讲座题目：Mathematical modeling and analysis of pro- and anti-tumor macrophages with time delays

主办单位：长江大学信息与数学学院

报告专家：董岳平（华中师范大学 副教授）

报告时间：2021年5月12（周三）  16:30-17:30

报告地点：8教406

专家简介：董岳平，华中师范大学硕士生导师，博士毕业于日本静冈大学，在日本东京大学、九州大学和青山学院大学做过博士后研究工作。主要从事生物数学，动力系统理论与应用等领域的研究。先后在 J. Theor. Biol., BMJ Open, Nonlinear Dyn., Appl. Math. Model., Appl. Math. Comput., Int. J. Bifurcat. Chaos, Nonlinear Anal. Real World Appl., DCDS-B 等学术期刊上发表SCI论文20多篇，主持1项国家自然科学基金青年项目和1项湖北省自然科学基金青年项目。

摘要：First, we propose a new ODEs model of interactions between tumor cells, M1 and M2 macrophages, and study the stability and bifurcations around the interior equilibrium. It is shown that the model exhibits stable periodic oscillations bifurcating from Hopf bifurcation, which indicates the long-term coexistence of tumor cells, M1 and M2 macrophages as well as long-term tumor relapse. Secondly, we incorporate M1 macrophages activation delay and M2 macrophages activation delay into previous model. The new findings show that M1 macrophages activation delay can only destabilize the interior equilibrium. However, M2 macrophages activation delay can not only destabilize the interior equilibrium but also stabilize the interior equilibrium. Several bifurcation diagrams are provided to support the theoretical results.