Michalski, Anatoli I Yashin, Anatoli I
Published in
Mathematical biosciences

Manifestation of hormesis in longevity was modelled by modification of the mortality rate during and after the period of a stress factor action. In heterogeneous population this can lead to observation of unchanged mortality during action of the stress and decrease in mortality after stress period. Stochastic simulations were made to investigate th...

Ball, Frank G Lyne, Owen D
Published in
Mathematical biosciences

This paper considers stochastic epidemics among a population partitioned into households, with mixing locally within households and globally throughout the population. The two levels of mixing have important implications for the threshold behaviour of the epidemic and consequently for the form and construction of optimal vaccination policies. Optim...

Arino, Julien Gouzé, Jean-Luc
Published in
Mathematical biosciences

We study a class of size-structured, ODE models of growth in the chemostat, that take into account cell maintenance and substrate dependent cell mortality. Unlike most classical chemostat models, they are supposed to be non-conservative, in the sense that they do not verify the mass conservation principle. However, using a change of time scale, we ...

Koopman, James S Chick, Stephen E Simon, Carl P Riolo, Christopher S Jacquez, Geoffrey
Published in
Mathematical biosciences

The effects of two levels of mixing on endemic infection levels are shown to differ for identically conformed deterministic compartmental (DC) and stochastic compartmental (SC) models. Both DC and SC models give similar endemic levels when populations are large, immunity is short lived, and mixing is universal. But local transmissions and/or transi...

Ball, Frank Neal, Peter
Published in
Mathematical biosciences

This paper is concerned with a general stochastic model for susceptible-->infective-->removed epidemics, among a closed finite population, in which during its infectious period a typical infective makes both local and global contacts. Each local contact of a given infective is with an individual chosen independently according to a contact distribut...

Keesman, K J Stigter, J D
Published in
Mathematical biosciences

In this paper the well-known problem of optimal input design is considered. In particular, the focus is on input design for the estimation of kinetic parameters in bioreactors. The problem is formulated as follows: given the model structure (f,g), which is assumed to be affine in the input, and the specific parameter of interest theta;(k) find a fe...

Biesele, John Foster, David Jacquez, Geoffrey M Phair, Robert D Simon, Carl
Published in
Mathematical biosciences

Braumann, Carlos A
Published in
Mathematical biosciences

In a previous paper [Math. Biosci. 156 (1999) 1], we have studied quite general stochastic differential equation models for the growth of populations subjected to harvesting in a random environment. We have obtained conditions for non-extinction and for the existence of stationary distributions (as well as expressions for such distributions) simila...

Voit, Eberhard O
Published in
Mathematical biosciences

As we are entering the post-genomic era, models-of-data, such as mining and filtering methods for gene sequences and microarrays and the clustering of co-expressed genes, must be complemented with models-of-processes that explain relationships between genomic information and phenomena at biochemical and physiological levels. Many of these models wi...

Webb, Steven D Sherratt, Jonathan A Fish, Reginald G
Published in
Mathematical biosciences

One proposed mechanism of tumour escape from immune surveillance is tumour up-regulation of the cell surface ligand FasL, which can lead to apoptosis of Fas receptor (Fas) positive lymphocytes. Based upon this 'counterattack', we have developed a mathematical model involving tumour cell-lymphocyte interaction, cell surface expression of Fas/FasL, a...