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30 results on '"Sauer, Niko"'

1. Epidemics: towards understanding undulation and decay

Author

Sauer, Niko

Subjects
Quantitative Biology - Populations and Evolution, Mathematics - Dynamical Systems
Abstract

Undulation of infection levels, usually called waves, are not well understood. In this paper we propose a mathematical model that exhibits undulation and decay towards a stable state. The model is a re-interpretation of the original SIR-model obtained by postulating different constitutive relations whereby classical logistic growth with recovery is obtained. The recovery relation is based on the premise that infectiousness only lasts for some time. This leads to a differential-difference (delay) equation which intrinsically exhibits periodicity in its solutions but not necessarily decay to asymptotically stable equilibrium. Limit cycles can indeed occur. An appropriate linearization of the governing equation provides a firm basis for heuristic reasoning as well as confidence in numerical calculations., Comment: 22 pages, 3 figures

Published
2022

14. Intertwined Markov processes: the extended Chapman–Kolmogorov equation.

Author

Lee, Wha-Suck and Sauer, Niko

Abstract

Uniformization transforms a pseudo-Poisson process with unequal intensities (leaving rates) into one with uniform intensity. Self-transitions is the price to pay. Two intensities arise when one considers an absorbing barrier of a Markov process as a body in its own right: a pair of Markov processes intertwined by an extended Chapman–Kolmogorov equation naturally arises. We show that Sauer's two-state space empathy theory handles such intertwined processes. The price of self-transitions is also avoided. [ABSTRACT FROM PUBLISHER]

Published
2018
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23. ON BOUNDARY PERMEATION IN NAVIER–STOKES AND SECOND GRADE INCOMPRESSIBLE FLUIDS.

Author

MARITZ, RIËTTE and SAUER, NIKO

Subjects
*FLUID dynamics, *NAVIER-Stokes equations, *PERMEABILITY, *STRAINS & stresses (Mechanics), *MATHEMATICAL models
Abstract

A mathematical model for the phenomenon of penetration of fluid into permeable walls is developed for second grade fluids. The model is based on mechanical principles which involve normal stresses at the boundary and contact forces at the fluid-boundary interface. Stability of the rest state is proved. The results are compared to that for the simplified case of a Navier–Stokes fluid. [ABSTRACT FROM AUTHOR]

Published
2006
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