Seasonal dynamics and thresholds governing recurrent epidemics

Driven by seasonality, many common recurrent infectious diseases are characterized by strong annual, biennial and sometimes irregular oscillations in the absence of vaccination programs. Using the seasonally forced SIR epidemic model, we are able to provide new insights into the dynamics of recurrent diseases and, in some cases, specific predictions about individual outbreaks. The analysis reveals a new threshold effect that gives clear conditions for the triggering of future disease outbreaks or their absence. The threshold depends critically on the susceptibility S ₀ of the population after an outbreak. We show that in the presence of seasonality, forecasts based on the susceptibility S ₀ are more reliable than those based on the classical reproductive number R ₀ from the conventional theory.      

Accuracy of Optimized Chemical-exchange Parameters Derived by Fitting CPMG R 2 Dispersion Profiles when R 2 0a ≠ R 2 0b

The transverse relaxation rate, R₂, measured as a function of the effective field (R₂ dispersion) using a Carr-Purcell-Meiboom-Gill (CPMG) pulse train, is well suited to detect conformational exchange in proteins. The dispersion data are commonly fitted by a two-site (sites a and b) exchange model with four parameters: the relative population, p_a, the difference in chemical shifts of the two sites, δω, the correlation time for exchange, τ_ex, and the intrinsic relaxation rate (i.e., transverse relaxation rate in the absence of chemical exchange), R₂⁰. Although the intrinsic relaxation rates of the two sites, R₂^0a and R₂^0b, can differ, they are normally assumed to be the same (i.e., R₂^0a = R₂^0b = R₂⁰) when fitting dispersion data. The purpose of this investigation is to determine the magnitudes of the errors in the optimized exchange parameters that are introduced by the assumption that R₂^0a = R₂^0b. In order to accomplish this goal, we first generated synthetic constant-time CPMG R₂ dispersion data assuming two-site exchange with R₂^0a ≠ R₂^0b, and then fitted the synthetic data assuming two-site exchange with R₂⁰ = R₂^0a = R₂^0b. Although all the synthetic data generated assuming R₂^0a ≠ R₂^0b were well fitted (assuming R₂^0a = R₂^0b), the optimized values of p_a and τ _ex differed from their true values, whereas the optimized values of δω values did not. A theoretical analysis using the Carver–Richards equation explains these results, and yields simple, general equations for estimating the magnitudes of the errors in the optimized parameters, as a function of ( R₂^0a − R₂^0b).     

Thresholds for macroparasite infections

We analyse here the equilibria of an infinite system of partial differential equations modelling the dynamics of a population infected by macroparasites. We find that it is possible to define a reproduction number R₀ that satisfies the intuitive definition, and yields a sharp threshold in the behaviour of the system: if R₀ < 1, the parasite-free equilibrium (PFE) is asymptotically stable and there are no endemic equilibria; if R₀ > 1, the PFE is unstable and there exists a unique endemic equilibrium. The results mainly confirm what had been obtained in simplified models, except for the fact that no backward bifurcation occurs in this model. The stability of equilibria is established by extending an abstract linearization principle and by analysing the spectra of appropriate operators.Revised version: 14 November 2003Supported in part by CNR under Grant n. 00.0142.ST74 Metodi e modelli matematici nello studio dei fenomeni biologici     

A comparison of a deterministic and stochastic model for Hepatitis C with an isolation stage

We formulate a deterministic epidemic model for the spread of Hepatitis C containing an acute, chronic and isolation class and analyse the effects of the isolation class on the transmission dynamics of the disease. We calculate the basic reproduction number R₀ and show that for R₀≤1, the disease-free equilibrium is globally asymptotically stable. In addition, it is shown that for a special case when R₀>1, the endemic equilibrium is locally asymptotically stable. Furthermore, an analogous stochastic epidemic model for Hepatitis C is formulated using a continuous time Markov chain. Numerical simulations are used to estimate the mean, variance and probability distributions of the discrete random variables and these are compared to the steady-state solutions of the deterministic model. Finally, the expected time to disease extinction is estimated for the stochastic model and the impact of isolation on the time to extinction is explored.     

