http://www.aimspress.com/journal/MBE MBE, 18(1): 745–763. DOI: 10.3934/mbe.2021040 Received: 03 October 2020 Accepted: 09 December 2020 Published: 18 December 2020 Research article Noise-induced transitions in a non-smooth SIS epidemic model with media alert Anji Yang 1 , Baojun Song 2 and Sanling Yuan 1, ∗ 1 College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China 2 Department of Applied Mathematics and Statistics, Montclair State University, Montclair, NJ 07043, USA * Correspondence: Email: sanling@usst.edu.cn. Abstract: We investigate a non-smooth stochastic epidemic model with consideration of the alerts from media and social network. Environmental uncertainty and political bias are the stochastic drivers in our mathematical model. We aim at the interfere measures assuming that a disease has already invaded into a population. Fundamental findings include that the media alert and social network alert are able to mitigate an infection. It is also shown that interfere measures and environmental noise can drive the stochastic trajectories frequently to switch between lower and higher level of infections. By constructing the confidence ellipse for each endemic equilibrium, we can estimate the tipping value of the noise intensity that causes the state switching. Keywords: SIS model; media alert; noise-induced state switching; stochastic sensitivity; confidence domains 1. Introduction These days have witnessed the horrible pandemic of COVID-19. As is known to the public, key characteristic of this killer is its silent spreads. Before we fully understand the virus, it has already established. In general, what do we do once a disease has invaded into a population? To mitigate the spread of a disease and eventually get a full control to the disease, the behavior changes at the population level can bend the infection curve. How to promote a massive behavior change? Two typical governing systems function differently. A central government can force a mandatory behavior change without any court challenge, period. If a mandatory preventive measure cannot be exercised or the administration failed to act following a scientific manner, media and social network are able to propagate the positive message in order to persuade behavior changes. A behavior change at the population level is highly media oriented. In fighting COVID-19 pandemic, WHO Director-General