which can help improve quantitative microbial risk assessment during food production and distribution.

Application of growth rate from kinetic model to calculate stochastic growth of a bacteria population at low contamination level.

Traditional predictive microbiology is not suited for cell growth predictions for low-level contamination, where individual cell heterogeneity becomes apparent. Accordingly, we simulated a stochastic birth process of bacteria population using kinetic parameters. We predicted the variation in behavior of Salmonella enterica serovar Typhimurium cells at low inoculum density. The modeled cells were grown in tryptic soy broth at 25 °C. Kinetic growth parameters were first determined empirically for an initial cell number of 104 cells. Monte Carlo simulation based on the growth kinetics and Poisson distribution for different initial cell numbers predicted the results of 50 replicate growth experiments with the initial cell number of 1, 10, and 64 cells. Indeed, measured behavior of 85% cells fell within the 95% prediction area of the simulation. The calculations link the kinetic and stochastic birth process with Poisson distribution. The developed model can be used to calculate the probability distribution of population size for exposure assessment and for the evaluation of a probability that a pathogen would exceed critical contamination level during food storage.

Translational medicine of the glutamate AMPA receptor.

Psychiatric and neurological disorders severely hamper patient's quality of life. Despite their high unmet needs, the development of diagnostics and therapeutics has only made slow progress. This is due to limited evidence on the biological basis of these disorders in humans. Synapses are essential structural units of neurotransmission, and neuropsychiatric disorders are considered as "synapse diseases". Thus, a translational approach with synaptic physiology is crucial to tackle these disorders. Among a variety of synapses, excitatory glutamatergic synapses play central roles in neuronal functions. The glutamate α-amino-3-hydroxy-5-methyl-4-isoxazole propionic acid receptor (AMPAR) is a principal component of glutamatergic neurotransmission; therefore, it is considered to be a promising translational target. Here, we review the limitations of current diagnostics and therapeutics of neuropsychiatric disorders and advocate the urgent need for the promotion of translational medicine based on the synaptic physiology of AMPAR. Furthermore, we introduce our recent translational approach to these disorders by targeting at AMPARs.

Population-based study of a free rubella-specific antibody testing and immunization campaign in Chiba city in response to the 2018-2019 nationwide rubella outbreak in Japan.

Japan has not been able to eliminate rubella; as a result, the large rubella epidemic has occurred. Considering the complicated history of the vaccine policy in Japan, some susceptible populations became infected with rubella, resulting in an outbreak. We conducted a large serosurveillance against rubella in Chiba city after initiating free rubella-specific antibody testing and an immunization campaign during 2018-2019. The total number of rubella specific antibody tests that was conducted in the nationwide campaign and Chiba city original campaign was 8277 and 6104, respectively. The proportion of participants with an antibody titer of ≤1:16 using the hemagglutination inhibition (HI) test was higher in those in their 20-30s. On the contrary, the proportion of participants with an antibody titer of <1:8 using the HI test was higher in men in their 40-50s. This discrepancy possibly reflects the complicated history of the vaccine policy. The number of participants in the nationwide immunization campaign in this city was 1517, whereas that in the Chiba city campaign was 3607. The Chiba city campaign was effective against women in their 20-30s (child-bearing generation); however, the nationwide campaign was not sufficiently effective against men in their 40-50s because many workers were did not visit medical facilities to receive the measles-rubella vaccine.

Modeling Invasion of Campylobacter jejuni into Human Small Intestinal Epithelial-Like Cells by Bayesian Inference.

