The influence of an appropriate reporting time and publicity intensity on the spread of infectious diseases

We present a stochastic time-delay susceptible-exposed-asymptomatic-symptom-vaccinated-recovered (SEAQVR) model with media publicity effect in this study. The model takes into account the impacts of noise, time delay and public sensitivity on infectious illness propagation. The stochastic dynamics of the system are analyzed at the Hopf bifurcation, using time delay and noise intensity as bifurcation parameters, and the theoretical conclusions are validated using numerical simulation. Increasing the time delay and sensitivity coefficient can effectively delay the occurrence of the peak number of infected individuals and mitigate the extent of infection. Additionally, time delay and noise intensity are shown to have specific thresholds, beyond which periodic infections occur. Notably, heightened public sensitivity reduces the threshold for time delay, and media publicity directly affects public sensitivity. The numerical simulation reveals that increasing media publicity intensity does not always yield better results, and that the sensitivity of the public at present is an important reference index for setting an appropriate publicity intensity.