Epidemics usually spread widely and can cause a great deal of loss to humans. In the real world, vaccination is the principal method for suppressing the spread of infectious diseases. The Susceptible-Infected-Susceptible (SIS) model suggests that voluntary vaccination may affect the spread of an epidemic. Most studies to date have argued that the infection rates of nodes in the SIS model are not heterogeneous. However, in reality, there exist differences in the neighbor network structure and the number of contacts, which may affect the spread of infectious diseases in society. As a consequence, it can be reasonably assumed that the infection rate of the nodes is heterogeneous because of the amount of contact among people. Here, we propose an improved SIS model with heterogeneity in infection rates, proportional to the degree of nodes. By conducting simulations, we illustrate that almost all vaccinated nodes have high degrees when the infection rate is positively correlated with the degree of a node. These vaccinated nodes can divide the whole network into many connected sub-graphs, which significantly slows down the propagation of an epidemic; the heterogeneity of infection rates has a strong inhibitory effect on epidemic transmission. On the other hand, when the infection rate is negatively related to the degrees of the infection rate nodes, it is difficult for most nodes to meet the inoculation conditions, and the number of inoculations is close to zero.

中文翻译：

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具有异质感染率的自愿接种疫苗下的流行病传播

流行病通常传播范围很广，会给人类造成很大的损失。在现实世界中，疫苗接种是抑制传染病传播的主要方法。易感-感染-易感（SIS）模型表明，自愿接种疫苗可能会影响流行病的传播。迄今为止，大多数研究都认为 SIS 模型中节点的感染率不是异质的。但在现实中，邻居网络结构和接触人数存在差异，可能会影响传染病在社会中的传播。因此，可以合理地假设节点的感染率是异质的，因为人们之间的接触量很大。在这里，我们提出了一种改进的 SIS 模型，其感染率具有异质性，与节点的程度成正比。通过进行模拟，我们说明当感染率与节点的程度呈正相关时，几乎所有接种疫苗的节点都具有高程度。这些已接种疫苗的节点可以将整个网络划分为许多相连的子图，从而显着减慢流行病的传播速度；感染率的异质性对流行病传播有很强的抑制作用。另一方面，当感染率与感染率节点的程度呈负相关时，大多数节点难以满足接种条件，接种数接近于零。这些已接种疫苗的节点可以将整个网络划分为许多相连的子图，从而显着减慢流行病的传播速度；感染率的异质性对流行病传播有很强的抑制作用。另一方面，当感染率与感染率节点的程度呈负相关时，大多数节点难以满足接种条件，接种数接近于零。这些已接种疫苗的节点可以将整个网络划分为许多相连的子图，从而显着减慢流行病的传播速度；感染率的异质性对流行病传播有很强的抑制作用。另一方面，当感染率与感染率节点的程度呈负相关时，大多数节点难以满足接种条件，接种数接近于零。