In this paper,we study a simplified Othmer-Stevens model with reproduction term. By making use of a smart function transformation,the comparative method and some special mathe-matical analysis,we prove the existence of global,blow-up or quenching solutions of the problem on different conditions. More interesting results are reached. The result of the paper not only verifies a real biological phenomenon,but also provides a theo-retical groundwork for numerical problems of the chemotaxis model.
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