Current approaches used for dose-response modeling of low-dose exposures of pathogens rely on assumptions and extrapolations. These models are important for quantitative microbial risk assessment of food. A mechanistic framework has been advocated as an alternative approach for evaluating dose-response relationships. The objectives of this study were to investigate the invasion behavior of Campylobacter jejuni, which could arise as a foodborne illness even if there are low counts of pathogens, into Caco-2 cells as a model of intestinal cells and to develop a mathematical model for invading cell counts to reveal a part of the infection dose-response mechanism. Monolayer-cultured Caco-2 cells and various concentrations of C. jejuni in culture were cocultured for up to 12 h. The numbers of C. jejuni bacteria invading Caco-2 cells were determined after coculture for different time periods. There appeared to be a maximum limit to the invading bacterial counts, which showed an asymptotic exponential increase. The invading bacterial counts were higher with higher exposure concentrations (maximum, 5.0 log CFU/cm2) than with lower exposure concentrations (minimum, 0.6 log CFU/cm2). In contrast, the ratio of invading bacteria (number of invading bacteria divided by the total number of bacteria exposed) showed a similar trend regardless of the exposure concentration. Invasion of C. jejuni into intestinal cells was successfully demonstrated and described by the developed differential equation model with Bayesian inference. The model accuracy showed that the 99% prediction band covered more than 97% of the observed values. These findings provide important information on mechanistic pathogen dose-response relationships and an alternative approach for dose-response modeling.IMPORTANCE One of the infection processes of C. jejuni, the invasion behavior of the bacteria in intestinal epithelial cells, was revealed, and a mathematical model for prediction of the cell-invading pathogen counts was developed for the purpose of providing part of a dose-response model for C. jejuni based on the infection mechanism. The developed predictive model showed a high accuracy of more than 97% and successfully described the C. jejuni invading counts. The bacterial invasion predictive model of this study will be essential for the development of a dose-response model for C. jejuni based on the infection mechanism.

Describing the Individual Spore Variability and the Parameter Uncertainty in Bacterial Survival Kinetics Model by Using Second-Order Monte Carlo Simulation.

The objective of this study was to separately describe the fitting uncertainty and the variability of individual cell in bacterial survival kinetics during isothermal and non-isothermal thermal processing. The model describing bacterial survival behavior and its uncertainties and variabilities during non-isothermal inactivation was developed from survival kinetic data for Bacillus simplex spores under fifteen isothermal conditions. The fitting uncertainties in the parameters used in the primary Weibull model was described by using the bootstrap method. The variability of individual cells in thermotolerance and the true randomness in the number of dead cells were described by using the Markov chain Monte Carlo (MCMC) method. A second-order Monte Carlo (2DMC) model was developed by combining both the uncertainties and variabilities. The 2DMC model was compared with reduction behavior under three non-isothermal profiles for model validation. The bacterial death estimations were validated using experimentally observed surviving bacterial count data. The fitting uncertainties in the primary Weibull model parameters, the individual thermotolerance heterogeneity, and the true randomness of inactivated spore counts were successfully described under all the iso-thermal conditions. Furthermore, the 2DMC model successfully described the variances in the surviving bacterial counts during thermal inactivation for all three non-isothermal profiles. As a template for risk-based process designs, the proposed 2DMC simulation approach, which considers both uncertainty and variability, can facilitate the selection of appropriate thermal processing conditions ensuring both food safety and quality.

Transforming kinetic model into a stochastic inactivation model: Statistical evaluation of stochastic inactivation of individual cells in a bacterial population.

Kinetic models performing point estimation are effective in predicting the bacterial behavior. However, the large variation of bacterial behavior appearing in a small number of cells, i.e. equal or less than 102 cells, cannot be expressed by point estimation. We aimed to predict the variation of Escherichia coli O157:H7 behavior during inactivation in acidified tryptone soy broth (pH3.0) through Monte Carlo simulation and evaluated the accuracy of the developed model. Weibullian fitted parameters were estimated from the kinetic survival data of E. coli O157:H7 with an initial cell number of 105. A Monte Carlo simulation (100 replication) based on the obtained Weibullian parameters and the Poisson distribution of initial cell numbers successfully predicted the results of 50 replications of bacterial inactivation with initial cell numbers of 101, 102, and 103 cells. The accuracy of the simulation revealed that more than 83% of the observed survivors were within predicted range in all condition. 90% of the distribution in survivors with initial cells less than 100 is equivalent to a Poisson distribution. This calculation transforms the traditional microbial kinetic model into probabilistic model, which can handle bacteria number as discrete probability distribution. The probabilistic approach would utilize traditional kinetic model towards exposure assessment.

