Waning and boosting: on the dynamics of immune status.

The aim is to describe the distribution of immune status (as captured by antibody level) on the basis of a within-host submodel for continuous waning and occasional boosting. Inspired by Feller's fundamental work and the more recent delay equation formulation of models for the dynamics of physiologically structured populations, we derive, for given force of infection, a linear renewal equation. The solution is obtained by generation expansion, with the generation number corresponding to the number of times the individual became infected. Our main result provides a precise characterization of the stable distribution of immune status.

Shallow genetic divergence and species delineations in the endemic Labeobarbus species flock of Lake Tana, Ethiopia.

To assess whether the species distinctions of Lake Tana's Labeobarbus spp. are supported by genetic information, microsatellite markers were used. A total of 376 Labeobarbus spp., belonging to 24 populations of 11 species from three regions of the lake (north, south and east), were sampled. Eight microsatellite markers were analysed. In general, differences between conspecific populations were smaller than differences between populations of different species. For six species, conspecific populations from different regions in the lake were consistently more similar than populations of other species from the same region. For four species this was not the case, while for one species two populations were similar, but different from the third population. River-spawning species appeared to be more distinct than presumed lake spawners. On the species level, there was a significant correlation between genetic and morphological differentiation, especially in morphological aspects associated with ecological functioning. This suggests that genetic differentiation arose together with adaptive radiation, although the overall genetic differentiation among the Lake Tana Labeobarbus spp. is small.

Separable mixing: The general formulation and a particular example focusing on mask efficiency.

The aim of this short note is twofold. First, we formulate the general Kermack-McKendrick epidemic model incorporating static heterogeneity and show how it simplifies to a scalar Renewal Equation (RE) when separable mixing is assumed. A key general feature is that all information about the heterogeneity is encoded in one nonlinear real valued function of a real variable. Next, we specialize the model ingredients so that we can study the efficiency of mask wearing as a non-pharmaceutical intervention to reduce the spread of an infectious disease. Our main result affirms that the best way to protect the population as a whole is to protect yourself. This qualitative insight was recently derived in the context of an SIR network model. Here, we extend the conclusion to proportionate mixing models incorporating a general function describing expected infectiousness as a function of time since infection.

Dynamic concurrent partnership networks incorporating demography.

We introduce a population model that incorporates From a mathematical point of view we deal with continuous-time Markov chains at the individual level, with the interaction between individuals captured by a global variable describing opportunities for new partnerships. We show that for large time a stationary distribution is attained and we deduce various statistical features of that distribution, with particular attention for concurrency, i.e. the overlap in time of multiple partnerships of one and the same individual. Our ultimate motivation is to model the spread of sexually transmitted infections in the population, for which the present paper serves as a prelude.

Modeling non-inherited antibiotic resistance.

A mathematical model is presented for the increase and decrease of non-inherited antibiotic resistance levels in bacteria. The model is applied to experimental data on E. coli exposed to amoxicillin or tetracyclin in different concentrations. The parameters of the model are estimated using a Monte Carlo Markov Chain method. The model accurately describes build-up and decline of antibiotic resistance caused by physiological adaptations as long as no genetic changes have occurred. The main conclusion of the analysis is that short time periods are sufficient to re-obtain low MIC-values after long-lasting exposure to these antibiotics.

The concept of population in clonal organisms: mosaics of temporally colonized patches are forming highly diverse meadows of Zostera marina in Brittany.

Seagrasses structure some of the world's key coastal ecosystems presently in decline due to human activities and global change. The ability to cope with environmental changes and the possibilities for shifts in distribution range depend largely on their evolvability and dispersal potential. As large-scale data usually show strong genetic structure for seagrasses, finer-grained work is needed to understand the local processes of dispersal, recruitment and colonization that could explain the apparent lack of exchange across large distances. We aimed to assess the fine-grained genetic structure of one of the most important and widely distributed seagrasses, Zostera marina, from seven meadows in Brittany, France. Both classic population genetics and network analysis confirmed a pattern of spatial segregation of polymorphism at both regional and local scales. One location exhibiting exclusively the variety 'angustifolia' did not appear more differentiated than the others, but instead showed a central position in the network analysis, confirming the status of this variety as an ecotype. This phenotypic diversity and the high allelic richness at nine microsatellites (2.33-9.67 alleles/locus) compared to levels previously reported across the distribution range, points to Brittany as a centre of diversity for Z. marina at both genetic and phenotypic levels. Despite dispersal potential of several 100 m, a significant pattern of genetic differentiation, even at fine-grained scale, revealed 'genetic patchiness'. Meadows seem to be composed of a mosaic of clones with distinct origins in space and time, a result that calls into question the accuracy of the concept of populations for such partially clonal species.

