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Immunotherapy with interleukin-2: A study based on mathematical modeling

Sandip Banerjee (2008)

International Journal of Applied Mathematics and Computer Science

The role of interleukin-2 (IL-2) in tumor dynamics is illustrated through mathematical modeling, using delay differential equations with a discrete time delay (a modified version of the Kirshner-Panetta model). Theoretical analysis gives an expression for the discrete time delay and the length of the time delay to preserve stability. Numerical analysis shows that interleukin-2 alone can cause the tumor cell population to regress.

Improving prediction models applied in systems monitoring natural hazards and machinery

Marek Sikora, Beata Sikora (2012)

International Journal of Applied Mathematics and Computer Science

A method of combining three analytic techniques including regression rule induction, the k-nearest neighbors method and time series forecasting by means of the ARIMA methodology is presented. A decrease in the forecasting error while solving problems that concern natural hazards and machinery monitoring in coal mines was the main objective of the combined application of these techniques. The M5 algorithm was applied as a basic method of developing prediction models. In spite of an intensive development...

Integrating Photosynthesis, Respiration, Biomass Partitioning, and Plant Growth: Developing a Microsoft Excel®-based Simulation Model of Wisconsin Fast Plant (Brassica rapa, Brassicaceae) Growth with Undergraduate Students

Y. L. Grossman, A. B. Berdanier, M. L. Custic, L. R. Feeley, S. F. Peake, A. J. Saenz, K. S. Sitton (2011)

Mathematical Modelling of Natural Phenomena

This paper demonstrates the development of a simple model of carbon flow during plant growth. The model was developed by six undergraduate students and their instructor as a project in a plant ecophysiology course. The paper describes the structure of the model including the equations that were used to implement it in Excel®, the plant growth experiments that were conducted to obtain information for parameterizing and testing the model, model performance, student responses to the modeling project,...

Intracellular Modelling of Cell-Matrix Adhesion during Cancer Cell Invasion

V. Andasari, M.A.J. Chaplain (2012)

Mathematical Modelling of Natural Phenomena

When invading the tissue, malignant tumour cells (i.e. cancer cells) need to detach from neighbouring cells, degrade the basement membrane, and migrate through the extracellular matrix. These processes require loss of cell-cell adhesion and enhancement of cell-matrix adhesion. In this paper we present a mathematical model of an intracellular pathway for the interactions between a cancer cell and the extracellular matrix. Cancer cells use similar...

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