Bonzi B, Fall A A, Iggidr A, Sallet G
Université de Ouagadougou, UFR SEA, Ouagadougou, Burkina Faso.
J Math Biol. 2011 Jan;62(1):39-64. doi: 10.1007/s00285-010-0327-y. Epub 2010 Feb 11.
We introduce classes of differential susceptibility and infectivity epidemic models. These models address the problem of flows between the different susceptible, infectious and infected compartments and differential death rates as well. We prove the global stability of the disease free equilibrium when the basic reproduction ratio R0≤1 and the existence and uniqueness of an endemic equilibrium when R0>1. We also prove the global asymptotic stability of the endemic equilibrium for a differential susceptibility and staged progression infectivity model, when R0>1. Our results encompass and generalize those of Hyman and Li (J Math Biol 50:626-644, 2005; Math Biosci Eng 3:89-100, 2006).
我们引入了差分易感性和传染性流行病模型的类别。这些模型解决了不同易感、感染和患病隔间之间的流动问题以及差分死亡率问题。我们证明了基本再生数(R_0\leq1)时无病平衡点的全局稳定性，以及(R_0>1)时地方病平衡点的存在性和唯一性。我们还证明了对于差分易感性和分阶段进展传染性模型，当(R_0>1)时地方病平衡点的全局渐近稳定性。我们的结果涵盖并推广了海曼和李的结果（《数学生物学杂志》50:626 - 644，2005；《数学生物科学工程》3:89 - 100，2006）。
