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Biomedical subjects

O Diekmann

Publications and source records attributed to O Diekmann.

At least 19 recordsLinked to original sources
PubMed2006

Controlling methicillin-resistant Staphylococcus aureus: quantifying the effects of interventions and rapid diagnostic testing.

Control of nosocomial transmission of methicillin-resistant Staphylococcus aureus (MRSA) has been unsuccessful in most countries. Yet, some countries have maintained low endemic levels by implementing nationwide MRSA-specific infection control measures, such as "search & destroy" (S&D). These strategies, however, are not based on well designed studies, and their use in countries with high levels of endemicity is controversial. We present a stochastic three-hospital model and an analytical one-hospital model to quantify the effectiveness of different infection control measures and to predict the effects of rapid diagnostic testing (RDT) on isolation needs. Isolation of MRSA carriers identified by clinical cultures is insufficient to control MRSA. However, combined with proactive search (of high-risk patients on admission and/or contacts of index patients), it will maintain prevalence levels <1%. Concerted implementation of S&D in countries with high nosocomial endemicity reduces nosocomial prevalence to <1% within 6 years. Stepwise implementation of control measures can reduce isolation capacities needed. RDT can reduce isolation needs by >90% in low-endemic settings and by 20% in high-endemic settings. Surveillance of colonization and improved hand hygiene can markedly increase control efficacy. These findings strongly suggest that: (i) causality exists between S&D and low MRSA prevalence; (ii) isolating MRSA carriers identified by clinical cultures as a single measure is insufficient for control; (iii) a combined approach of isolation and screening confers efficacy; and (iv) MRSA-prevalence levels can be reduced to <1% in high-endemic settings by S&D or a stepwise approach to interventions. RDT can markedly enhance feasibility.

Carrier State↗
PubMed2005

On the (dis) advantages of cannibalism.

Cannibalism is an interaction between individuals that can produce counter- intuitive effects at the population level. A striking effect is that a population may persist under food conditions such that the non-cannibalistic variant is doomed to go extinct. This so-called life boat mechanism has received considerable attention. Implicitly, such studies sometimes suggest, that the life boat mechanism procures an evolutionary advantage to the cannibalistic trait. Here we compare, in the context of a size structured population model, the conditions under which the life boat mechanism works, with those that guarantee, that a cannibalistic mutant can invade successfully under the steady environmental conditions as set by a non-cannibalistic resident. We find qualitative agreement and quantitative difference. In particular, we find that a prerequisite for the life boat mechanism is, that cannibalistic mutants are successful invaders. Roughly speaking, our results show that cannibalism brings advantages to both the individuals and the population when adult food is limiting.

Animals↗
PubMed2003

Year class coexistence or competitive exclusion for strict biennials?

We consider a discrete time model of semelparous biennial population dynamics. Interactions between individuals are modelled with the aid of an "environmental" variable I. The impact on and the sensitivity to the environmental condition is age specific. The main result is that competitive exclusion between the year classes is possible as is their coexistence. For moderate values of the basic reproduction ratio R(0) there is a strict dichotomy: depending on the other parameters we either find competitive exclusion or coexistence. We characterize rather precisely the patterns of age specific impact and sensitivity that lead to either of these outcomes.

Aging↗
PubMed2003

Steady-state analysis of structured population models.

Our systematic formulation of nonlinear population models is based on the notion of the environmental condition. The defining property of the environmental condition is that individuals are independent of one another (and hence equations are linear) when this condition is prescribed (in principle as an arbitrary function of time, but when focussing on steady states we shall restrict to constant functions). The steady-state problem has two components: (i). the environmental condition should be such that the existing populations do neither grow nor decline; (ii). a feedback consistency condition relating the environmental condition to the community/population size and composition should hold. In this paper we develop, justify and analyse basic formalism under the assumption that individuals can be born in only finitely many possible states and that the environmental condition is fully characterized by finitely many numbers. The theory is illustrated by many examples. In addition to various simple toy models introduced for explanation purposes, these include a detailed elaboration of a cannibalism model and a general treatment of how genetic and physiological structure should be combined in a single model.

Cannibalism↗
PubMed2001

The resident strikes back: invader-induced switching of resident attractor.

