摘要
利用常微分方程的定性理论以及传染病模型的研究方法讨论具有急性和慢性两个阶段的SIVR流行病模型,得到了模型在无病平衡点和地方病平衡点再生数R0的阈值。当R0<1时,利用构造Dulac函数的方法证明模型在无病平衡点的全局渐近稳定性;当R0>1时,用构造Liapunov函数方法得到地方病平衡点的全局渐近稳定性的充分条件,并从生物学的角度给以解释。
An SIVR epidemic model with stage-structured is researched with using the stability theory of differential equation and infectious disease model theory. The thresholds value R0 of equilibrium point is found in the disease model. At the same time, when R0 〈 1 , use method of construct Dulac function testify the global stability at the disease-free equilibrium point of the model. When R0 〉 1 , construct the Liapunov function testify the global stability conditions at the endemic equilibrium. And the model is explanated from the point of view of ecology.
出处
《科学技术与工程》
2008年第7期1643-1648,共6页
Science Technology and Engineering
基金
陕西省教育厅自然科学基金项目(06JK301)资助
关键词
急慢性阶段
流行病模型
再生数
平衡点
全局渐近稳定
acute and chronic infection stages epidemic model reproductive numbers equilibrium point global stability.
