Displaying similar documents to “Modelling tumour-immunity interactions with different stimulation functions”

Autowaves in the Model of Infiltrative Tumour Growth with Migration-Proliferation Dichotomy

A.V. Kolobov, V.V. Gubernov, A.A. Polezhaev (2011)

Mathematical Modelling of Natural Phenomena

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A mathematical model of infiltrative tumour growth is investigated taking into account transitions between two possible states of malignant cells: proliferation and migration. These transitions are considered to depend on oxygen level in a threshold manner where high oxygen concentration allows cell proliferation, while concentration below a certain critical value induces cell migration. The infiltrative tumour spreading rate dependence on model parameters is obtained. It is shown that...

A mathematical model of HIV-1 infection including the saturation effect of healthy cell proliferation

Mahiéddine Kouche, Bedr'eddine Ainseba (2010)

International Journal of Applied Mathematics and Computer Science

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In this paper we derive a model describing the dynamics of HIV-1 infection in tissue culture where the infection spreads directly from infected cells to healthy cells trough cell-to-cell contact. We assume that the infection rate between healthy and infected cells is a saturating function of cell concentration. Our analysis shows that if the basic reproduction number does not exceed unity then infected cells are cleared and the disease dies out. Otherwise, the infection is persistent...