Numerical equilibrium analysis for structured consumer resource models.

In this paper, we present methods for a numerical equilibrium and stability analysis for models of a size structured population competing for an unstructured resource. We concentrate on cases where two model parameters are free, and thus existence boundaries for equilibria and stability boundaries can be defined in the (two-parameter) plane. We numerically trace these implicitly defined curves using alternatingly tangent prediction and Newton correction. Evaluation of the maps defining the curves involves integration over individual size and individual survival probability (and their derivatives) as functions of individual age. Such ingredients are often defined as solutions of ODE, i.e., in general only implicitly. In our case, the right-hand sides of these ODE feature discontinuities that are caused by an abrupt change of behavior at the size where juveniles are assumed to turn adult. So, we combine the numerical solution of these ODE with curve tracing methods. We have implemented the algorithms for "Daphnia consuming algae" models in C-code. The results obtained by way of this implementation are shown in the form of graphs.

Can a species keep pace with a shifting climate?

Consider a patch of favorable habitat surrounded by unfavorable habitat and assume that due to a shifting climate, the patch moves with a fixed speed in a one-dimensional universe. Let the patch be inhabited by a population of individuals that reproduce, disperse, and die. Will the population persist? How does the answer depend on the length of the patch, the speed of movement of the patch, the net population growth rate under constant conditions, and the mobility of the individuals? We will answer these questions in the context of a simple dynamic profile model that incorporates climate shift, population dynamics, and migration. The model takes the form of a growth-diffusion equation. We first consider a special case and derive an explicit condition by glueing phase portraits. Then we establish a strict qualitative dichotomy for a large class of models by way of rigorous PDE methods, in particular the maximum principle. The results show that mobility can both reduce and enhance the ability to track climate change that a narrow range can severely reduce this ability and that population range and total population size can both increase and decrease under a moving climate. It is also shown that range shift may be easier to detect at the expanding front, simply because it is considerably steeper than the retreating back.

Calculating the time to extinction of a reactivating virus, in particular bovine herpes virus.

The expected time to extinction of a herpes virus is calculated from a rather simple population-dynamical model that incorporates transmission, reactivation and fade-out of the infectious agent. We also derive the second and higher moments of the distribution of the time to extinction. These quantities help to assess the possibilities to eradicate a reactivating infection. The key assumption underlying our calculations is that epidemic outbreaks are fast relative to the time scale of demographic turnover. Four parameters influence the expected time to extinction: the reproduction ratio, the reactivation rate, the population size, and the demographic turn-over in the host population. We find that the expected time till extinction is very long when the reactivation rate is high (reactivation is expected more than once in a life time). Furthermore, the infectious agent will go extinct much more quickly in small populations. This method is applied to bovine herpes virus (BHV) in a cattle herd. The results indicate that without vaccination, BHV will persist in large herds. The use of a good vaccine can induce eradication of the infection from a herd within a few decades. Additional measures are needed to eradicate the virus from a whole region within a similar time-span.

Enhanced cleavage of type II collagen by collagenases in osteoarthritic articular cartilage.

We demonstrate the direct involvement of increased collagenase activity in the cleavage of type II collagen in osteoarthritic human femoral condylar cartilage by developing and using antibodies reactive to carboxy-terminal (COL2-3/4C(short)) and amino-terminal (COL2-1/4N1) neoepitopes generated by cleavage of native human type II collagen by collagenase matrix metalloproteinase (MMP)-1 (collagenase-1), MMP-8 (collagenase-2), and MMP-13 (collagenase-3). A secondary cleavage followed the initial cleavage produced by these recombinant collagenases. This generated neoepitope COL2-1/4N2. There was significantly more COL2-3/4C(short) neoepitope in osteoarthritis (OA) compared to adult nonarthritic cartilages as determined by immunoassay of cartilage extracts. A synthetic preferential inhibitor of MMP-13 significantly reduced the unstimulated release in culture of neoepitope COL2-3/4C(short) from human osteoarthritic cartilage explants. These data suggest that collagenase(s) produced by chondrocytes is (are) involved in the cleavage and denaturation of type II collagen in articular cartilage, that this is increased in OA, and that MMP-13 may play a significant role in this process.

