一类病菌与免疫系统作用模型的定性分析

Qualitative Analysis of a Model with the Action Between Immune System and Bacteria

考虑病菌的一种信息交流机理,建立了一类时滞传染病模型.分析了模型平衡点的存在性、渐近稳定性及Hopf分歧的存在性及方向.最后,运用计算机数值模拟验证所得理论结果,为传染病的控制和预防提供了理论基础和数值依据.

Taking into account an exchanging information mechanism of bacteria,an epidemic model with time delay is formulated.The existence and stability of positive equilibrium of the model are investigated,and the length of delay preserving the stability of the positive equilibrium is estimated.Moreover,the existence and direction of Hopf bifurcation are discussed.At last,numerical simulations are curried out to verify the theory results.The results obtained in this paper provide a theoretical and numerical basis to control and prevent the epidemic disease.