一类具有非线性发生率和治疗函数的传染病模型研究

传染病动力学系统的数学建模中,合理的使用非线性发生率往往更能使模型与实际相吻合.并且在实际的疾病防治过程中,由于受到空间人力物力资源的影响一般存在最大治疗容量的限制.结合这两种情况建立了一类含非线性发生率和最大治疗容量限制的传染病模型.通过分析这个模型,得到无病平衡点和正平衡点的存在性、稳定性.进一步取发生率和治疗系统达到最大容量时的感染者人数作为分支参数,得到了Hopf分支和Bogdanov-Takens分支的存在条件,并进行了数值模拟.

The Study on an Epidemic Model with Nonlinear Incidence and Piecewise Treatment Function

During the modeling of dynamic epidemic systems,it is usually the reasonable usage of nonlinear incidence that makes the model fitting with reality much better than linear ones.Also in reality mostly we have limitations of treatment capacity due to the limitation of resources during the treatment process.In this paper we established a new epidemic model with nonlinear incidence and maximum treatment capacity by combining the two situations above.Throughout analysis of this model we had existence and stability of the disease-free equilibrium and positive equilibria.Furthermore we take the infection rate and the infective level at which the healthcare system reaches capacity as a parameter,we got the conditions of parameters for the existence of Hopf bifurcation and Bogdanov-Takens bifurcations,which we also did some numerical simulations on existence of equilibrium and branches.