Riluzole-induced interstitial lung disease is a rare and potentially life-threatening adverse event successfully treated with high-dose steroid therapy: Case reports and review of the literature.

Riluzole (RZ)-induced interstitial lung disease (RZ-ILD) is a rare and potentially life-threatening adverse event in amyotrophic lateral sclerosis (ALS) patients, which is rarely reported. Therefore, the optimal treatment for RZ-ILD is unclear. We describe herein three Japanese cases of ALS complicated with RZ-ILD, of which two were successfully treated with high-dose steroid therapy. In our all ALS cases with RZ-ILD, the duration of RZ exposure until RZ-ILD onset was within 2 months. All three cases showed respiratory symptoms, dorsal predominant ground-glass opacities by imaging analysis, and abnormal laboratory findings associated with interstitial lung diseases, such as Krebs von den Lungen-6 and surfactant protein-D. Intravenous high-dose steroid therapy together with the discontinuation of RZ in two cases with respiratory symptoms markedly ameliorated their symptoms and abnormal findings of RZ-ILD. One case showed mild respiratory symptoms compared with the others and recovered after the withdrawal of RZ only. According to previous case reports and our cases, RZ-ILD may develop 2 months after initiating RZ and exacerbate respiratory symptoms rapidly in ALS patients with severe respiratory muscle involvement or complicating aspiration pneumonia. Transient high-dose steroid therapy in addition to discontinuation of RZ might be a good therapeutic option for RZ-ILD.

Stochastic modeling of variability in survival behavior of Bacillus simplex spore population during isothermal inactivation at the single cell level using a Monte Carlo simulation.

The control of bacterial reduction is important to maintain food safety during thermal processing. The goal of this study was to illustrate and describe variability in bacterial population behavior during thermal processing as a probability distribution based on individual cell heterogeneity regarding heat resistance. Toward this end, we performed a Monte Carlo simulation via computer, and compared and validated the simulated estimations with observed values. Weibullian fitted parameters were estimated from the kinetic survival data of Bacillus simplex during thermal treatment at 94 °C. The variability in reductions of bacterial sporular populations was illustrated using Monte Carlo simulation based on the Weibull distribution of the parameters. In particular, variabilities in viable spore counts and survival probability of the B. simplex spore population were simulated in various replicates. We also experimentally determined the changes in survival probability and distributions of survival spore counts; notably, these were successfully predicted by the Monte Carlo simulation based on the kinetic parameters. The kinetic parameter-based Monte Carlo simulation could thus successfully illustrate bacterial population behavior variability during thermal processing as a probability distribution. The simulation approach may contribute to improving food quality through risk-based processing designs and enhance risk assessment model accuracy.

Calculating stochastic inactivation of individual cells in a bacterial population using variability in individual cell inactivation time and initial cell number.

The traditional log-linear inactivation kinetics model considers microbial inactivation as a process that follows first-order kinetics. A basic concept of log reduction is decimal reduction time (D-value), which means time/dose required to kill 90% of the relevant microorganisms. D-value based on the first-order survival kinetics model is insufficient for reliable estimations of bacterial survivors following inactivation treatment. This is because the model does not consider the inactivation curvature and variability in bacterial inactivation. However, although the D-value has some limitations, it is widely used for risk assessment and sterilization time estimation. In this study, stochastic inactivation models are used in place of the conventional D-value to describe the probability of a population containing survivors. As representative bacterial inactivation normally follows a log-linear or log-Weibull model, we calculate the time required for a specific decrease in the number of cells and the number of survival cells as a probability distribution using the stochastic inactivation of individual cells in a population. We compare the probability of a population containing survivors calculated via the D-value, an inactivation kinetics model, and the stochastic formula. The stochastic calculation can be approximately estimated via a kinetic curvature model with less than 5% difference below the probability of a population containing survivors 0.1. This stochastic formula indicates that the D-value model would over- or under-estimate the probability of a population containing survivors when applied to inactivation kinetics with curvature. The results presented in this study show that stochastic analysis using mathematical models that account for variability in the individual cell inactivation time and initial cell number would lead to a realistic and probabilistic estimation of bacterial inactivation.