Production and molecular characterization of clinical phase i anti-melanoma mouse IgG3 monoclonal antibody R24.

R24 is a mouse IgG3 monoclonal antibody (mab) that reacts with the ganglioside GD3 expressed by cells of neuroectodermal origin. The anti-tumor activity of R24 has been demonstrated in initial phase I and pilot trials in patients suffering from metastatic melanoma. The purpose of this study was to investigate the biotechnological production and particularly the glycosylation of this clinically important antibody. Growth, metabolism, and IgG production of R24 secreting hybridoma cells were analyzed on 1 L bioreactor bench scale using repeated-batch mode. The amount of 57 mg of pure mab was obtained from 1.6 L crude supernatant by protein A chromatography. Western blot binding assays with sugar-specific lectins revealed glycosylation of the heavy chains, whereas no carbohydrates were detectable on the light chains. Because glycosylation is essential for antibody effector functions in vivo (such as complement fixation or binding to macrophage Fc receptors), mab R24 was subjected to both enzymatic deglycosylation using PNGase F and chemical deglycosylation by hydrazinolysis. Released glycans were structurally characterized by high pH anion exchange chromatography with pulsed amperometric detection (HPAEC-PAD), matrix assisted laser desorption ionization time-of-flight (MALDI-TOF), and electrospray ionization quadrupole time-of-flight (ESI-QTOF) mass spectrometry. Six major biantennary chains of the complex glycosylation phenotype were found with variations in galactosylation and core fucosylation. The predominant N-linked structure, indicating the high degree of agalactosyl glycoforms, was the agalacto biantennary chain with a relative percentage of 57% (51% core-fucosylated, 6% nonfucosylated). The second most abundant oligosaccharide was the monogalacto biantennary chain amounting to 30% (26% core- and 4% nonfucosylated). The antibody contained 0.46 microg sialic acid per mg protein, which splits into 0.243 microg Neu5Gc and 0.217 microg Neu5Ac, corresponding to a Neu5Ac:Neu5Gc ratio of 1:1.06. Furthermore, the antigen specificity of R24 was determined by immunodetection of GD3 on thin-layer chromatograms, and real time GD3-antibody binding interactions were measured with an optical biosensor (BIAcore). From the structural data obtained in this study it is concluded that glycosylation of the antibody may be important in the clinical outcome of targeted anti-cancer immunotherapy.

Degradation of kinins, angiotensins and substance P by polymorphonuclear matrix metalloproteinases MMP 8 and MMP 9.

1. The kinetics of the degradation of the kinins bradykinin and Met-Lys-bradykinin, angiotensins I and II and the tachykinin substance P by PMNL-collagenase (MMP 8), PMNL-gelatinase (MMP 9) and by the recombinant catalytic domain of MMP 8 (rcd-PMNL-c) was examined by RP-HPLC. The resulting fragments were identified by automated Edman degradation or by amino acid analysis. 2. The initial degradation rates of substance P at a substrate concentration of 25 microM were 5 min-1 for MMP 9 and 150 min-1 for MMP 8. The kinetic constants KM and kcat were determined by concentration-dependent measurements. For MMP 8/substance P the constants were KM = 78 +/- 14 microM and kcat = 412 +/- 67 min-1. For MMP 9/substance P the constants were KM = 91 +/- 15 microM and kcat = 25 +/- 4 min-1. Both enzymes cleaved substance P between Gln6 and Phe7 and between Gly9 and Leu10. 3. Under the same conditions, MMP 8 degraded angiotensin I at an initial rate of 20 h-1, resulting mainly in the vasoactive fragments angiotensin II and angiotensin(1-7). At a substrate concentration of 25 microM and an enzyme/substrate ratio of 1:100, angiotensin II was degraded very slowly (19% in 24 h) by MMP 8. Under these conditions, MMP 9 degraded angiotensin I to a lesser extent than MMP 8 (25% in 24 h) and was unable to cleave angiotensin II. 4. Under the same conditions, bradykinin and Met-Lys-bradykinin were cleaved by PMNL-collagenase at a rate of 20% in 24 h, producing BK(1-7) and BK(1-8). PMNL-gelatinase was unable to cleave the kinins under these conditions. 5. In all cases, rcd-PMNL-c produced the same fragments as wild type PMNL-collagenase, but at a significantly lower rate.

