In this paper we discuss the tumor growth of GB (Glioblastoma) with piecewise constant arguments represented in the following equation \ndx(t)/dt=x(t)r(1-αx(t)-β_0 ⟦t⟧x(⟦t⟧)-β_1 ⟦t-1⟧x(⟦t-1⟧))-γ_1 ⟦t⟧x(t)x(⟦t⟧)-γ_2 ⟦t-1⟧x(t)x(⟦t-1⟧),\nwhere the parameters α,β_0,β_1,γ_1 ,γ_(2 )and r belong to R^+ and ⟦t⟧ is the integer part of t∈[0,∞). The parameter γ_1 represents the effect of the treatment on the tumor, while γ_2 is embedded to show the rate that causes a negative effect from the immune system to the tumor population. We embed ⟦t⟧ and ⟦t-1⟧ as coefficients to the equation to emphasize the treatment therapy for specific time. We investigate some theoretical results on the local and global stability of the positive equilibrium point. In addition, we prove that the discrete equation undergoes period doubling (flip) and Neimark-Sacker bifurcation. For an early detection of Glioblastoma, we incorporate an Allee function of time t to analyze the behavior for a strong Allee effect. Numerical simulations are performed to validate the theoretical results.

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