Infectious diseases are among the most prominent threats to mankind. Mathematical modeling of infectious diseases, by using delay differential equations, has an important role in the epidemiological aspect of disease control (Capasso, Mathematical structure of epidemic systems. Lecture notes in biomathematics, vol 97, Springer, Berlin, 1993; Mackey and Glass, Science 197:287–289, 1977). Several epidemic models, with various characteristics, have been described and investigated in the literature. Most of these models are based on the susceptible-infected-removed (SIR) model.