We describe a new mechanistic bioeconomic model for simulating the spread of Mycobacterium avium subsp. paratuberculosis (MAP) within a dairy cattle herd. The model includes age-dependent susceptibility for infection; age-dependent sensitivity for detection; environmental MAP build up in five separate areas of the farm; in utero infection; infection via colostrum and waste milk, and it allows for realistic culling (i.e., due to other diseases) by including a ranking system. We calibrated the model using a unique dataset from Denmark, including 102 random farms with no control actions against spread of MAP. Likewise, four control actions recommended in the Danish MAP control program were implemented in the model based on reported management strategies in Danish dairy herds in a MAP control scheme. We tested the model parameterization in a sensitivity analysis. We show that a test-and-cull strategy is on average the most cost-effective solution to decrease the prevalence and increase the total net revenue on a farm with low hygiene, but not more profitable than no control strategy on a farm with average hygiene. Although it is possible to eradicate MAP from the farm by implementing all four control actions from the Danish MAP control program, it was not economically attractive since the expenses for the control actions outweigh the benefits. Furthermore, the three most popular control actions against the spread of MAP on the farm were found to be costly and inefficient in lowering the prevalence when used independently.

General anesthetics are known to cause depression of the freezing point of transitions in biomembranes. This is a consequence of ideal mixing of the anesthetic drugs in the membrane fluid phase and exclusion from the solid phase. Such a generic law provides physical justification of the famous Meyer-Overton rule. We show here that general anesthetics, barbiturates, and local anesthetics all display the same effect on melting transitions. Their effect is reversed by hydrostatic pressure. Thus, the thermodynamic behavior of local anesthetics is very similar to that of general anesthetics. We present a detailed thermodynamic analysis of heat capacity profiles of membranes in the presence of anesthetics. Using this analysis, we are able to describe experimentally observed calorimetric profiles and predict the anesthetic features of arbitrary molecules. In addition, we discuss the thermodynamic origin of the cutoff effect of long-chain alcohols and the additivity of the effect of general and local anesthetics.

More than 30% of E. coli strains sampled from pig farms in Denmark over the last five years were resistant to the commonly used antimicrobial tetracycline. This raises a number of questions: How is this high level sustained if resistant bacteria have reduced growth rates? Given that there are multiple susceptible and resistant bacterial strains in the pig intestines, how can we describe their coexistence? To what extent does the composition of these multiple strains in individual pigs influence the total bacterial population of the pig pen? What happens to a complex population when antimicrobials are used? To investigate these questions, we created a model where multiple strains of bacteria coexist in the intestines of pigs sharing a pen, and explored the parameter limits of a stable system; both with and without an antimicrobial treatment. The approach taken is a deterministic bacterial population model with stochastic elements of bacterial distributions and transmission. The rates that govern the model are process-oriented to represent growth, excretion, and uptake from environment, independent of herd and meta-population structures. Furthermore, an entry barrier and elimination process for the individual strains in each pig were implemented. We demonstrate how competitive growth between multiple bacterial strains in individual pigs, and the transmission between pigs in a pen allow for strains of antimicrobial resistant bacteria to persist in a pig population to different extents, and how quickly they can become dominant if antimicrobial treatment is initiated. The level of spread depends in a non-linear way of the parameters that govern excretion and uptake. Furthermore, the sampling of initial distributions of strains and stochastic transmission events give rise to large variation in how homogenous and how resistant the bacterial population becomes. Most important: resistant bacteria are demonstrated to survive with a disadvantage in growth rate of well over 10%.

Precise estimates of disease transmission rates are critical for epidemiological simulation models. Most often these rates must be estimated from longitudinal field data, which are costly and time-consuming to conduct. Consequently, measures to reduce cost like increased sampling intervals or subsampling of the population are implemented. To assess the impact of such measures we implement two different SIS models to simulate disease transmission: A simple closed population model and a realistic dairy herd including population dynamics. We analyze the accuracy of different methods for estimating the transmission rate. We use data from the two simulation models and vary the sampling intervals and the size of the population sampled. We devise two new methods to determine transmission rate, and compare these to the frequently used Poisson regression method in both epidemic and endemic situations. For most tested scenarios these new methods perform similar or better than Poisson regression, especially in the case of long sampling intervals. We conclude that transmission rate estimates are easily biased, which is important to take into account when using these rates in simulation models.Simulation models are widely used to model spread and control of many different infectious diseases in both human and veterinary medicine 1 , for instance malaria 2 , SARS 3 , STDs 4 , influenza 5 , MRSA 6 , Ebola 7 , rabies 8 , scrapie 9 and mastitis 10. In these models, transmission rates are used to describe the flow of individuals in a population going from a susceptible state to an infected state, and it is important to obtain a realistic estimate of the transmission rates in order to create a useful and realistic simulation models for decision support [11][12][13] . Accurate estimation of this rate is important because it can have a major influence on model predictions and conclusions (e.g. refs 11 and 14). The rate may have different names depending on the specific mathematical representation of transfer between susceptible and disease states, e.g. infection rate, transmission coefficient and transmission rate. This key parameter is difficult to estimate for most host-pathogen models because natural processes are stochastic, and transmission events are influenced by other parameters than what can be included in a transmission model 1,15 . Thus, large datasets are often needed to reach a good estimate.Experiments that can be used to estimate the transmission rate are often both difficult and time-consuming to conduct 12 . A means to obtain longitudinal data for estimation of the transmission rate can be to sample a subpopulation instead of the whole population, as for instance the study of Backer et al. 16 where field data were used to estimate transmission rate of hepatitis E virus in pigs, subsampling down to 5% of the population. This can be the case for instance if animals must be caught prior to sampling, if the population is large, or if the test for disease is expensive 17 . In such situations subsampling can be a convenie...

