Seasonal Treatment of an Infectious Disease is a Social Driver of Sustained Oscillations in the Disease Incidence

ABSTRACT

We analyze a seasonal SIR model that assumes a periodic treatment rate. Using the Leray-Schauder degree theory, we prove that model shows periodic solutions. This result shows that sustained oscillations in the incidence of the disease are related to the periodic application of a treatment against the disease. So, we can say that the periodic application of treatment can be considered a seasonal driver of the sustained oscillations.

Keywords:
seasonal treatment rate; periodic orbit; Leray-Schauder degree; SIRS models; reproduction number