Abstract
In this study, we present a Lotka-Volterra predator-prey like model for the interaction dynamics of tumor-immune system. The model consists of system of differential equations with piecewise constant arguments and based on the model of tumor growth constructed by Sarkar and Banerjee. The solutions of differential equations with piecewise constant arguments leads to system of difference equations. Sufficient conditions are obtained for the local and global asymptotic stability of a positive equilibrium point of the discrete system by using Schur-Cohn criterion and a Lyapunov function . In addition, we investigate periodic solutions of discrete system through Neimark-Sacker bifurcation and obtain a stable limit cycle which implies that tumor and immune system undergo oscillation.
Highlights
In this study, we present a Lotka-Volterra predator-prey like model for the interaction dynamics of tumor-immune system
Cells (Cytotoxic T lymphocytes) and resting predator cells have constructed the model by using the time delay factor (T-Helper cells) which are main struggle of immune as follows: system
In study [17], Cooke model to study the role of IL-2 in tumor dynamics. and Györi show that differential equation with piecewise
Summary
We present a Lotka-Volterra predator-prey like model for the interaction dynamics of tumor-immune system. Many authors have considered delay differential equation included time delay factor for tumor cells and effector cells such as hunting predator modeling tumor growth [10,11,12,13,14,15,16]. A familiar model where M(t), N(t) and Z(t) are the number of tumor, included ordinary differential equations is constructed hunting and resting cells respectively.
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