Considering the influence of media lagging publicity on the awareness rate of epidemic situation, this paper introduces the accumulation of epidemic awareness variables, establishes the SISM infectious disease model influenced by media publicity, and gives the sufficient conditions for the global asymptotic stability of the model disease-free equilibrium, the stability of the endemic disease equilibrium and the existence of the Hopf bifurcation. The variation trend of different effects of delayed media publicity on the outbreak is simulated. Based on the data of A (H1N1), the interference degree of the parameters in the model is analyzed. The results show that shortening the lag time of the media report and increasing the implementation rate and the transfer rate of media propaganda can effectively control the epidemic and gradually end the epidemic.
Keywords: Hopf bifurcation; SISM model; numerical simulation; time delay.