Integral equation models for endemic infectious diseases.

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.