International Scholarly Research Notices · 2014 · 23 citations · 18 references
MedicineImmunologyOncologyCancer ImmunologyTumor ImmunologyTumor ProgressionAntitumor T Cell ResponsesCell Population DynamicsDynamic Systems ModelingImmune FunctionImmune System ModelingTumor Growth KineticsGlobal StabilityGlobal Stability AnalysisNumerical SimulationPredator - Prey DynamicsPredator-prey ModelsPrey-predator CoevolutionTumor Growth ModelingTumor Progression Dynamics
This paper aims to develop the mathematical model that explores the immune response to a tumor system as a prey-predator system. A deterministic model defining the dynamics of tumor growth progression and regression has been analyzed. Our analysis indicates the tumor recurring and dormancy on the cellular level in combination with resting and hunting cells. The model considered in the present study is a generalization of El-Gohary (2008) by introducing the Michaelis-Menten function. This function describes the stimulation process of the resting cells by the tumor cells in the presence of tumor specific antigens. Local and global stability analysis have been performed along with the numerical simulation to support our findings.
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