A mathematical model for the transmission of Salmonella Typhimurium within a grower-finisher pig herd in Great Britain

Staged progression epidemic models for the transmission of invasive nontyphoidal Salmonella (iNTS) with treatment

We develop and analyze a stage-progression compartmental model to study the emerging invasive nontyphoidal Salmonella (iNTS) epidemic in sub-Saharan Africa. iNTS bloodstream infections are often fatal, and the diverse and non-specific clinical features of iNTS make it difficult to diagnose. We focus our study on identifying approaches that can reduce the incidence of new infections. In sub-Saharan Africa, transmission and mortality are correlated with the ongoing HIV epidemic and severe malnutrition. We use our model to quantify the impact that increasing antiretroviral therapy (ART) for HIV infected adults and reducing malnutrition in children would have on mortality from iNTS in the population. We consider immunocompromised subpopulations in the region with major risk factors for mortality, such as malaria and malnutrition among children and HIV infection and ART coverage in both children and adults. We parameterize the progression rates between infection stages using the branching probabilities and estimated time spent at each stage. We interpret the basic reproduction number R0 as the total contribution from an infinite infection loop produced by the asymptomatic carriers in the infection chain. The results indicate that the asymptomatic HIV+ adults without ART serve as the driving force of infection for the iNTS epidemic. We conclude that the worst disease outcome is among the pediatric population, which has the highest infection rates and death counts. Our sensitivity analysis indicates that the most effective strategies to reduce iNTS mortality in the studied population are to improve the ART coverage among high-risk HIV+ adults and reduce malnutrition among children.

An SEIR model of influenza A virus infection and reinfection within a farrow-to-finish swine farm

Influenza A virus (IAV) in swine is a pathogen that causes a threat to the health as well as to the production of swine. Moreover, swine can spread this virus to other species including humans. The virus persists in different types of swine farms as evident in a number of studies. The core objectives of this study are (i) to analyze the dynamics of influenza infection of a farrow-to-finish swine farm, (ii) to explore the reinfection at the farm level, and finally (iii) to examine the effectiveness of two control strategies: vaccination and reduction of indirect contact. The analyses are conducted using a deterministic Susceptible-Exposed-Infectious-Recovered (SEIR) model. Simulation results show that the disease is maintained in gilts and piglets because of new susceptible pigs entering the population on a weekly basis. A sensitivity analysis shows that the results are not sensitive to variation in the parameters. The results of the reinfection simulation indicate that the virus persists in the entire farm. The control strategies studied in this work are not successful in eliminating the virus within the farm.

Bayesian model for tracing Salmonella contamination in the pig feed chain

Salmonella infections in pigs are in most cases asymptomatic, posing a risk of salmonellosis for pork consumers. Salmonella can transmit to pigs from various sources, including contaminated feed. We present an approach for quantifying the risk to pigs from contaminations in the feed chain, based on a Bayesian model. The model relies on Salmonella surveillance data and other information from surveys, reports, registries, statistics, legislation and literature regarding feed production and pig farming. Uncertainties were probabilistically quantified by synthesizing evidence from the available information over a categorically structured flow chain of ingredients mixed for feeds served to pigs. Model based probability for infection from feeds together with Salmonella subtyping data, were used to estimate the proportion of Salmonella infections in pigs attributable to feed. The results can be further used in assessments considering the human health risk linked to animal feed via livestock. The presented methods can be used to predict the effect of changes in the feed chain, and they are generally applicable to other animals and pathogens.

Understanding the effects of intermittent shedding on the transmission of infectious diseases: example of salmonellosis in pigs

A number of environmentally transmitted infectious diseases are characterized by intermittent infectiousness of infected hosts. However, it is unclear whether intermittent infectiousness must be explicitly accounted for in mathematical models for these diseases or if a simplified modelling approach is acceptable. To address this question we study the transmission of salmonellosis between penned pigs in a grower-finisher facility. The model considers indirect transmission, growth of free-living Salmonella within the environment, and environmental decontamination. The model is used to evaluate the role of intermittent fecal shedding by comparing the behaviour of the model with constant versus intermittent infectiousness. The basic reproduction number, [Formula: see text], is used to determine the long-term behaviour of the model regarding persistence or extinction of infection. The short-term behaviour of the model, relevant to swine production, is considered by examining the prevalence of infection at slaughter. Comparison of the two modelling approaches indicates that neglecting the intermittent pattern of infectiousness can result in biased estimates for [Formula: see text] and infection prevalence at slaughter. Therefore, models for salmonellosis or similar infections should explicitly account for the mechanism of intermittent infectiousness.