Genes determining leucine aminopeptidase and mildew resistance from the ornamental apple, ‘White Angel’

Mildew resistance in the ornamental apple White Angel was found to be determined by complementary genes. The gene R _w was found to be necessary for the expression of resistance controlled by the resistance gene Pl _w . The close linkage between the isoenzyme gene, Lap-2, for leucine aminopeptidase and P1 _w was confirmed. The efficiency of Lap-2 as a marker in screening for mildew resistance is limited, as it cannot account for susceptible plants with the r _w r _w P1 _w p1 _w genotype. It has, however, an important role to play in combining resistance genes from different sources. The genotypes of White Angel (R _w r _w , Pl _w pl _w , Lap-2an), Jester (R _w r _w , p1 _w p _w , Lap-2an) Katja (R _w r _w ,p1 _w p1 _w , Lap-2an) and Gloster 69 (r _w r _w , p1 _w p1 _w , Lap-2an) were determined. It also appeared that R _w might influence Lap-2 activity in young seedlings.     

Genomics of the<Emphasis Type="Italic"> ccoNOQP</Emphasis>-encoded<Emphasis Type="Italic"> cbb</Emphasis><Subscript>3</Subscript> oxidase complex in bacteria

Many bacteria adapt to microoxic conditions by synthesizing a particular cytochrome c oxidase (cbb ₃) complex with a high affinity for O₂, encoded by the ccoNOQP operon. A survey of genome databases indicates that ccoNOQP sequences are widespread in all sub-branches of Proteobacteria but otherwise are found only in bacteria of the CFB group (Cytophaga, Flexibacter, Bacteroides). Our analysis of available genome sequences suggests four major strategies of regulating ccoNOQP expression in response to O₂. The most widespread strategy involves direct regulation by the O₂-responsive protein Fnr. The second strategy involves an O₂-insensitive paralogue of Fnr, FixK, whose expression is regulated by the O₂-responding FixLJ two-component system. A third strategy of mixed regulation operates in bacteria carrying both fnr and fixLJ-fixK genes. Another, not yet identified, strategy is likely to operate in the -Proteobacteria Helicobacter pylori and Campylobacter jejuni which lack fnr and fixLJ-fixK genes. The FixLJ strategy appears specific for the -subclass of Proteobacteria but is not restricted to rhizobia in which it was originally discovered.     

Relationship of the Escherichia coli TrkA System of Potassium Ion Uptake with the F0F1-ATPase Under Growth Conditions Without Anaerobic or Aerobic Respiration

K⁺ uptake by the Escherichia coli TrkA system is unusual in that it requires both ATP and ; a relation withH⁺ circulation through the membrane is thereforesuggested. The relationship of this system with theF₀F₁-ATPase was studied in intact cells grownunder different conditions. A significant increase of theN,N-dicyclohexylcarbodiimide(DCCD)-inhibitedH⁺ efflux through the F₀F₁ by 5 mMK⁺, but not by Na⁺ added into thepotassium-free medium was revealed only in fermenting wild-type orparent cells, that were grown under anaerobic conditions withoutanaerobic or aerobic respiration and with the production ofH₂. Such an increase disappeared in the unc or the trkA mutants that have alteredF₀F₁ or defective TrkA, respectively.This finding indicates a closed relationship between TrkA andF₀F₁, with these transport systems beingassociated in a single mechanism that functions as an ATP-drivenH⁺–K⁺-exchanging pump. ADCCD-inhibited H⁺–K⁺-exchangethrough these systems with the fixed stoichiometry of H⁺and K⁺ fluxes(2H⁺/K⁺) and a higherK⁺ gradient between the cytoplasm and the externalmedium were also found in these bacteria. They were not observed incells cultured under anaerobic conditions in the presence of nitrate orunder aerobic conditions with respiration and without production ofH₂. The role of anaerobic or aerobic respiration as adeterminant of the relationship of the TrkA with theF₀F₁ is postulated. Moreover, an increase ofDCCD-inhibited H⁺ efflux by added K⁺, aswell as the characteristics of DCCD-sensitiveH⁺–K⁺-exchange found in a parentstrain, were lost in the arcA mutant with a defectiveArc system, suggesting a repression of enzymes in respiratorypathways. In addition, K⁺ influx in the latest mutantwas not markedly changed by valinomycin or with temperature. ThearcA gene product or the Arc system is proposed to beimplicated in the regulation of the relationship between TrkAand F₀F₁.     

