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Hopf bifurcation analysis and numerical simulations in an ODE model of the immune system with positive immune response. (English) Zbl 1128.92020
Summary: We consider an ordinary differential equations (ODE) model for the tumor-immune system with positive immune response and a unique nontrivial positive equilibrium. Its dynamics are studied in terms of the local stability and the description of the Hopf bifurcation which is proven to exist as the parameter of the normal rate of the flow of adult effector cells (ECs) into the tumor site crosses some critical values. We illustrate these results numerically.

MSC:
92C50 Medical applications (general)
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
37N25 Dynamical systems in biology
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