Fransson Carolina, Trapman Pieter
Department of Mathematics, Stockholm University, 106 91, Stockholm, Sweden.
J Math Biol. 2019 Jun;78(7):2369-2398. doi: 10.1007/s00285-019-01347-2. Epub 2019 Apr 10.
In this paper we consider Susceptible [Formula: see text] Infectious [Formula: see text] Recovered (SIR) epidemics on random graphs with clustering. To incorporate group structure of the underlying social network, we use a generalized version of the configuration model in which each node is a member of a specified number of triangles. SIR epidemics on this type of graph have earlier been investigated under the assumption of homogeneous infectivity and also under the assumption of Poisson transmission and recovery rates. We extend known results from literature by relaxing the assumption of homogeneous infectivity both in individual infectivity and between different kinds of neighbours. An important special case of the epidemic model analysed in this paper is epidemics in continuous time with arbitrary infectious period distribution. We use branching process approximations of the spread of the disease to provide expressions for the basic reproduction number [Formula: see text], the probability of a major outbreak and the expected final size. In addition, the impact of random vaccination with a perfect vaccine on the final outcome of the epidemic is investigated. We find that, for this particular model, [Formula: see text] equals the perfect vaccine-associated reproduction number. Generalizations to groups larger than three are discussed briefly.
在本文中，我们考虑具有聚类的随机图上的易感-感染-恢复（SIR）流行病模型。为了纳入基础社会网络的群体结构，我们使用配置模型的广义版本，其中每个节点是指定数量三角形的成员。此前已在均匀感染性假设以及泊松传播率和恢复率假设下，对这类图上的SIR流行病进行了研究。我们通过放宽个体感染性以及不同类型邻居之间的均匀感染性假设，扩展了文献中的已知结果。本文分析的流行病模型的一个重要特殊情况是具有任意感染期分布的连续时间流行病。我们使用疾病传播的分支过程近似来给出基本再生数、重大疫情爆发概率和预期最终规模的表达式。此外，还研究了使用完美疫苗进行随机接种对流行病最终结果的影响。我们发现，对于这个特定模型， 等于与完美疫苗相关的再生数。还简要讨论了对大于三个节点的群体的推广。
