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Bacteriophage Infection Dynamics: Multiple Host Binding Sites

H. L. Smith, R. T. Trevino (2009)

Mathematical Modelling of Natural Phenomena

We construct a stochastic model of bacteriophage parasitism of a host bacteria that accounts for demographic stochasticity of host and parasite and allows for multiple bacteriophage adsorption to host. We analyze the associated deterministic model, identifying the basic reproductive number for phage proliferation, showing that host and phage persist when it exceeds unity, and establishing that the distribution of adsorbed phage on a host is binomial with slowly evolving mean. Not surprisingly,...

Bifurcation Thresholds in an SIR Model with Information-Dependent Vaccination

A. d'Onofrio, P. Manfredi, P. Manfredi (2010)

Mathematical Modelling of Natural Phenomena

Simple epidemiological models with information dependent vaccination functions can generate sustained oscillations via Hopf bifurcation of the endemic state. The onset of these oscillations depend on the shape of the vaccination function. A “global” approach is used to characterize the instability condition and identify classes of functions that always lead to stability/instability. The analysis allows the identification of an analytically determined “threshold vaccination function” having...

Bilinear system as a modelling framework for analysis of microalgal growth

Štěpán Papáček, Sergej Čelikovský, Dalibor Štys, Javier Ruiz (2007)

Kybernetika

A mathematical model of the microalgal growth under various light regimes is required for the optimization of design parameters and operating conditions in a photobioreactor. As its modelling framework, bilinear system with single input is chosen in this paper. The earlier theoretical results on bilinear systems are adapted and applied to the special class of the so-called intermittent controls which are characterized by rapid switching of light and dark cycles. Based on such approach, the following...

Building Mathematical Models and Biological Insight in an Introductory Biology Course

A. E. Weisstein (2011)

Mathematical Modelling of Natural Phenomena

A growing body of literature testifies to the importance of quantitative reasoning skills in the 21st-century biology curriculum, and to the learning benefits associated with active pedagogies. The process of modeling a biological system provides an approach that integrates mathematical skills and higher-order thinking with existing course content knowledge. We describe a general strategy for teaching model-building in an introductory biology course,...

Building the library of RNA 3D nucleotide conformations using the clustering approach

Tomasz Zok, Maciej Antczak, Martin Riedel, David Nebel, Thomas Villmann, Piotr Lukasiak, Jacek Blazewicz, Marta Szachniuk (2015)

International Journal of Applied Mathematics and Computer Science

An increasing number of known RNA 3D structures contributes to the recognition of various RNA families and identification of their features. These tasks are based on an analysis of RNA conformations conducted at different levels of detail. On the other hand, the knowledge of native nucleotide conformations is crucial for structure prediction and understanding of RNA folding. However, this knowledge is stored in structural databases in a rather distributed form. Therefore, only automated methods...

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