On some properties of a nonlinear delay integral equation used in epidemiology

This paper discusses some relevant properties of a nonlinear integral equation such as the positivity and boundedness of its solution as well as its controllability under impulsive controls. The model can describe an infection evolution and the acting impulsive controls can be interpreted in particular as either vaccination actions or as variations of the infected population due to infected immigration or lost of infective numbers due to lost of infected population.