Ecosystem respiration depends strongly on photosynthesis in a temperate heath

We measured net ecosystem CO₂ flux (F _n) and ecosystem respiration (R _E), and estimated gross ecosystem photosynthesis (P _g) by difference, for two years in a temperate heath ecosystem using a chamber method. The exchange rates of carbon were high and of similar magnitude as for productive forest ecosystems with a net ecosystem carbon gain during the second year of 293 ± 11 g C m⁻² year⁻¹ showing that the carbon sink strength of heather-dominated ecosystems may be considerable when C. vulgaris is in the building phase of its life cycle. The estimated gross ecosystem photosynthesis and ecosystem respiration from October to March was 22% and 30% of annual flux, respectively, suggesting that both cold-season carbon gain and loss were important in the annual carbon cycle of the ecosystem. Model fit of R _E of a classic, first-order exponential equation related to temperature (second year; R ² = 0.65) was improved when the P _g rate was incorporated into the model (second year; R ² = 0.79), suggesting that daytime R _E increased with increasing photosynthesis. Furthermore, the temperature sensitivity of R _E decreased from apparent Q ₁₀ values of 3.3 to 3.9 by the classic equation to a more realistic Q ₁₀ of 2.5 by the modified model. The model introduces R _photo, which describes the part of respiration being tightly coupled to the photosynthetic rate. It makes up 5% of the assimilated carbon dioxide flux at 0°C and 35% at 20°C implying a high sensitivity of respiration to photosynthesis during summer. The simple model provides an easily applied, non-intrusive tool for investigating seasonal trends in the relationship between ecosystem carbon sequestration and respiration.     

High Efficiency Transgene Segregation in Co-Transformed Maize Plants using an Agrobacterium Tumefaciens 2 T-DNA Binary System

For regulatory issues and research purposes it would be desirable to have the ability to segregate transgenes in co-transformed maize. We have developed a highly efficient system to segregate transgenes in maize that was co-transformed using an Agrobacterium tumefaciens 2 T-DNA binary system. Three vector treatments were compared in this study; (1) a 2 T-DNA vector, where the selectable marker gene bar (confers resistance to bialaphos) and the -glucuronidase (GUS) reporter gene are on two separate T-DNA's contained on a single binary vector; (2) a mixed strain treatment, where bar and GUS are contained on single T-DNA vectors in two separate Agrobacterium strains; (3) and a single T-DNA binary vector containing both bar and GUS as control treatment. Bialaphos resistant calli were generated from 52 to 59% of inoculated immature embryos depending on treatment. A total of 93.4% of the bialaphos selected calli from the 2 T-DNA vector treatment exhibited GUS activity compared to 11.7% for the mixed strain treatment and 98.2% for the cis control vector treatment. For the 2 T-DNA vector treatment, 86.7% of the bialaphos resistant/GUS active calli produced R₀ plants exhibiting both transgenic phenotypes compared to 10% for the mixed strain treatment and 99% for the single T-DNA control vector treatment. A total of 87 Liberty herbicide (contains bialaphos as the active ingredient) resistant/GUS active R₀ events from the 2 T-DNA binary vector treatment were evaluated for phenotypic segregation of these traits in the R₁ generation. Of these R₀ events, 71.4% exhibited segregation of Liberty resistance and GUS activity in the R₁ generation. A total of 64.4% of the R₀ 2 T-DNA vector events produced Liberty sensitive/GUS active (indicating selectable-marker-free) R₁ progeny. A high frequency of phenotypic segregation was also observed using the mixed strain approach, but a low frequency of calli producing R₀ plants displaying both transgenic phenotypes makes this method less efficient. Molecular analyses were then used to confirm that the observed segregation of R₁ phenotypes were highly correlated to genetic segregation of the bar and GUS genes. A high efficiency system to segregate transgenes in co-transformed maize plants has now been demonstrated.     

