School of Mathematics, North University of China, Taiyuan, 030051, Shanxi, People's Republic of China.
Shanxi Institute of Technology, Taiyuan, 030051, Shanxi, People's Republic of China.
J Math Biol. 2022 Oct 12;85(5):49. doi: 10.1007/s00285-022-01816-1.
To study disease transmission with vaccination based on the network, we map an SIR model to a site-bond percolation model. In the case where the vaccination probability is zero, this model degenerates into a bond percolation model without the immunization. Using the method of generation functions, we obtain exact theoretical results for the epidemic threshold and the average outbreak size. From these exact solutions, we find that the epidemic threshold increases while the average outbreak size decreases with vaccination probability. Numerical simulations show that the size of giant component S increases with transmissibility T but decreases with the probability of vaccination. In addition, we compare the epidemic threshold and the size of the giant component for a Poisson network, an exponential network and a power-law network using numerical simulations. When the probability of vaccination is fixed, the epidemic threshold is the smallest for heterogeneous networks and the size of giant component S in homogeneous networks becomes largest for large transmissibility T(T close to 1).
为了基于网络研究接种疫苗的疾病传播，我们将 SIR 模型映射到一个站点键渗流模型上。在接种概率为零的情况下，该模型退化为没有免疫的键渗流模型。使用生成函数的方法，我们得到了流行阈值和平均爆发规模的精确理论结果。从这些精确解中，我们发现流行阈值随着接种概率的增加而增加，而平均爆发规模则随着接种概率的增加而减小。数值模拟表明，巨成分 S 的大小随着传播性 T 的增加而增加，但随着接种概率的增加而减小。此外，我们还使用数值模拟比较了泊松网络、指数网络和幂律网络的流行阈值和巨成分大小。当接种概率固定时，异质网络的流行阈值最小，而在大传播性 T（T 接近 1）时，同质网络中的巨成分 S 最大。
