一类具有阶段结构种群传染病模型的定性分析

Qualitative Analysis of a Class of Infectious Disease Model with Stage Structure

建立一类具有阶段结构的种群传染病模型,主要考虑疾病仅在成年个体间传播.基于成年个体之间的种内竞争和疾病传播现象,研究了疾病传播对于种群的影响.一方面,讨论了种群持久的条件;另一方面,在种群持久的条件下,研究了无病平衡点和多个地方病平衡点的存在性和稳定性.结果表明仅在成年阶段传播的疾病可能会引起后向分支现象的发生.

In this paper,a class of population disease models with stage structure has been established,mainly considering that the disease is only transmitted among adult individuals.Based on intraspecific competition and disease transmission among adult individuals,the effects of disease transmission on populations have been studied.On the one hand,the conditions for persistent populations have been discussed.And on the other hand,under the conditions for persistent populations,the existence and stability of the disease-free equilibrium and multiple endemic equilibrium points been studied.The results show that the disease transmitted only in adult stage may cause the phenomenon of backward bifurcation.