Mathematical Modeling Tools to Study Preharvest Food Safety

This article provides an overview of the emerging field of mathematical modeling in preharvest food safety. We describe the steps involved in developing mathematical models, different types of models, and their multiple applications. The introduction to modeling is followed by several sections that introduce the most common modeling approaches used in preharvest systems. We finish the chapter by outlining potential future directions for the field.

Modelling the within-herd transmission of Mycoplasma hyopneumoniae in closed pig herds

Background

A discrete time, stochastic, compartmental model simulating the spread of Mycoplasma hyopneumoniae within a batch of industrially raised pigs was developed to understand infection dynamics and to assess the impact of a range of husbandry practices. A ‘disease severity’ index was calculated based on the ratio between the cumulative numbers of acutely and chronically diseased and infectious pigs per day in each age category, divided by the length of time that pigs spent in this age category. This is equal to the number of pigs per day, either acutely or chronically infectious and diseased, divided by the number of all pigs per all days in the model. The impact of risk and protective factors at batch level was examined by adjusting ‘acclimatisation of gilts’, ‘length of suckling period’, ‘vaccination of suckling pigs against M. hyopneumoniae’, ‘contact between fattening pigs of different age during restocking of compartments’ and ‘co-infections in fattening pigs’.

Results

The highest ‘disease severity’ was predicted, when gilts do not have contact with live animals during their acclimatisation, suckling period is 28 days, no vaccine is applied, fatteners have contact with pigs of other ages and are suffering from co-infections. Pigs in this scenario become diseased/infectious for 26.1 % of their lifetime. Logistic regression showed that vaccination of suckling pigs was influential for ‘disease severity’ in growers and finishers, but not in suckling and nursery pigs. Lack of contact between gilts and other live pigs during the acclimatisation significantly influenced the ‘disease severity’ in suckling pigs but had less impact in growing and finishing pigs. The length of the suckling period equally affected the severity of the disease in all age groups with the strongest association in nursery pigs. The contact between fatteners of different groups influenced the course of infection among finishers, but not among other pigs. Finally, presence of co-infections was relevant in growers and finishers, but not in younger pigs.

Conclusion

The developed model allows comparison of different prevention programmes and strategies for controlling transmission of M. hyopneumoniae.

Electronic supplementary material

The online version of this article (doi:10.1186/s40813-016-0026-1) contains supplementary material, which is available to authorized users.

Oral vaccination with a rough attenuated mutant of S. Infantis increases post-wean weight gain and prevents clinical signs of salmonellosis in S. Typhimurium challenged pigs

We show that oral inoculation of 14 day old conventional piglets with a rough attenuated Salmonella enterica serovar Infantis 1326/28Ф(r) (serogroup C1), 24h prior to oral challenge with S. enterica serovar Typhimurium 4/74 (serogroup B), resulted in significant weight gain (~10%) measured at 14 days post-weaning (38 days of age). Two days after challenge the S. Typhimurium induced stunting and, in some cases loss, of villi but this was prevented by pre-inoculation with the S. Infantis strain. The clinical signs of disease associated with S. Typhimurium 4/74 challenge and faecal shedding were also significantly (P<0.05) reduced by pre-inoculation with the S. Infantis mutant. Pre-inoculation of pigs with the S. Infantis mutant also increased weight gain in pigs challenged with pathogenic Escherichia coli. However, Mycobacterium bovis BCG, an unrelated intracellular bacterium, did not protect against challenge with S. Typhimurium 4/74.

