Abstract
We present and analyze a three-species mathematical model of tumor progression and regression using prey-predator dynamics. The tumor cell population is supposed to be the prey species and the cytotoxic T-lymphocytes (CTL) and macrophages (which are killer cells of the immune system) as their predator. Using a ratio-dependent predation functional form, the ODE model is analyzed for stability criteria. A discrete time delay required for destruction of tumor cells is then incorporated into the basic model and the resulting delayed model is studied to explore the significance of various system parameters controlling the stability of the system. The active killer cells are shown to be the key population species controlling the system dynamics. A range of the delay parameter is estimated that ensures stability of different system components. Numerical simulations are performed to support analytical findings.
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