The coupled dynamics of awareness and disease: Based on the adaptive mechanism and the surroundings reinforcement

In the context of disease spreading, two factors merit particular attention. One factor involves individuals instinctively seeking advantages while avoiding the risk of infection. The second factor pertains to the influence of the environment in which individuals reside. This paper introduces an adaptive mechanism and the surroundings reinforcement in a two-layer network. Meanwhile, a novel model, named aUAU-sSIR, is proposed to explore the impact of the adaptive mechanism and the surroundings reinforcement on disease spreading in the two-layer network. Then, based on micro Markov chain approach (MMCA), we derive the corresponding MMCA equation for the newly proposed model and articulate the mathematical expression of disease transmission threshold. Finally, comprehensive simulations demonstrate the feasibility and effectiveness of the theoretical analysis, elucidating the impact of both the adaptive mechanism and the surroundings reinforcement. The simulations reveal that adaptive behavior within the awareness-layer impedes the awareness diffusion and promotes the disease spreading. Additionally, our findings indicate that increasing the surrounding reinforcement factor can effectively accelerate disease spread.