Mathematical and Computational BiologyOpen Access

MATHEMATICAL MODELING OF TUMOR CELL GROWTH AND IMMUNE SYSTEM INTERACTIONS

FATHALLA A. RIHAN

Department of Mathematical Sciences, United Arab Emirates University, Al-Ain, 1755, UAE

Permanent address: Faculty of Science, Helwan University, Cairo, Egypt.

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MUNTASER SAFAN

Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt

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MOHAMED A. ABDEEN

Department of Mathematics, Helwan University, Cairo, Egypt

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, and

DUAA H. ABDEL-RAHMAN

Department of Mathematical Sciences, United Arab Emirates University, Al-Ain, 1755, UAE

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https://doi.org/10.1142/S2010194512005156Cited by:7 (Source: Crossref)

Abstract

In this paper, we provide a family of ordinary and delay differential equations to describe the dynamics of tumor-growth and immunotherapy interactions. We explore the effects of adoptive cellular immunotherapy on the model and describe under what circumstances the tumor can be eliminated. The possibility of clearing the tumor, with a strategy, is based on two parameters in the model: the rate of influx of the effector cells, and the rate of influx of IL2. The critical tumor-growth rate, below which endemic tumor does not exist, has been found. One can use the model to make predictions about tumor-dormancy.

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