This paper establishes the global existence and boundedness of classical solutions for a parabolic-elliptic chemotaxis system coupled with nonlinear reaction dynamics, which models key aspects of tumor-immune evasion interactions. The model under consideration is given by: \(\begin{aligned} {\left\{ \begin{array}{ll} u_{t}=\Delta u-\nabla \cdot (u\nabla v)+\mu u-\mu u^r,& \quad x\in \Omega ,t>0,\\ 0=\Delta v-v+w,& \quad x\in \Omega ,t>0,\\ w_{t}=auz-w,& \quad x\in \Omega ,t>0,\\ z_{t}=\Delta z-uz+w,& \quad x\in \Omega ,t>0 \end{array}\right. } \end{aligned}\) subject to no-flux boundary conditions in a bounded domain \(\Omega \subset \mathbb {R}^N(N\ge 2)\) , where \(r>1\) , \(0<a\le 1\) and \(\mu >0\) . The main result demonstrates that bounded global classical solutions exist under the following parameter constraints: (i) For \(N = 2\) , with \(r > 1\) ; (ii) For \(N \ge 3\) , with \(r > 1 + \frac{N}{2}\) .