Mathematical modeling of influenza A virus dynamics within swine farms and the effects of vaccination

Influenza A virus infections are widespread in swine herds across the world. Influenza negatively affects swine health and production, and represents a significant threat to public health due to the risk of zoonotic infections. Swine herds can act as reservoirs for potentially pandemic influenza strains. In this study, we develop mathematical models based on experimental data, representing typical breeding and wean-to-finish swine farms. These models are used to explore and describe the dynamics of influenza infection at the farm level, which are at present not well understood. In addition, we use the models to assess the effectiveness of vaccination strategies currently employed by swine producers, testing both homologous and heterologous vaccines. An important finding is that following an influenza outbreak in a breeding herd, our model predicts a persistently high level of infectious piglets. Sensitivity analysis indicates that this finding is robust to changes in both transmission rates and farm size. Vaccination does not eliminate influenza throughout the breeding farm population. In the wean-to-finish herd, influenza infection may persist in the population only if recovered individuals become susceptible to infection again. A homologous vaccine administered to the entire wean-to-finish population after the loss of maternal antibodies eliminates influenza, but a vaccine that only induces partial protection (heterologous vaccine) has little effect on influenza infection levels. Our results have important implications for the control of influenza in swine herds, which is crucial in order to reduce both losses for swine producers and the risk to public health.

Understanding the role of cleaning in the control of Salmonella Typhimurium in grower-finisher pigs: a modelling approach

Salmonella Typhimurium (STM) infection in pigs represents a considerable food safety concern. This study used mathematical modelling to evaluate the effectiveness of cleaning (faeces removal) as a measure to control STM spread among grower-finisher pigs. A modified Susceptible-Infected-Recovered-Susceptible (SIRS) model of STM transmission through a contaminated environment was developed. Infected pigs were divided into three states according to the pathogen level being shed in their faeces. Infection transmission was evaluated using the basic reproduction number (R 0) and the prevalence of infectious pigs at slaughter age. Although increased frequency and efficiency of cleaning did reduce the prevalence of STM shedding at the time of slaughter, these efforts alone were not capable of eliminating the infection from the population. The level of STM faecal shedding by infectious pigs strongly influenced the infection spread and prevalence at slaughter. To control STM in pigs, cleaning should be combined with vaccination and/or isolation of high-level shedders.

Effectiveness of simulated interventions in reducing the estimated prevalence of Salmonella in UK pig herds

Salmonella spp are a major foodborne zoonotic cause of human illness. Consumption of pork products is believed to be a major source of human salmonellosis and Salmonella control throughout the food-chain is recommended. A number of on-farm interventions have been proposed, and some have been implemented in order to try to achieve Salmonella control. In this study we utilize previously developed models describing Salmonella dynamics to investigate the potential effects of a range of these on-farm interventions. As the models indicated that the number of bacteria shed in the faeces of an infectious animal was a key factor, interventions applied within a high-shedding scenario were also analysed. From simulation of the model, the probability of infection after Salmonella exposure was found to be a key driver of Salmonella transmission. The model also highlighted that minimising physiological stress can have a large effect but only when shedding levels are not excessive. When shedding was high, weekly cleaning and disinfection was not effective in Salmonella control. However it is possible that cleaning may have an effect if conducted more often. Furthermore, separating infectious animals, shedding bacteria at a high rate, from the rest of the population was found to be able to minimise the spread of Salmonella.

Semi-stochastic models for Salmonella infection within finishing pig units in the UK

A multi-group semi-stochastic model is formulated to describe Salmonella dynamics on a pig herd within the UK and assess whether farm structure has any effect on the dynamics. The models include both direct transmission and indirect (via free-living infectious units in the environment and airborne infection). The basic reproduction number R0 is also investigated. The models estimate approximately 24.6% and 25.4% of pigs at slaughter weight will be infected with Salmonella within a slatted-floored and solid-floored unit respectively, which corresponds to values found in previous abattoir and farm studies, suggesting that the model has reasonable validity. Analysis of the models identified the shedding rate to be of particular importance in the control of Salmonella spread, a finding also evident in an increase in the R0 value.

