中文摘要：

研究了一类既包含高致病禽流感病毒，又包含低致病禽流感病毒的人禽动力学模型，还考虑到人类会对染病的禽类进行有针对性的宰杀．通过讨论得到了两个基本再生数R1，R2，并得到了无病平衡态和染病平衡态的全局稳定性条件．证明了当两类病毒还未共存时，可以通过有效治疗和宰杀禽类来控制疾病传播；当两类病毒已共存时，治疗和宰杀禽类反而会促使两类病毒共存，并发展为地方病．因此只有趁两类病毒还未共存时控制，才能可有效抑制禽流感在人类的传播．

英文摘要：

Abstract In this paper we consider a human-poultry dynamic model to describe the behavior of both high pathogenic avian influenza and low pathogenic avian influenza strains in poultry population with targeted culling. Through discussion we get two basic reproductive number R1, R2, and the global stability conditions of the disease- free equilibrium and the infected equilibria. It is proved that when the two viruses are not coexisting, the disease transmission can be controlled by effective treatment and culling of poultry. When the two viruses have been coexisting, the treatment and culling of poultry can promote the coexistence of the two viruses and become endemic diseases. So it can be effective to inhibit the spread of avian flu in human beings only when the two viruses are not coexisting. Keywords Epidemic model, basic reproduction, stability, disease control