Analysis of the Dynamic Properties of a Discrete Epidemic Model Affected by Media Coverage

This study investigates the dynamic behaviors of the discrete epidemic model influenced by media coverage through integrated analytical and numerical approaches. The primary objective is to quantitatively assess the impact of media coverage on disease outbreak patterns using mathematical modeling. Firstly, the Euler method is used to discretize the model (2), and the periodic solution is strictly analyzed. Secondly, the coefficients and conditions of restricted flip and Neimark–Sacker bifurcation are studied by using the center manifold theorem and bifurcation theory. By calculating the largest Lyapunov exponent near the critical bifurcation point, the occurrence of chaos and limit cycles is proved. On this basis, the chaotic control of the system is carried out by using state feedback and hybrid control. Under certain conditions, the chaos and bifurcation of the system can be stabilized by control strategies. Numerical simulations further reveal bifurcation dynamics, chaotic behaviors, and control technologies. Our results show that media coverage is a key factor in regulating the intensity of disease transmission and chaos. The control technology can effectively prevent the large-scale outbreak of epidemic diseases. Importantly, enhanced media coverage can effectively promote public awareness and defensive behaviors, thereby contributing to the mitigation of disease transmission.