Media impact research: a discrete SIR epidemic model with threshold switching and nonlinear infection forces

The media's coverage has the potential to impact human behavior and aid in the control of emergent infectious diseases. We aim to quantify and evaluate the extent to which media coverage can influence infectious disease control through a mathematical model, thus proposing a switching epidemic model that considers the effect of media coverage. The threshold strategy incorporates media influence only when the number of infected cases surpasses a specific threshold; otherwise, it is disregarded. When conducting qualitative analysis of two subsystems, focusing on the existence and stability of equilibria. Using numerical methods, the codimension-2 bifurcation analysis is adopted here to investigate the various types of equilibria within the switching system that play a vital role in pest control. On the other hand, codimension-1 bifurcation analysis reveals the existence of periodic, chaotic solutions, period-doubling bifurcations, multiple attractors and other complexities within the proposed model, which could pose challenges in disease control. Additionally, the impact of key parameters on epidemic outbreaks is analyzed, such as the initial values of susceptible and infective individuals, and discuss the potential benefits of mass media coverage in preventing emerging infectious diseases. The modeling and analytical techniques developed for threshold control strategies can be applied to other disease control efforts.