Peng Xiao-Long, Xu Xin-Jian, Fu Xinchu, Zhou Tao
Department of Mathematics, Shanghai University, Shanghai 200444, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Feb;87(2):022813. doi: 10.1103/PhysRevE.87.022813. Epub 2013 Feb 20.
Vaccination is an important measure available for preventing or reducing the spread of infectious diseases. In this paper, an epidemic model including susceptible, infected, and imperfectly vaccinated compartments is studied on Watts-Strogatz small-world, Barabási-Albert scale-free, and random scale-free networks. The epidemic threshold and prevalence are analyzed. For small-world networks, the effective vaccination intervention is suggested and its influence on the threshold and prevalence is analyzed. For scale-free networks, the threshold is found to be strongly dependent both on the effective vaccination rate and on the connectivity distribution. Moreover, so long as vaccination is effective, it can linearly decrease the epidemic prevalence in small-world networks, whereas for scale-free networks it acts exponentially. These results can help in adopting pragmatic treatment upon diseases in structured populations.
接种疫苗是预防或减少传染病传播的一项重要措施。本文在瓦茨-斯托加茨小世界网络、巴拉巴西-阿尔伯特无标度网络和随机无标度网络上研究了一个包含易感、感染和不完全接种疫苗 compartments 的流行病模型。分析了流行阈值和流行率。对于小世界网络，提出了有效的疫苗接种干预措施，并分析了其对阈值和流行率的影响。对于无标度网络，发现阈值强烈依赖于有效疫苗接种率和连通性分布。此外，只要疫苗接种有效，它就能线性降低小世界网络中的流行率，而对于无标度网络，它的作用是指数性的。这些结果有助于在结构化人群中对疾病采取务实的治疗方法。