Error estimation and global fitting in transverse-relaxation dispersion experiments to determine chemical-exchange parameters

Off-resonance effects can introduce significant systematic errors in R₂ measurements in constant-time Carr-Purcell-Meiboom-Gill (CPMG) transverse relaxation dispersion experiments. For an off-resonance chemical shift of 500 Hz, ¹⁵N relaxation dispersion profiles obtained from experiment and computer simulation indicated a systematic error of ca. 3%. This error is three- to five-fold larger than the random error in R₂ caused by noise. Good estimates of total R₂ uncertainty are critical in order to obtain accurate estimates in optimized chemical exchange parameters and their uncertainties derived from χ² minimization of a target function. Here, we present a simple empirical approach that provides a good estimate of the total error (systematic + random) in ¹⁵N R₂ values measured for the HIV protease. The advantage of this empirical error estimate is that it is applicable even when some of the factors that contribute to the off-resonance error are not known. These errors are incorporated into a χ² minimization protocol, in which the Carver–Richards equation is used fit the observed R₂ dispersion profiles, that yields optimized chemical exchange parameters and their confidence limits. Optimized parameters are also derived, using the same protein sample and data-fitting protocol, from ¹H R₂ measurements in which systematic errors are negligible. Although ¹H and ¹⁵N relaxation profiles of individual residues were well fit, the optimized exchange parameters had large uncertainties (confidence limits). In contrast, when a single pair of exchange parameters (the exchange lifetime, τ_ex, and the fractional population, p_a), were constrained to globally fit all R₂ profiles for residues in the dimer interface of the protein, confidence limits were less than 8% for all optimized exchange parameters. In addition, F-tests showed that quality of the fits obtained using τ_ex, p_a as global parameters were not improved when these parameters were free to fit the R₂ profiles of individual residues. Finally, nearly the same optimized global τ_ex, p_a values were obtained, when the ¹H and ¹⁵N data sets for residues in the dimer interface, were fit independently; the difference in optimized global parameters, ca. 10%, was of marginal significance according to the F-test.     

1H NMR study of the interaction of bacteriophage λ Cro protein with the O R 3 operator

The 17 base pair operator O _R ³ oligonucleotide, which is the preferential binding site for the Cro repressor of phage , was studied by two-dimensional NMR spectroscopy. A sequential assignment procedure based on two-dimensional Nuclear Overhauser Effect (NOESY) and scalar coupling correlated (COSY) NMR spectroscopy, together with the knowledge of the oligodesoxynucleotide sequence, made it possible to assign the non-exhangeable base protons and the H1 and the H2-H2 sugar protons of the O _R ³ operator DNA. The pattern of the observed NOE connectivities is consistent with a right-handed helical DNA structure. The base and sugar proton assignments provide the necessary information for further studies of the O _R ³ operator — Cro repressor interaction.Abbreviations COSY correlated spectroscopy - FID free induction decay - NOE nuclear Overhauser effect - NOESY nuclear Overhauser effect spectroscopy - RD relaxation delay - TSP sodium 3-trimethylsilyl-(2,2,3,3-²H₄)propionate - EDTA sodium ethylendiamine tetraacetate     

The Influences of I h on Temporal Summation in Hippocampal CA1 Pyramidal Neurons: A Modeling Study

Recent experimental and theoretical studies have found that active dendritic ionic currents can compensate for the effects of electrotonic attenuation. In particular, temporal summation, the percentage increase in peak somatic voltage responses invoked by a synaptic input train, is independent of location of the synaptic input in hippocampal CA1 pyramidal neurons under normal conditions. This independence, known as normalization of temporal summation, is destroyed when the hyperpolarization-activated current, I _h, is blocked [Magee JC (1999a), Nature Neurosci. 2: 508–514]. Using a compartmental model derived from morphological recordings of hippocampal CA1 pyramidal neurons, we examined the hypothesis that I _h was primarily responsible for normalization of temporal summation. We concluded that this hypothesis was incomplete. With a model that included I _h, the persistent Na⁺ current (I _NaP), and the transient A-type K⁺ current (I _A), however, we observed normalization of temporal summation across a wide range of synaptic input frequencies, in keeping with experimental observations.     

Effect of temperature on the CO2/O2 specificity of ribulose-1,5-bisphosphate carboxylase/oxygenase and the rate of respiration in the light