Modelling batch farrowing management within a farrow-to-finish pig herd: influence of management on contact structure and pig delivery to the slaughterhouse

Pathogen spread within pig host populations can vary depending on within-herd interactions among pigs also called the contact structure. The recommended batch farrowing management, allowing for a fixed-interval mating for groups of sows of equal size, called batches, leads to an all-in/all-out management of pigs in which animals in different batches have no contact. To maintain a profitable pig delivery, producers have to deliver groups of pigs at a given weight, what needs sometimes herd management adaptations. However, producers' adaptations that avoid delivering pigs below slaughtering weight (out-of-range pigs), result in increasing the contact between animals from different batches. To study the influence of herd management on contact structure and on pig delivery, a stochastic mathematical model representing population dynamics within a farrow-to-finish herd was elaborated. Sixteen management systems were represented combining or not the all-in/all-out management system with producers' decisions: batch mixing, use of an extra room, suppression of the drying period and sale of post-weaning batches. Two types of contact were considered: via the animals themselves, when batch mixing occurred; and via the room, when decontamination was not complete. The impact of producers' decisions on contact structure and on pig delivery, differed radically when pig growth was normal and when it was slow (i.e. mean age at slaughtering weight increased by 20%). When pig growth was normal, the all-in/all-out management prevented both contact via the animals and via the room but resulted in 9% of pigs delivered out of range. The use of an extra room or batch mixing decreased this percentage, the latter resulting in very frequent contact between batches via the animals. When pig growth was slow, the all-in/all-out management led to a very high percentage of pigs delivered out of range (almost 80%). The suppression of the drying period at the end of the finishing period and the sale of post-weaning batches induced a significant decrease in this percentage (down to 2% to 20%), the latter allowing to reduce the percentage of batches that made contact via the room (40% instead of 80%). This pig herd model helped to understand the compromise for producers between implementing internal biosecurity or maintaining a profitable pig delivery. Our results show that there was no unique optimal system and that efficient producers' decisions (for biosecurity and delivery) may differ, depending on pig growth.

Salmonella fecal shedding and immune responses are dose- and serotype- dependent in pigs

Despite the public health importance of Salmonella infection in pigs, little is known about the associated dynamics of fecal shedding and immunity. In this study, we investigated the transitions of pigs through the states of Salmonella fecal shedding and immune response post-Salmonella inoculation as affected by the challenge dose and serotype. Continuous-time multistate Markov models were developed using published experimental data. The model for shedding had four transient states, of which two were shedding (continuous and intermittent shedding) and two non-shedding (latency and intermittent non-shedding), and one absorbing state representing permanent cessation of shedding. The immune response model had two transient states representing responses below and above the seroconversion level. The effects of two doses [low (0.65×10⁶ CFU/pig) and high (0.65×10⁹ CFU/pig)] and four serotypes (Salmonella Yoruba, Salmonella Cubana, Salmonella Typhimurium, and Salmonella Derby) on the models' transition intensities were evaluated using a proportional intensities model. Results indicated statistically significant effects of the challenge dose and serotype on the dynamics of shedding and immune response. The time spent in the specific states was also estimated. Continuous shedding was on average 10–26 days longer, while intermittent non-shedding was 2–4 days shorter, in pigs challenged with the high compared to low dose. Interestingly, among pigs challenged with the high dose, the continuous and intermittent shedding states were on average up to 10–17 and 3–4 days longer, respectively, in pigs infected with S. Cubana compared to the other three serotypes. Pigs challenged with the high dose of S. Typhimurium or S. Derby seroconverted on average up to 8–11 days faster compared to the low dose. These findings highlight that Salmonella fecal shedding and immune response following Salmonella challenge are dose- and serotype-dependent and that the detection of specific Salmonella strains and immune responses in pigs are time-sensitive.

