The SIS Great Circle Epidemic Model
The SIS Great Circle Epidemic Model
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SIS 大圈流行病模型
作者：
P. Neal
我们考虑一个随机SIS模型的传播流行病的人口之间的n个人是等距的圆周上的圆周。当具有传染性时，我说，一个个体在齐次泊松点过程的点上进行局部和全局的传染性接触。全球接触是与整个人口的成员随机进行的，而地方接触是根据以感染者为中心的接触分布进行的。在感染期结束时，个体会恢复到易感状态，并可能再次感染。本文的重点是当种群规模n → ∞时的渐近结果。因此，引入了一个具有全局传染的接触过程来表示循环传染病的n → ∞极限行为.推导出了流行病早期阶段的分支过程近似，并得到了大爆发的地方病平衡点。此外，假设指数传染期，一个主要的流行病爆发的概率和传染性的人口比例在地方病平衡满足相同的方程的特征的流行病过程。
We consider a stochastic SIS model for the spread of an epidemic amongst a population of n individuals that are equally spaced upon the circumference of a circle. Whilst infectious, an individual, i say, makes both local and global infectious contacts at the points of homogeneous Poisson point processes. Global contacts are made uniformly at random with members of the entire population, whilst local contacts are made according to a contact distribution centred upon the infective. Individuals at the end of their infectious period return to the susceptible state and can be reinfected. The emphasis of the paper is on asymptotic results as the population size n → ∞. Therefore, a contact process with global infection is introduced representing the limiting behaviour as n → ∞ of the circle epidemics. A branching process approximation for the early stages of the epidemic is derived and the endemic equilibrium of a major outbreak is obtained. Furthermore, assuming exponential infectious periods, the probability of a major epidemic outbreak and the proportion of the population infectious in the endemic equilibrium are shown to satisfy the same equation which characterises the epidemic process.