Abstract: Artificial immune system has been an important branch of artificial intelligence.But we are still not very familiar with immune system.It provides a new way for researching artificial immune system by simulating and modeling immune system.It presents here a model of partial differential equation，which modeling clone expanding，selection and mutation in immune response.It sets up an affinity function representing the ability of a certain class of lymphocytes to recognize a foreign antigen.Carrying out some analytical and numerical studies，it determines the critical values for the parameters ruling the selection and mutation.Some analytical studies on its dynamics are carried out.And at the same time，a numerical resolution of the corresponding discrete model is developed.Based on the model，new mutation operator can be researched in further for designing artificial immune algorithm.

摘要： 人工免疫系统已经成为人工智能领域的一个重要分支，但目前对免疫系统还缺乏许多认识。利用计算机仿真和建模方法研究免疫系统为人工免疫系统研究提供了一个新途径。开发了一个偏微分方程系统，模拟免疫系统应答中的克隆扩增、变异和选择。模型设置一个亲和力函数，使其能表达一种确定类型的淋巴细胞识别外部抗原的能力。通过数值分析和研究，确定控制选择和变异的重要参数值。对其动力学性能进行分析研究，同时研究了对应离散模型的数值解答方法。基于该模型可以进一步研究新的变异算子，设计人工免疫算法。