Hethcote H W, Tudor D W
J Math Biol. 1980 Mar;9(1):37-47. doi: 10.1007/BF00276034.
Endemic infectious diseases for which infection confers permanent immunity are described by a system of nonlinear Volterra integral equations of convolution type. These constant-parameter models include vital dynamics (birth and deaths), immunization and distributed infectious period. The models are shown to be well posed, the threshold criteria are determined and the asymptotic behavior is analysed. It is concluded that distributed delays do not change the thresholds and the asymptotic behaviors of the models.
感染可赋予永久免疫力的地方性传染病，由一类卷积型非线性沃尔泰拉积分方程组来描述。这些常参数模型包括生命动态（出生和死亡）、免疫接种以及分布感染期。证明了这些模型是适定的，确定了阈值准则并分析了渐近行为。得出的结论是，分布时滞不会改变模型的阈值和渐近行为。
