基于禽流感的一类模型建立与性态研究

The Study of Dynamic Behaviors for a Model on Avian Influenza

禽流感是当前流行的一类复杂的疾病,它可以由动物传染给人类,因此为了研究它的流行性态和防治方案,建立了一类带有预防接种的传染病动力学模型.计算了基本再生数R0,通过分析这个模型,我们得到了如果当R0<1时,只存在一个无病平衡点,疾病消除;当R0>1时,存在惟一的地方病平衡点,即疾病流行.并且构造了适当的Liapunov函数证明了该模型的无病平衡点和地方病平衡点的全局稳定性.

As a complex epidemic today, avian influenza can be transmitted to human by animals. In order to study its epidemiology feature and find effective control methods for preventing its transmission, we establish a epidemic model with vaccination. The basic reproduction number R0 is obtained. If R0 〈 1, there exist a unique disease-free equilibrium, which means the disease would die out finally. If R0 〉 1, then there exist unique endemic equilibrium which means the disease would become epidemic. We prove the global stability of the disease＇s disease-free equilibrium and endemic equilibrium using certain Liapunov function method.