Biomedical subjects

Andreas Handel

Publications and source records attributed to Andreas Handel.

6 recordsLinked to original sources

PubMed2006

Transient dynamics and nonlinear stability of spatially extended systems.

As studies of various systems have shown, the sole focus on the eigenvalues in a linear stability analysis can be misleading, especially when the dynamics of disturbances is characterized by strong transient growth. The aim of this paper is to extend the generalized stability analysis, in the context of spatially extended systems, by examining the role of the nonlinear terms in the destabilization process. The critical noise level leading to destabilization is often found to scale as a power of the magnitude of transient amplification. In what follows we show that the power law exponent sensitively depends on the type of nonlinear terms and their potential for generating self-sustaining noise amplification cycles (bootstrapping). We find, however, that the exponents are not universal and also depend on the more subtle details of the transient dynamics. We also show that the basin of attraction of a spatially uniform state is bounded by the stable manifold(s) of nearby saddle(s) which play a major role in the transition.

Journal Article↗

PubMed2006

Transmissibility and mortality impact of epidemic and pandemic influenza, with emphasis on the unusually deadly 1951 epidemic.

There are important gaps in our current understanding of the influenza virus behavior. In particular, it remains unclear why some inter-pandemic seasons are associated with unusually high mortality impact, sometimes comparable to that of pandemics. Here we compare the epidemiological patterns of the unusually deadly 1951 influenza epidemic (A/H1N1) in England and Wales and Canada with those of surrounding epidemic and pandemic seasons, in terms of overall mortality impact and transmissibility. Based on the statistical and mathematical analysis of vital statistics and morbidity epidemic curves in these two countries, we show that the 1951 epidemic was associated with both higher mortality impact and higher transmissibility than the 1957 and 1968 pandemics. Surprisingly in Liverpool, considered the 'epicenter' of the severe 1951 epidemic, the mortality impact and transmissibility even surpassed the 1918 pandemic.

Communicable Disease Control↗

PubMed2006

The role of compensatory mutations in the emergence of drug resistance.

Pathogens that evolve resistance to drugs usually have reduced fitness. However, mutations that largely compensate for this reduction in fitness often arise. We investigate how these compensatory mutations affect population-wide resistance emergence as a function of drug treatment. Using a model of gonorrhea transmission dynamics, we obtain generally applicable, qualitative results that show how compensatory mutations lead to more likely and faster resistance emergence. We further show that resistance emergence depends on the level of drug use in a strongly nonlinear fashion. We also discuss what data need to be obtained to allow future quantitative predictions of resistance emergence.

Computational Biology↗

PubMed2005

Pattern selection and control via localized feedback.

Many theoretical analyses of feedback control of pattern-forming systems assume that feedback is applied at every spatial location, something that is often difficult to accomplish in experiments. This paper considers an experimentally more feasible scenario where feedback is applied at a sparse array of discrete spatial locations. We show how such feedback can be computed analytically for a class of reaction-diffusion systems and use generalized linear stability analysis to determine how dense the actuator array needs to be to select or maintain control of a given pattern state in the presence of noise. The one-dimensional Swift-Hohenberg equation is used to illustrate our theoretical results and explain earlier experimental observations on the control of the Rayleigh-Bénard convection.

Journal Article↗

PubMed2002

Spectral theory for the failure of linear control in a nonlinear stochastic system.

We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur in systems described by linearly stable but strongly non-normal evolution operators. In spatially extended systems the non-normality manifests itself in two different but complementary ways: transient amplification and spectral focusing of disturbances. We show that temporal and spatial aspects of the non-normality and the type of nonlinearity are all crucially important to understand and describe the mechanism of nonlinear instability. Presented results are expected to apply equally to other physical systems where strong non-normality is due to the presence of mean flow rather than the action of control.

Journal Article↗

PubMed2002

Non-normality and the localized control of extended systems.

The idea of controlling the dynamics of spatially extended systems using a small number of localized perturbations is very appealing-such a setup is easy to implement in practice. However, when the distance between controllers generating the perturbations becomes large, control fails due to extreme sensitivity of the system to noise. This sensitivity results from strong non-normality of the evolution operator governing the dynamics of disturbances in the controlled system. We investigate how non-normality can arise in an originally normal system and study how the noise amplification depends on the distance between controllers.

Journal Article↗