The dynamics of war between benign cells, malignant cells, and killer agents

Kjell Hausken and John F. Moxnes

Mathematical and Computer Modelling of Dynamical Systems, 2007, vol. 13, issue 2, 143-161

Abstract: This article provides a dynamic description of the interaction modelled as war between malignant cells (cancer), benign cells, and killer agents. Killer agents are, firstly, killer cells generated by the immune system and, secondly, chemotherapy, X-ray treatment, laser treatment, radiotherapy, surgery, etc. We allow killer cells to be generated proportionally to the number of benign cells, or proportionally to the number of malignant cells. Killer cells attack only the malignant cells, and can do so in a non-targeting or targeting manner. The equations for non-targeting and targeting interaction are shown to be equivalent, though with different interpretations of the terms. The killer agents due to chemotherapy and X-ray treatment are assumed to be non-targeting. We show that equilibrium between benign and malignant cells is possible in living tissue. Suitably adjusting the mitosis ratio or the death ratio for benign and malignant cells, and various other parameters, the article demonstrates mathematically and by simulations the dynamics by which malignant cells can be completely removed through the introduction of killer agents.

Date: 2007
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DOI: 10.1080/13873950600621810

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