Asymptotically periodic solutions to Volterra integral equations in epidemic models

Through the use of the limiting equation, conditions are given under which a scalar nonlinear Volterra integral equation, of either convolution or nonconvolution type, has an asymptotically periodic solution. Periodicity can be in either the forcing function or the kernel of the integral equation. The results are applied in several models for the spread of gonorrhea to gain insight into the causes of the observed oscillations in the infective populations.