The necessity of describing the dynamics of infectious diseases has brought in the last century the study of mathematical epidemic models. These compartmental models have been extensively studied due to their applications beyond epidemiology. The deterministic SIRS model framework is particularly suited for diseases that allow temporary immunity and its scalar formulation has been deeply investigated. The introduction of network structure on these classical models has provided a way to avoid the assumption of homogeneity, since real-world contacts within populations are quite often highly heterogeneous. In this thesis, we present an SIRS model on a finite, strongly connected network, and we investigate its dynamic behavior.