Biomedical subjects

Odo Diekmann

Publications and source records attributed to Odo Diekmann.

5 recordsLinked to original sources

PubMed2005

The dynamics of adaptation: an illuminating example and a Hamilton-Jacobi approach.

Our starting point is a selection-mutation equation describing the adaptive dynamics of a quantitative trait under the influence of an ecological feedback loop. Based on the assumption of small (but frequent) mutations we employ asymptotic analysis to derive a Hamilton-Jacobi equation. Well-established and powerful numerical tools for solving the Hamilton-Jacobi equations then allow us to easily compute the evolution of the trait in a monomorphic population when this evolution is continuous but also when the trait exhibits a jump. By adapting the numerical method we can, at the expense of a significantly increased computing time, also capture the branching event in which a monomorphic population turns dimorphic and subsequently follow the evolution of the two traits in the dimorphic population. From the beginning we concentrate on a caricatural yet interesting model for competition for two resources. This provides the perhaps simplest example of branching and has the great advantage that it can be analyzed and understood in detail.

Adaptation, Biological↗

PubMed2004

Double-Jump migration and diffusive instability.

In order to look into the stability consequences of a particular migration process in which individuals choose to settle, we formulated a continuous-time multi-species multi-patch model in which individuals migrate by one or two instantaneous jumps while making the second jump with a certain probability that possibly depends on the conditions at the end point of the first jump. It turned out that a second jump has some quantitative effects on diffusive instability even when it occurs in the absence of density-dependent mechanisms. When a second jump happens as a natural interspecific response of individuals, and such a response is sufficiently strong, it has crucial effects on diffusive instability: it leads to diffusive instability in the case of competitive interactions, whereas it annihilates diffusive instability in the case of prey-predator interactions. We demonstrated these results in the context of two specific examples.

Animals↗

PubMed2003

Interspecific influence on mobility and Turing instability.

In this paper we formulate a multi-patch multi-species model in which the per-capita emigration rate of one species depends on the density of some other species. We then focus on Turing instability to examine if and when this cross-emigration response has crucial effects. We find that the type of interaction matters greatly. In the case of competition a cross-emigration response promotes pattern formation by exercising a destabilizing influence; in particular, it may lead to diffusive instability provided that the response is sufficiently strong, which contrasts sharply with the well-known fact that the standard competition system does not exhibit Turing instability. In the case of prey-predator or activator-inhibitor interaction it acts against pattern formation by exerting a stabilizing effect; in particular, the diffusive instability, even though it may happen in a standard system, never occurs when the response is sufficiently strong. We conclude that the cross-emigration response is an important factor that should not be ignored when pattern formation is the issue.

Animals↗

PubMed2002

How to assess the relative importance of different colonization routes of pathogens within hospital settings.

The emergence of antibiotic resistance among nosocomial pathogens has reemphasized the need for effective infection control strategies. The spread of resistant pathogens within hospital settings proceeds along various routes of transmission and is characterized by large fluctuations in prevalence, which are typical for small populations. Identification of the most important route of colonization (exogenous by cross-transmission or endogenous caused by the selective pressure of antibiotics) is important for the design of optimal infection control strategies. Such identification can be based on a combination of epidemiological surveillance and costly and laborious as well as time-consuming methods of genotyping. Furthermore, analysis of the effects of interventions is hampered by the natural fluctuations in prevalence. To overcome these problems, we introduce a mathematical algorithm based on a Markov chain description. The input is longitudinal prevalence data only. The output is estimates of the key parameters characterizing the two colonization routes. The algorithm is tested on two longitudinal surveillance data sets of intensive care patients. The quality of the estimates is determined by comparing them to accurate estimates based on additional information obtained by genotyping. The results warrant optimism that this algorithm may help to quantify transmission dynamics and can be used to evaluate the effects of infection control interventions more carefully.

Algorithms↗

PubMed2002

Modeling and real-time prediction of classical swine fever epidemics.

We propose a new method to analyze outbreak data of an infectious disease such as classical swine fever. The underlying model is a two-type branching process. It is used to deduce information concerning the epidemic from detected cases. In particular, the method leads to prediction of the future course of the epidemic and hence can be used as a basis for control policy decisions. We test the model with data from the large 1997-1998 classical swine fever epidemic in The Netherlands. It turns out that our results are in good agreement with the data.

Animals↗