关键词: 基本再生数;全局渐近稳定, Lyapunov 函数;不可约合作系统, Metzler矩阵

Abstract: A malaria model with population dynamic in two patches is established, which the hosts can migrate between patches, but not the vectors. The model is irreducible cooperative and strongly monotone.   The basic reproduction number R0 is computed. If R0≤1, then the disease-free equilibrium is globally asymptotically stable. When R0>1, there exists a unique endemic equilibrium, which is globally asymptotically stable.

Key words: Metzler matrix, Lyapunov function, irreducible cooperative system, basic reproduction number, global asymptotically stable