Fluctuations in a SIS epidemic model with variable size population

In an epidemiological model, time spent in one compartment is often modeled by a delay in the model. In general the presence of delay in differential equations can change the stability of an equilibrium to instability and causes the appearance of oscillatory solutions. In this paper we consider a SIS epidemiological model with demographic effects: birth, mortality and mortality caused by infection. The delay is the period of infection. We define the concept of oscillation in the sense that solutions of the model studied fluctuate around a steady state. Our goal is to show that in this model, there are oscillating solutions for certain parameters values. We determine a large set of initial data for which solutions of this model are slowly oscillating.