Responses of the rate of net CO₂ assimilation (A) to the intercellular partial pressure of CO₂ (p _i ) were measured on intact spinach (Spinacia oleracea L.) leaves at different irradiances. These responses were analysed to find the value of p _i at which the rate of photosynthetic CO₂ uptake equalled that of photorespiratory CO₂ evolution. At this CO₂ partial pressure (denoted ), net rate of CO₂ assimilation was negative, indicating that there was non-photorespiratory CO₂ evolution in the light. Hence was lower than the CO₂ compensation point, . Estimates of were obtained at leaf temperatures from 15 to 30°C, and the CO₂/O₂ specificity of ribulose 1,5-bisphosphate (RuBP) carboxylase/oxygenase (E.C. 4.1.1.39) was calculated from these data, taking into account changes in CO₂ and O₂ solubilities with temperature. The CO₂/O₂ specificity decreased with increasing temperature. Therefore we concluded that temperature effects on the ratio of photorespiration to photosynthesis were not solely the consequence of differential effects of temperature on the solubilities of CO₂ and O₂. Our estimates of the CO₂/O₂ specificity of RuBP carboxylase/oxygenase are compared with in-vitro measurements by other authors. The rate of nonphotorespiratory CO₂ evolution in the light (R _d ) was obtained from the value of A at . At this low CO₂ partial pressure, R _d was always less than the rate of CO₂ evolution in darkness and appeared to decrease with increasing irradiance. The decline was most marked up to about 100 mol quanta m^-2 s^-1 and less marked at higher irradiances. At one particular irradiance, however, R _d as a proportion of the rate of CO₂ evolution in darkness was similar in different leaves and this proportion was unaffected by leaf temperature or by [O₂] (ambient and greater). After conditions of high [CO₂] and high irradiance for several hours, the rate of CO₂ evolution in darkness increased and R _d also increased.Abbreviations and symbols A rate of net CO₂-assimilation - CO₂ compensation point - CO₂ compensation point in the absence of R _d - p _i intercellular partial pressure of CO₂ - R _d (day respiration) rate of non-photorespiratory CO₂ evolution in the light - R _n (night respiration) rate of CO₂ evolution in darkness - RuBP ribulose-1,5-bisphosphate - Rubisco RuBP carboxylase/oxygenase     

N-andO-glycosylation of glycoprotein C synthesized by Herpes simplex virus type 1-infected ricin resistant cells

The progeny of Herpes simplex virus type 1 (HSV-1) grown in ricin-resistant 14 cells (Ric^R14) lackingN-acetylglucosaminyltransferase I was released in the extracellular medium at a very low rate. By using a monoclonal antibody immobilized on Sepharose we purified from HSV-1-infected Ric^R14 cells a viral glycoprotein (gC), which carries bothN-andO-linked oligosaccharides. Glycopeptides obtained from [³H]mannoselabeled gC by Pronase digestion were entirely susceptible to endo--N-acetylglucosaminidase H, and the major oligosaccharide released was Man₄GlcNAc. The accumulation of this high-mannose species was related to the enzymic defect of the host cells and to the long retention of the viral glycoprotein within the cells. The extent ofO-glycosylation evaluated in [¹⁴C]glucosamine-labeled gC from Ric^R14 cells as compared to that of gC from wild type cells did not appear to be significantly modified.Abbreviations Con A concanavalin A - BHK cells baby hamster kidney cells - HSV Herpes simplex virus     

A discrete branching process model for the spread of HIV via steady sexual partnerships

The transmission of HIV in a monogamous heterosexual population structured by the ordinal number of the current partnership is considered. The sexual carreer of a man (woman) is thought to be a succession of k(m) partnerships, and a multitype Galton-Watson process is defined, in which the objects are infections and the types are related to the ordinal number of the partnership during which a person has acquired the infection. Contrary to multitype models in which the types are not age-related in some sense, this process contains at least two singular types, namely infections acquired in the last partnership of a man or a woman. The criticality parameter of this branching process is the epidemic threshold parameter R₀. In the case k=m an epidemic is impossible, however large k may be, if the difference between the ordinal numbers of the partners in a pair is never > 1. When the frequency of pairs in which this difference is 2 increases, then R₀ increases. This is demonstrated for the cases k=m=3 and k=4,m=3. The formulae obtained show also the joint influence of the mixing pattern and of variable infectivity. The result for the case of uniform mixing implies that a formula of May and Anderson (1987) is an approximation for k and m large.Mathematics Subject Classification (2000): 92D (primary), 60J (secondary)     

Is F ST obsolete?

