Time-delayed information can induce the periodic outbreaks of infectious diseases

Abstract

Typically, an outbreak of infectious disease can change the behaviors of people, such as reducing out, taking vaccination, paying attention to hygiene, etc. These behavioral changes have the significant influences on the transmissions of diseases and the control effects. In order to characterize the impacts of these behavioral changes, in this paper, we propose an improved SIRS epidemic model, where susceptible individuals can be divided into two different states—unprotected state ( S u) and protected state ( S p). Susceptible individuals switch between unprotected state and protected state relying on their perceived risk of diseases. The transition probability from S u to S p increases with the number of infections they acquired. On the contrary, the transition probability from S p to S u decreases with the number of infections they acquired. Meanwhile, we assume that perceived risk of diseases estimated by people depends on the information of disease that they acquired. By Monte-Carlo method and Markov chain method, we find that the time-delayed information of diseases can induce the periodic outbreaks of infectious diseases.