BackgroundAntimicrobial resistance is a global health problem that demands all possible means to control it. Mathematical modelling is a valuable tool for understanding the mechanisms of AMR development and spread, and can help us to investigate and propose novel control strategies. However, it is of vital importance that mathematical models have a broad utility, which can be assured if good modelling practice is followed.ObjectiveThe objective of this study was to provide a comprehensive systematic review of published models of AMR development and spread. Furthermore, the study aimed to identify gaps in the knowledge required to develop useful models.MethodsThe review comprised a comprehensive literature search with 38 selected studies. Information was extracted from the selected papers using an adaptation of previously published frameworks, and was evaluated using the TRACE good modelling practice guidelines.ResultsNone of the selected papers fulfilled the TRACE guidelines. We recommend that future mathematical models should: a) model the biological processes mechanistically, b) incorporate uncertainty and variability in the system using stochastic modelling, c) include a sensitivity analysis and model external and internal validation.ConclusionMany mathematical models of AMR development and spread exist. There is still a lack of knowledge about antimicrobial resistance, which restricts the development of useful mathematical models.

BackgroundThe complex relationship between drug concentrations and bacterial growth rates require not only the minimum inhibitory concentration but also other parameters to capture the dynamic nature of the relationship. To analyse this relationship between tetracycline concentration and growth of Escherichia coli representative of those found in the Danish pig population, we compared the growth of 50 randomly selected strains. The observed net growth rates were used to describe the in vitro pharmacodynamic relationship between drug concentration and net growth rate based on Emax model with three parameters: maximum net growth rate (αmax); concentration for a half-maximal response (Emax); and the Hill coefficient (γ).ResultsThe net growth rate in the absence of antibiotic did not differ between susceptible and resistant isolates (P = 0.97). The net growth rate decreased with increasing tetracycline concentrations, and this decline was greater in susceptible strains than resistant strains. The lag phase, defined as the time needed for the strain to reach an OD600 value of 0.01, increased exponentially with increasing tetracycline concentration. The pharmacodynamic parameters confirmed that the between susceptible and resistant strains in the absence of a drug was not different. EC50 increased linearly with MIC on a log–log scale, and γ was different between susceptible and resistant strains.ConclusionsThe in vitro model parameters described the inhibition effect of tetracycline on E. coli when strains were exposed to a wide range of tetracycline concentrations. These parameters, along with in vivo pharmacokinetic data, may be useful in mathematical models to predict in vivo competitive growth of many different strains and for development of optimal dosing regimens for preventing selection of resistance.

This study describes the results of a randomized clinical trial investigating the effect of oxytetracycline treatment dose and mode of administration on the selection of antibiotic-resistant coliform bacteria in fecal samples from nursery pigs. Nursery pigs (pigs of 4 to 7 weeks of age) in five pig herds were treated with oxytetracycline for Lawsonia intracellularis-induced diarrhea. Each group was randomly allocated to one of five treatment groups: oral flock treatment with a (i) high (20 mg/kg of body weight), (ii) medium (10 mg/kg), or (iii) low (5 mg/kg) dose, (iv) oral pen-wise (small-group) treatment (10 mg/kg), and (v) individual intramuscular injection treatment (10 mg/kg). All groups were treated once a day for 5 days. In all groups, treatment caused a rise in the numbers and proportions of tetracyclineresistant coliform bacteria right after treatment, followed by a significant drop by the time that the pigs left the nursery unit. The counts and proportions of tetracyclineresistant coliforms did not vary significantly between treatment groups, except immediately after treatment, when the highest treatment dose resulted in the highest number of resistant coliforms. A control group treated with tiamulin did not show significant changes in the numbers or proportions of tetracycline-resistant coliforms. Selection for tetracycline-resistant coliforms was significantly correlated to selection for ampicillin-and sulfonamide-resistant strains but not to selection for cefotaximeresistant strains. In conclusion, the difference in the dose of oxytetracycline and the way in which the drug was applied did not cause significantly different levels of selection of tetracycline-resistant coliform bacteria under the conditions tested.IMPORTANCE Antimicrobial resistance is a global threat to human health. Treatment of livestock with antimicrobials has a direct impact on this problem, and there is a need to improve the ways that we use antimicrobials in livestock production. We hypothesized that antibiotic resistance development following treatment of diarrhea in nursery pigs could be reduced either by lowering the dose of oxytetracycline or by replacing the commonly used practice of flock treatment with individual or smallgroup treatments, since this would reduce the number of pigs treated. However, the study showed no significant difference between treatment groups with respect to the number or proportion of tetracycline-resistant coliforms selected. The most important conclusion is that under practical field conditions, there will be no added value, in terms of lowering resistance development, by exchanging flock treatment for individual or small-group treatment of nursery pigs. The reason for the lack of an

Bluetongue is a disease of ruminants which reached Denmark in 2007. We present a process-based stochastic simulation model of vector-borne diseases, where host animals are not confined to a central geographic farm coordinate, but can be distributed onto pasture areas. Furthermore vectors fly freely and display search behavior to locate areas with hosts. We also include wind spread of vectors, host movements, and vector seasonality. Results show that temperature and seasonality of vectors determines the period in which an incursion of Bluetongue may lead to epidemic spread in Denmark. Within this period of risk the number of infected hosts is affected by temperature, vector abundance, vector behavior, vectors' ability to locate hosts, and use of pasture. These results indicate that restricted grazing during outbreaks can reduce the number of infected hosts and the size of the affected area. The model can be implemented on other vector-borne diseases of grazing animals.