Since the introduction of allozyme methods inthe mid 1960s it has been a standard practiceto report Wright's measure of populationsubdivision, F _ST, for surveys ofgenetic variation. Its widespread use hasprovided us with a sense of what values can beexpected in particular situations and how theycan be interpreted. With some theoreticaljustification, F _ST has also beenused to estimate rates of gene flow. Howeverthere are conditions under which F _STis inappropriate for gene flow estimation andcan lead to incorrect or even absurdconclusions. These pitfalls have promptedcritics to suggest that F _ST hasfailed to deliver what its proponents havepromised and should be abandoned. A furtherchallenge has been the development of newmethods that offer even greater promise. Thusit is reasonable to ask if perhaps it is timeto retire F _ST and turn to new andmore powerful methods for the inference of geneflow from genetic markers. Here I will arguethat although gene flow should be estimated bymore powerful approaches whenever practical,F _ST remains a useful measure of theaverage effects of gene flow and will continueto be used for comparative purposes.     

全球陆地生态系统光合作用与呼吸作用的温度敏感性

基于全球647套通量数据,定量分析了全球尺度下生态系统光合作用和呼吸作用的温度敏感性(Q10)随纬度、气候和植被的分布规律。结果表明:在全球尺度下,光合作用和呼吸过程的温度敏感性(Q10,G和Q10,R)都随纬度的升高而增加,其中Q10,G和Q10,R的均值分别为3.99±0.21和2.28±0.074。除热带多树草原、常绿落叶林外,Q10,G均大于Q10,R值。不同植被类型的温度敏感性存在显著性差异,表现为:针叶林阔叶林;落叶林常绿林,其中生态系统的季节性变异是造成差异的主要原因。当植被类型和纬度区域共同影响Q10值时,植被类型对Q10值的总变异贡献更大。气候类型对Q10,G和Q10,R都有显著影响。在气候带上,干旱带的Q10,G最小,而冷温带的Q10,G最高。不同气候类型下(除温带草原气候外)的Q10,G都大于Q10,R。在极端条件下,温度可能不在是主导因素,而水分对温度敏感性的影响不可忽略,今后的研究需要更多的关注生态系统温度敏感性对水分变化的响应。     

Modification of phenotype in Belgian endive (Cichorium intybus) through genetic transformation byAgrobacterium rhizogenes: conversion from biennial to annual flowering

Belgian endive (Cichorium intybus) was genetically transformed usingAgrobacterium rhizogenes to insert wild type root-inducing, leftward, transferred DNA (Ri T_L-DNA) into the nuclear genome. Transformed root cultures gave rise to plants (R₀ generation) having the transformed phenotype described for other species, including increased branching, sterility, annual flowering and wrinkled leaves. Transformation circumvented the need for vernalization in order to flower, but not the need for inductive day length. Progeny (R₁ generation) were analysed by molecular hybridization and phenotypes were characterized relative to normal controls and to the R₀ generation. The extent of the T _l -DNA varied among siblings, with restriction fragmentEco R1 15, containing open reading frames 10, 11 and 12 (rol A, B and C), segregating as a single insertion. Phenotypic alterations in these plants indicate that the transformed phenotype in endive is at least partially due to the genes carried on theEco R1 fragment 15.     

A ‘phase-shift’ fusion system for the regulation of foreign gene expression by lambda represser in Gram-negative bacteria

A ‘phase-shift’ translation fusion vector was constructed in which mutually compatible restriction sites BamHI, BelI and BglII are positioned in such a manner that the cut point is in a different reading frame, immediately following the ATG start codon and ribosome-binding site of the λ cro gene. The λ cro gene is expressed from promoter p_R and controlled by a thermosensitive (cI857) λ repressor. The usefulness of the expression vector was demonstrated using a gal gene lacking the ATG start codon and fusing this to the p_R promoter and ATG start codon of the λ cro gene, resulting in cI857-regulated expression of galactokinase. The vector is of general use for foreign gene expression in Escherichia coli when the target gene has a compatible cohesive end (5′-GATC-3′) at the N terminus (provided, for example, by a BamHI linker). The A λ cI857-p_R-cro-galK cassette was cloned into pJRD215, a wide-host-range plasmid and transferred by conjugation to a variety of Gram-negative bacteria. In all cases, thermosensitive regulation of galactokinase could be demonstrated, though the levels of induction varied considerably. These results show that the powerful λ p_R promoter and the efficient A repressor can be used to regulate expression of foreign genes in Gram-negative organisms other than E. coli.     

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$R_0$ 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$R_0$ value.