Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission
Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission
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DOI：
10.1007/s11538-005-9037-9
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发表时间：
2006-04-01
影响因子：
3.5
通讯作者：
Korobeinikov, Andrei
中科院分区：
文献类型：
--
作者：
Korobeinikov, Andrei
构建了二维 SIR 和 SIRS 区室流行病模型的 Lyapunov 函数，该模型具有受一些生物学上可行的条件约束的非常一般形式 f(S.I) 的非线性传播率。由此建立了这些模型的全局属性，包括具有垂直和水平传输的模型。证明了在种群规模恒定的假设下，函数f(S.I)相对于感染宿主数量I的凹性保证了正流行平衡状态的唯一性和全局稳定性。
Lyapunov functions for two-dimension SIR and SIRS compartmental epidemic models with non-linear transmission rate of a very general form f(S. I) constrained by a few biologically feasible conditions are constructed. Global properties of these models including these with vertical and horizontal transmission, are thereby established. It is proved that, under the constant population size assumption, the concavity of the function f(S. I) with respect to the number of the infective hosts I ensures the uniqueness and the global stability of the positive endemic equilibrium state.