Mathematical modelling of infectious diseases gains growing attention in epidemiology during the last decades. The major benefits of simulating compartmental models are the prediction of the consequences of potential ...
详细信息
Mathematical modelling of infectious diseases gains growing attention in epidemiology during the last decades. The major benefits of simulating compartmental models are the prediction of the consequences of potential ...
详细信息
Mathematical modelling of infectious diseases gains growing attention in epidemiology during the last decades. The major benefits of simulating compartmental models are the prediction of the consequences of potential interventions, a deeper understanding of epidemic dynamics and clinical decision support. The main limitation is however that several parameters are based on uncertain expert guesses (default values) and are not estimated from the study data. In this paper we build a bridge between the well-known deterministic S-I-R (Susceptible-Infectious-Removed) model which can be described with differential equations and the stochastic counterpart which can be used for statistical inference if outbreak data on an individual patient level are available. The possibly time-dependent transmission rate as well as the (basic) reproduction number are the main epidemiological parameters of interest. Furthermore, one important type of heterogeneity is considered: individuals may vary due to their susceptibility, i.e., risk factors for infection may be investigated. The Cox-Aalen survival model that is based on a multiplicative-additive hazard structure turned out to be a suitable tool for that purpose. The results give valuable informations for clinicians working in infection control and public health.
Cross-spectral and synchronization analysis of two independent, identical chaotic Rössler systems suggest a coupling although there is no interaction. This spuriously detected interaction can either be explained ...
详细信息
Cross-spectral and synchronization analysis of two independent, identical chaotic Rössler systems suggest a coupling although there is no interaction. This spuriously detected interaction can either be explained by the absence of mixing or by finite size effects. To decide which alternative holds the phase dynamics is studied by a model of the fluctuations derived from the system’s equations. The basic assumption of the model is a diffusive character for the system which corresponds to mixing. Comparison of theoretical properties of the model with empirical properties of the Rössler system suggests that the system is mixing but the rate of mixing appears to be rather low.
The identification of a differential equation underlying a measured time series is a prerequisite for numerous types of applications. In the validation of a proposed parameterized model one often faces the dilemma tha...
The identification of a differential equation underlying a measured time series is a prerequisite for numerous types of applications. In the validation of a proposed parameterized model one often faces the dilemma that it is hard to decide whether possible discrepancies between the measured time series and the simulated model output are caused by an inappropriate model or by wrongly specified parameters in a correct type of model. We propose a combination of parametric modelling based on Bock's multiple shooting algorithm and nonparametric modelling based on optimal transformations as a strategy to test proposed models and if rejected suggest and test new ones. We exemplify this strategy on an experimental time series from a nonlinear chaotically oscillating circuit where we finally obtain an extremely accurate reconstruction of the observed attractor.
Invasive electroencephalograph (EEG) recordings of ten patients suffering from focal epilepsy were analyzed using the method of renormalized entropy. Introduced as a complexity measure for the different regimes of a d...
Invasive electroencephalograph (EEG) recordings of ten patients suffering from focal epilepsy were analyzed using the method of renormalized entropy. Introduced as a complexity measure for the different regimes of a dynamical system, the feature was tested here for its spatiotemporal behavior in epileptic seizures. In all patients a decrease of renormalized entropy within the ictal phase of seizure was found. Furthermore, the strength of this decrease is monotonically related to the distance of the recording location to the focus. The results suggest that the method of renormalized entropy is a useful procedure for clinical applications like seizure detection and localization of epileptic foci.
暂无评论