The aim of this paper is two-fold: (a) by way of example, we elucidate the phenomenon of invader-induced switches in a resident attractor; (b) we expose in detail how resonance and phase have a strong impact when semelparous organisms (as, e.g. Pacific salmon) with different life-cycle lengths compete in a self-induced periodically fluctuating environment. We analyse a simple model for the competition between annuals and biennials, focusing on the situation that the annual population in isolation converges to a two-cycle. Well-timed biennial mutants sample the periodically varying environment more efficiently than the annual resident. They can invade successfully even when they are inferior to the resident, in the sense that they have lower viability and/or fertility. Successful invasion can lead to resonance-mediated coexistence if the invader is rather inferior to the resident. Remarkably, for mutants that are less inferior to the resident, successful invasion by a mutant strategy will inevitably be followed by the extinction of the former invader and concurrent re-establishment of the resident. The expulsion of the invader is brought about by an invasion-induced phase shift or attractor switch. We call this phenomenon "the resident strikes back" and say that the resident strategy is invasible, yet invincible. After the resident has struck back, other mutants can successfully invade again. On a longer time-scale, this might lead to an intermittent occurrence of ultimately inferior strategies. The results show that even in a deterministic setting, successful invasion does not necessarily lead to establishment and that mutual invasibility is not always sufficient for coexistence.

Ecosystem↗
PubMed2001

Predator migration in response to prey density: what are the consequences?

A predator-prey metapopulation model with two identical patches and only migration of the predator is investigated. Local predator-prey interaction is described by the so-called Rosenzweig-MacArthur model, while the migration term of the predator is put in a nonlinear form, which is derived by extending the Holling time budget argument to migration. In particular, a dimensionless parameter theta is introduced to quantify the migration tendency of predators while they are handling their prey, which gives rise to a family of models connecting two extremes: predators have no inclination to migrate while handling prey (theta = 0) and standard diffusion (theta = 1). Various aspects of the model, including changes in the number and the stability of equilibria and limit cycles, are investigated. We then focus on the key question: "Does spatial structure lead to a substantial damping of the violent oscillations exhibited by many predator-prey models?". It is known that the answer is "yes" if one adopts standard diffusion (theta = 1). However, we present substantial evidence that the answer is "no" if one takes theta = 0. We conclude that the migration submodel is an important constituent of a spatial predator-prey model and that the issue deserves scrutiny, both experimentally and theoretically.

Animals↗
PubMed2001

On the formulation and analysis of general deterministic structured population models. II. Nonlinear theory.

This paper is as much about a certain modelling methodology, as it is about the constructive definition of future population states from a description of individual behaviour and an initial population state. The key idea is to build a nonlinear model in two steps, by explicitly introducing the environmental condition via the requirement that individuals are independent from one another (and hence equations are linear) when this condition is prescribed as a function of time. A linear physiologically structured population model is defined by two rules, one for reproduction and one for development and survival, both depending on the initial individual state and the prevailing environmental condition. In Part I we showed how one can constructively define future population state operators from these two ingredients. A nonlinear model is a linear model together with a feedback law that describes how the environmental condition at any particular time depends on the population size and composition at that time. When applied to the solution of the linear problem, the feedback law yields a fixed point problem. This we solve constructively by means of the contraction mapping principle, for any given initial population state. Using subsequently this fixed point as input in the linear population model, we obtain a population semiflow. We then say that we solved the nonlinear problem.

Animals↗
PubMed2000

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.

Animals↗
PubMed1998

Modelling the spread of phocine distemper virus among harbour seals.

Data presented in earlier publications on the 1988 epizootic among seals in North West Europe show a pattern that is somewhat inconsistent with the predictions of the standard mathematical model of epidemics. We argue that for animals living in herds or colonies, such as seals, the mutual contact behaviour is such that models for the transmission of infectious diseases should be applied with special care for the distinction between numbers and densities. This is demonstrated by using a mechanistic description of the contacts among seals, which leads to a slightly different formulation of the model. Results of the analysis of this formulation are more in line with the data. The model introduced here can be applied to epidemics among all kinds of animals living in herds and in fact to any species with constant local density, independent of the total population size (i.e., occupying a variable area). Application of the traditional formulation, using different parameters for herds of different sizes, will give equally good results for non-lethal diseases. However, especially for diseases with a low R0 and high death rates, such as the phocine distemper virus (PDV) disease, the two model formulations give quite different results. Further analysis of the model is performed to determine the most important factors influencing such an epidemic. The survival of infected animals turns out to have a disproportionately great influence on the intensity of the epidemic. Therefore in the case of the PDV epizootic we conclude that marine pollution may not only have contributed to the high death rates, but, if so, it has intensified the epizootic as well.

Animals↗
PubMed1998

Identification and characterization of autoantibodies against catalase and alpha-enolase in patients with primary sclerosing cholangitis.

