A discrete SIR epidemic model incorporating media impact, resource limitaions and threshold switching strategies

Abstract

The paper explores the effects of media influence and limited medical resources on the spread of infectious diseases using mathematical modeling. We construct a switching epidemic model that incorporates a media influence factor, an inoculation function, and a cure function. This model is subsequently discretized and studied via Euler's method. The number of susceptible individuals serves as the switching threshold, determining when media influence and healthcare resources intervene. By conducting an in-depth analysis of the equilibria of two subsystems, we have not only demonstrated the existence and stability conditions of the equilibria but also proposed the flip bifurcation theory for $S_{G_1}$. Through single-parameter bifurcation analysis, we identify complex dynamic behaviors such as stability, periodicity, and chaos, and examined the impact of key parameters on these dynamics. We also compared the dynamic behaviors of the discrete and continuous models. Additionally, we delve into the interaction between initial populations of susceptible and infected individuals and its effect on outbreak outcomes, as well as the coexistence of attractors. Our research sheds light on the intricate relationship between media influence, constrained medical resources, and infectious disease propagation, offering recommendations for disease control and intervention approaches.