The COVID-19 pandemic has witnessed the role of online social networks (OSNs) in the spread of infectious diseases. The rise in severity of the epidemic augments the need for proper guidelines, but also promotes the propagation of fake news-items. The popularity of a news-item can reshape the public health behaviors and affect the epidemic processes. There is a clear inter-dependency between the epidemic process and the spreading of news-items. This work creates an integrative framework to understand the interplay. We first develop a population-dependent 'saturated branching process' to continually track the propagation of trending news-items on OSNs. A two-time scale dynamical system is obtained by integrating the news-propagation model with SIRS epidemic model, to analyze the holistic system. It is observed that a pattern of periodic infections emerges under a linear behavioral influence, which explains the waves of infection and reinfection that we have experienced in the pandemic. We use numerical experiments to corroborate the results and use Twitter and COVID-19 data-sets to recreate the historical infection curve using the integrative model.