Primary sclerosing cholangitis (PSC) is a chronic cholestatic liver disease of unknown aetiology. Recent studies have shown that genetic factors and both cellular and humoral immunological abnormalities are important in the pathogenesis of PSC. The most prominent autoantibodies in PSC are anti-neutrophil cytoplasmic antibodies (ANCA). The autoepitopes of ANCA in PSC are not well defined. The aim of this study was to identify corresponding ANCA autoantigens in patients with PSC. A biochemical approach with enrichment and partial purification of soluble neutrophil proteins, detection of autoantibodies by Western blot and partial amino acid sequencing were used. Two new autoantigen/autoantibody systems in patients with PSC were detected: catalase and alpha-enolase. The presence of catalase autoantibodies in 9/15 (60%) and alpha-enolase autoantibodies in 4/15 (27%) was confirmed by ELISA and Western blot. Furthermore, we showed immunoreactions of PSC sera with human biliary epithelial cells, showed the reduction of fluorescence in anti-catalase absorption experiments and observed partial co-localization of anti-catalase antibodies and PSC sera in double-staining experiments on biliary epithelial cells. The anti-catalase antibody-positive PSC patients had a more severe course of disease with a significantly higher alkaline phosphatase compared with the anti-catalase-negative PSC patients (P < 0.06). All ulcerative colitis control sera were anti-catalase antibody-negative. The identified antigens catalase and alpha-enolase can partly explain the ANCA fluorescence on ethanol-fixed and formaldehyde-fixed granulocytes in patients with PSC. Catalase is an important anti-oxidant enzyme and prevents cell damage from highly reactive oxygen-derived free radicals. Catalase autoantibodies might play a pathogenic role in patients with PSC. Our findings support the hypothesis that oxidative stress is one of the pathogenic mechanisms in patients with PSC.

Amino Acid Sequence↗
PubMed1997

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.

Adult↗
PubMed1994

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.

Algorithms↗
PubMed1994

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.

Amino Acid Sequence↗
PubMed1991

Patterns in the effects of infectious diseases on population growth.

An infectious disease may reduce or even stop the exponential growth of a population. We consider two very simple models for microparasitic and macroparasitic diseases, respectively, and study how the effect depends on a contact parameter kappa. The results are presented as bifurcation diagrams involving several threshold values of kappa. The precise form of the bifurcation diagram depends critically on a second parameter xi, measuring the influence of the disease on the fertility of the hosts. A striking outcome of the analysis is that for certain ranges of parameter values bistable behaviour occurs: either the population grows exponentially or it oscillates periodically with large amplitude.

Birth Rate↗
PubMed1990

On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations.

The expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population is mathematically defined as the dominant eigenvalue of a positive linear operator. It is shown that in certain special cases one can easily compute or estimate this eigenvalue. Several examples involving various structuring variables like age, sexual disposition and activity are presented.

Age Factors↗
PubMed1986

Sloppy size control of the cell division cycle.

In an asynchronous, exponentially proliferating cell culture there is a great deal of variability among individual cells in size at birth, size at division and generation time (= age at division). To account for this variability we assume that individual cells grow according to some given growth law and that, after reaching a minimum size, they divide with a certain probability (per unit time) which increases with increasing cell size. This model is called sloppy size control because cell division is assumed to be a random process with size-dependent probability. We derive general equations for the distribution of cell size at division, the distribution of generation time, and the correlations between generation times of closely related cells. Our theoretical results are compared in detail with experimental results (obtained by Miyata and coworkers) for cell division in fission yeast, Schizosaccharomyces pombe. The agreement between theory and experiment is superior to that found for any other simple models of the coordination of cell growth and division.

Cell Division↗
PubMed1982

Prelude to Hopf bifurcation in an epidemic model: analysis of a characteristic equation associated with a nonlinear Volterra integral equation.

We discuss a simple deterministic model for the spread, in a closed population, of an infectious disease which confers only temporary immunity. The model leads to a nonlinear Volterra integral equation of convolution type. We are interested in the bifurcation of periodic solutions from a constant solution (the endemic state) as a certain parameter (the population size) is varied. Thus we are led to study a characteristic equation. Our main result gives a fairly detailed description (in terms of Fourier coefficients of the kernel) of the traffic of roots across the imaginary axis. As a corollary we obtain the following: if the period of immunity is longer than the preceding period of incubation and infectivity, then the endemic state is unstable for large population sizes and at least one periodic solution will originate.

Communicable Diseases↗