Salmonella control measures with special focus on vaccination and logistic slaughter procedures

This study focussed on the effectiveness of Salmonella control measures to decrease Salmonella prevalence at slaughter. Considered measures were the control of hygiene and husbandry management as well as vaccination and logistic slaughter procedures. Results emphasized the capabilities of the farrowing stage to influence slaughter pig prevalence. Limited Salmonella entry by the implementation of hygiene control measures at farrowing farms obtained a significant decrease in prevalence after lairage at slaughterhouse. In contrast, hygiene control measures at finishing stage were less effective. Husbandry control measures, preventing physical contacts between pigs, were proved to decrease slaughter pig prevalence whether they were implemented at farrowing or finishing stage. Furthermore, the vaccination of sows and piglets was an appropriate control measure to decrease slaughter pig prevalence, if a large part of farms established this control measure. Simultaneous implementation of control measures showed that vaccination and especially hygiene measures are mutually supportive. Concerning logistic slaughter procedures it became obvious that with decreasing prevalence, infections at transport and lairage become more and more important. The herd status separation significantly decreased the percentage of infected pigs that became infected at lairage.

Development of a self-regulated dynamic model for the propagation of Salmonella Typhimurium in pig farms

A self-regulated epidemic model was developed to describe the dynamics of Salmonella Typhimurium in pig farms and predict the prevalence of different risk groups at slaughter age. The model was focused at the compartment level of the pig farms and it included two syndromes, a high and a low propagation syndrome. These two syndromes generated two different classes of pigs, the High Infectious and the Low Infectious, respectively, which have different shedding patterns. Given the two different classes and syndromes, the Infectious Equivalent concept was used, which reflected the combination of High and Low Infectious pigs needed for the high propagation syndrome to be triggered. Using the above information a new algorithm was developed that decides, depending on the Infectious Equivalent, which of the two syndromes should be triggered. Results showed that the transmission rate of S. Typhimurium for the low propagation syndrome is around 0.115, pigs in Low Infectious class contribute to the transmission of the infection by 0.61-0.80 of pigs in High Infectious class and that the Infectious Equivalent should be above 10-14% of the population in order for the high propagation syndrome to be triggered. This self-regulated dynamic model can predict the prevalence of the classes and the risk groups of pigs at slaughter age for different starting conditions of infection.

Impact of antimicrobial usage on the transmission dynamics of antimicrobial resistant bacteria among pigs

There is increasing evidence showing that antimicrobial consumption provides a powerful selective force that promotes the emergence of resistance in pathogenic, commensal as well as zoonotic bacteria in animals. The main aim of this study was to develop a modeling framework that can be used to assess the impact of antimicrobial usage in pigs on the emergence and transmission of resistant bacteria within a finisher pig farm. The transmission dynamics of drug-sensitive and drug-resistant bacteria among pigs in the herd were characterized by studying the local and global stability properties of steady state solutions of the system. Numerical simulations demonstrating the influence of factors such as initial prevalence of infection, presence of pre-existing antimicrobial resistant mutants, and frequency of treatment on predicted prevalence were performed. Sensitivity analysis revealed that two parameters had a huge influence on the predicted proportion of pigs carrying resistant bacteria: (a) the transmission coefficient between uninfected pigs and those infected with drug-resistant bacteria during treatment (beta(2)) and after treatment stops (beta(3)), and (b) the spontaneous clear-out rate of drug-resistant bacteria during treatment (gamma(2)) and immediately after treatment stops (gamma(3)). Control measures should therefore be geared towards reducing the magnitudes of beta(2) and beta(3) or increasing those of gamma(2) and gamma(3).

Modelling Salmonella spread within a farrow-to-finish pig herd

Delivery of infected pigs to the slaughterhouse is a major source of pork meat contamination by bacterial hazards to humans. We propose a model of Salmonella spread within a farrow-to-finish pig herd, assuming the prevalence in infected delivered pigs depends on the whole pig life-time and growing process. This stochastic discrete-time model represents both the population dynamics in a farrow-to-finish pig herd using batch management, and Salmonella spread. Four mutually exclusive individual health states were considered: Salmonella-free, seronegative shedder, seropositive shedder and seropositive not shedding carrier, making the distinction between seropositive animals and shedders. Since indirect transmission is the main route of transmission, the probability of infection depends on the quantity of Salmonella in the pigs' environment (Q). A dose effect function is used with two thresholds, assuming saturation in exposure for high Q vs. a minimum exposure for low Q. Salmonella is introduced in an initially Salmonella-free 150-sow herd. Prevalence of shedders and seroprevalence are calculated over time in batches of sows and pigs, and in groups of delivered pigs, composed of pigs from different batches. The model shows very variable seroprevalence over time within a herd among delivered groups, as well as among replications. The mean seroprevalence and the mean shedding prevalence are 19.3% and 13.8% respectively. A sensitivity analysis shows that the Salmonella quantity shed and the maternal protective factor are the most influential parameters on Salmonella prevalence in delivered pigs.

