Epidemic dynamics of complex networks based on information dependence

Vaccination has played a significant role in suppressing the spread of epidemics. In this paper, A Susceptible-Vaccinated-Infected-Recovered (SVIR) epidemic model including degree-dependent transmission rates and imperfect vaccination is proposed. Based on game theory, individuals adopt vaccine and disease information for a period of time to decide whether or not to vaccinate, reflecting the information dependence of individual decisions by introducing a distributed delay. The vaccination rate is determined by the level of epidemic propagation, functioning as a time-varying variable rather than a fixed constant. Explicit expressions for the basic reproduction number and epidemic thresholds related to degree are derived through the next-generation matrix approach. Several sufficient conditions for the existence of five equilibria are presented. Additionally, the stability of the disease-free equilibrium and the persistence of the epidemic are demonstrated. Particularly, considering that individual decisions are influenced only by current information, the global attractivity of the unique endemic equilibrium is verified through the monotone iteration technique. Finally, based on a real contact network from a gallery exhibition in Dublin, we investigate the impact of information-dependent vaccination decisions on epidemic transmission and study the effect of various system parameters on the epidemic thresholds.