Stochastic SIR epidemic model dynamics on scale-free networks

This study introduces a stochastic SIR (Susceptible–Infectious–Recovered) model on complex networks, utilizing a scale-free network to represent inter-human contacts. The model incorporates a threshold parameter, denoted as $R_{\sigma }$, which plays a decisive role in determining whether the disease will persist or become extinct. When $R_{\sigma }<1$, the disease exhibits exponential decay and eventually disappear. Conversely, when $R_{\sigma }>1$, the disease persists. The critical case of $R_{\sigma }=1$ is also examined. Furthermore, we establish a unique stationary distribution for $R_{\sigma }>1$. Our findings highlight the significance of network topology in modeling disease spread, emphasizing the role of social networks in epidemiology. Additionally, we present computational simulations that consider the scale-free network’s topology, offering comprehensive insights into the behavior of the stochastic SIR model on complex networks. These results have substantial implications for public health policy, disease control strategies, and epidemic modeling in diverse contexts.