Testing an ecological model for transmission of Salmonella enterica in swine production ecosystems using genotyping data

An ecological model for transmission of Salmonella enterica in swine production ecosystems was developed, identifying host species, environmental reservoirs, and temporal, spatial, and functional (i.e., stage of production) dimensions. It was hypothesized that transmission was most likely within spatial and functional compartments, between hosts of the same species and abiotic compartments of the same type. Eighteen swine production systems in Illinois, USA, were sampled in four collection cycles (1998, 1999, 2000, 2003). There were 11,873 samples collected, including feces from swine and other mammals and birds, and samples from insects, pen floors, boots, feed, and water. The 460 Salmonella isolates obtained were genotyped using repetitive sequence PCR with three primers-REP, BOX, and ERIC. All isolates from 2000 and 2003 were serotyped, as well as a subsample from 1998 and 1998. Genetic relatedness was estimated from the similarity of fragmentation patterns after gel electrophoresis of PCR products. Cluster analysis identified genetically related isolates. Linking of isolates in tight clusters (similarity >or=85%) was viewed as evidence for transmission. Five farms had a sufficient number of tight clusters for hypothesis testing. The factors most differentiating isolates genetically were farm of origin and time of sampling. Isolates were also differentiated genetically by site, building, room, and pen. There was no consistent association of genotype with stage of production or host/environment reservoir. Serotype analysis confirmed that Salmonella lineages were differentiated by visit and site. Thus, Salmonella transmission was primarily over short distances, i.e., within the same pen or room, with some transmission between rooms and buildings on the same site, but with limited transmission between sites. Transmission was observed across a variety of ecological niches represented by different host species and environmental reservoirs. Genetic differences over time reflected multiple introductions into the ecosystem of different Salmonella genotypes, as well as evolutionary changes within lineages. Intervention strategies to reduce Salmonella prevalence within swine production ecosystems would be best targeted at maintaining spatial barriers to transmission, whereas intervention targeted at specific biological hosts or environmental reservoirs is less likely to be effective.

Dynamics of Salmonella transmission on a British pig grower-finisher farm: a stochastic model

Previous modelling studies have estimated that between 1% and 10% of human salmonella infections are attributable to pig meat consumption. In response to this food safety threat the British pig industry have initiated a salmonella monitoring programme. It is anticipated that this programme will contribute to achieving a UK Food Standards Agency target for reducing salmonella levels in pigs at slaughter by 50% within 5 years. In order to better inform the monitoring programme, we have developed a stochastic transmission model for salmonella in a specialist grower-finisher pig herd, where data from a Danish longitudinal study have been used to estimate some of the key model parameters. The model estimates that about 17% of slaughter-age pigs will be infected with salmonella, and that of these infected pigs about 4% will be excreting the organism. In addition, the model shows that the most effective control strategies will be those that reduce between-pen transmission.

A mathematical model of the dynamics of Salmonella Cerro infection in a US dairy herd

We developed a mathematical model of the transmission dynamics of salmonella to describe an outbreak of S. Cerro infection that occurred in a Pennsylvania dairy herd. The data were collected as part of a cooperative research project between the Regional Dairy Quality Management Alliance and the Agricultural Research Service. After the initial detection of a high prevalence of S. Cerro infection in the herd, a frequent and intensive sampling was conducted and the outbreak was followed for 1 year. The data showed a persistent presence of S. Cerro with a high prevalence of infection in the herd. The dynamics of host and pathogen were modelled using a set of nonlinear differential equations. A more realistically distributed (gamma-distributed) infectious period using multiple stages of infection was considered. The basic reproduction number was calculated and relevance to the intervention strategies is discussed.