The basic reproduction ratio for sexually transmitted diseases: I. Theoretical considerations.

It is shown how one can calculate the basic reproduction ratio R0 for infectious disease models where an arbitrary but finite number of disease states are recognized and where the phenomena of pair formation and separation are taken into account. Several examples are discussed.

Subcritical endemic steady states in mathematical models for animal infections with incomplete immunity.

Many classical mathematical models for animal infections assume that all infected animals transmit the infection at the same rate, all are equally susceptible, and the course of the infection is the same in all animals. However for some infections there is evidence that seropositives may still transmit the infection, albeit at a lower rate. Animals can also experience more than one episode of the infection although those who have already experienced it have a partial immune resistance. Animals who experience a second or subsequent period of infection may not necessarily exhibit clinical symptoms. The main example discussed is bovine respiratory syncytial virus (BRSV) amongst cattle. We consider simple models with vaccination and homogeneous and proportional mixing between seropositives and seronegatives. We derive an expression for the basic reproduction number, R(o), and perform an equilibrium and stability analysis. We find that it may be possible for there to be two endemic equilibria (one stable and one unstable) for R(o)<1 and in this case at R(o)=1 there is a backwards bifurcation of an unstable endemic equilibrium from the infection-free equilibrium. Then the implications for control strategies are considered. Finally applications to Aujesky's disease (pseudorabies virus) in pigs are discussed.

The computation of R0 for discrete-time epidemic models with dynamic heterogeneity.

An explicit algorithm is given for the computation of the basic reproduction ratio R0 (or the net reproduction ratio R in the case of a not wholly susceptible population) for a class of discrete-time epidemic models. These models allow for a finite number of different individual types, type changes at fixed type-dependent intervals, arbitrary contact intensity between individuals of the various types, and variable infectivity. The models reflect the situation where an infectious disease spreads in a population of animals that are reared in different stables on farms. In addition, it is shown analytically that the reproduction ratio depends, for any given type, on the product of the susceptibility and the total infectivity of that type and not on these factors separately. We call this product the transmission weight of the type. The maximum overall transmission weight gives an upper bound for the reproduction ratio, irrespective of the particular submodels for type change and contact structure. Reduction of all transmission weights below 1, by vaccination or some other control measure, will result in R < 1 and will hence lead to eradication of the disease.

A two-phase within-host model for immune response and its application to serological profiles of pertussis.

We present a simple phenomenological within-host model describing both the interaction between a pathogen and the immune system and the waning of immunity after clearing of the pathogen. We implement the model into a Bayesian hierarchical framework to estimate its parameters for pertussis using Markov chain Monte Carlo methods. We show that the model captures some essential features of the kinetics of titers of IgG against pertussis toxin. We identify a threshold antibody level that separates a large increase in antibody level upon infection from a small increase and accordingly might be interpreted as a threshold separating clinical from subclinical infections. We contrast predictions of the model with observations reported in the literature and based on independent data and find a remarkable correspondence.

A didactical note on the advantage of using two parameters in Hopf bifurcation studies.

In order to maximize the information that a linearized stability analysis provides, one should work with two free parameters rather than one. Moreover, it is recommended to first consider coefficients in the characteristic equation as parameters and in a second step (try to) invert the map that defines the coefficients in terms of the parameters as they occur in the original equation. Our aim is to substantiate these claims by way of a delay equation example taken from the literature.

The protective effects of temporary immunity under imposed infection pressure.

The aim of this paper is to show in explicit detail that, due to the effects of waning and boosting of immunity, an increasing force of infection does not necessarily lead to an increase in the incidence of disease. Under certain conditions, a decrease of the force of infection may in fact lead to an increase of the incidence of disease. Thus we confirm and reinforce the conclusions from Águas et al. (2006), concerning pertussis. We do so, however, in the context of Campylobacter infections in humans deriving from animal reservoirs. For such an externally 'driven' epidemic we can ignore the transmission feedback cycle and treat the force of infection as a parameter. As this parameter is, to a certain extent, under public health control, our findings constitute an important warning: reducing exposure may not necessarily lead to a reduction in the occurrence of clinical illness. In a second part of the paper we relate the model parameters to the available data concerning campylobacteriosis.

On the formulation of epidemic models (an appraisal of Kermack and McKendrick).

The aim of this paper is to show that a large class of epidemic models, with both demography and non-permanent immunity incorporated in a rather general manner, can be mathematically formulated as a scalar renewal equation for the force of infection.